{"id":2965,"date":"2018-03-23T12:11:25","date_gmt":"2018-03-23T04:11:25","guid":{"rendered":"http:\/\/www.YinYangBalance.asia\/blog\/the-science-and-technology-in-china-mathematics-volume-%e4%b8%ad%e5%9b%bd%e7%a7%91%e5%ad%a6%e6%8a%80%e6%9c%af%e5%8f%b2%c2%b7%e6%95%b0%e5%ad%a6%e5%8d%b7-post\/2965\/"},"modified":"2021-04-07T01:06:31","modified_gmt":"2021-04-06T17:06:31","slug":"the-science-and-civilization-in-china-mathematics-volume-%e4%b8%ad%e5%9b%bd%e7%a7%91%e5%ad%a6%e6%8a%80%e6%9c%af%e5%8f%b2%c2%b7%e6%95%b0%e5%ad%a6%e5%8d%b7-isbn-9787030290533","status":"publish","type":"post","link":"https:\/\/www.yinyangbalance.asia\/blog\/the-science-and-civilization-in-china-mathematics-volume-%e4%b8%ad%e5%9b%bd%e7%a7%91%e5%ad%a6%e6%8a%80%e6%9c%af%e5%8f%b2%c2%b7%e6%95%b0%e5%ad%a6%e5%8d%b7-isbn-9787030290533\/2965\/","title":{"rendered":"The Science and Civilization in China: Mathematics Volume \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u53f2\u00b7\u6570\u5b66\u5377 ISBN: 9787030290533"},"content":{"rendered":"\n    \n    <div class='SearchByTag-popup l_google_search=1\";'  onmouseover = 'popup_mouseenter();'  onmouseout = 'popup_mouseleave();'>\n        <div class='SearchByTag-popup-top'><\/div>\n        <div class='SearchByTag-popup-content'>\n            <ul>\n                                <li ><a class=\"sbt-google-search\" href=\"http:\/\/www.google.com?cx=partner-pub-9761369273396159:6077738498&ie=UTF-8&q=1\" target=\"_blank\">Search TagX on Google<\/a><\/li>\n                                                <li ><a class=\"sbt-wp-search\" href=\"1\" target=\"_blank\">View all posts tagged as Tagx<\/a><\/li>\n                                                <li class=\"last\"> <a class=\"sbt-wiki-search\" href=\"http:\/\/en.wikipedia.org\/wiki\/1\" target=\"_blank\">Find TagX related info in WikiPedia<\/a><\/li>\n                            <\/ul>    \n        <\/div>\n        <div class='SearchByTag-popup-bottom'><\/div>\n    <\/div>\n<script 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\u660e\u4ee3\u6570\u5b66\u4e3b\u6d41\u7684\u8f6c\u53d8<br>\n\u4e00 \u660e\u4ee3\u6570\u5b66\u8457\u4f5c\u6982\u51b5<br>\n\u4e8c \u660e\u4ee3\u6570\u5b66\u7684\u4e3b\u6d41\u53ca\u6768\u8f89\u7684\u5f71\u54cd<br>\n\u7b2c\u4e8c\u5341\u4e09\u7ae0 \u5143\u4e2d\u53f6\u81f3\u660e\u672b\u7684\u4e3b\u8981\u6570\u5b66\u5bb6\u548c\u6570\u5b66\u8457\u4f5c<br>\n\u7b2c\u4e00\u8282 \u5143\u4e2d\u540e\u671f\u7684\u6570\u5b66\u5bb6\u548c\u6570\u5b66\u8457\u4f5c<br>\n\u4e00 \u300a\u900f\u5e18\u7ec6\u8349\u300b<br>\n\u4e8c \u4e01\u5de8\u53ca\u5176\u300a\u4e01\u5de8\u7b97\u6cd5\u300b<br>\n\u4e09 \u8d3e\u4ea8\u7684\u300a\u7b97\u6cd5\u5168\u80fd\u96c6\u300b<br>\n\u56db \u300a\u8be6\u660e\u7b97\u6cd5\u300b<br>\n\u7b2c\u4e8c\u8282 \u660e\u521d\u7684\u6570\u5b66\u5bb6\u548c\u6570\u5b66\u8457\u4f5c<br>\n\u4e00 \u4e25\u606d\u53ca\u5176\u300a\u901a\u539f\u7b97\u6cd5\u300b<br>\n\u4e8c \u5218\u4ed5\u9686\u53ca\u5176\u300a\u4e5d\u7ae0\u901a\u660e\u7b97\u6cd5\u300b<br>\n\u4e09 \u590f\u6e90\u6cfd\u7684\u300a\u6307\u660e\u7b97\u6cd5\u300b<br>\n\u56db \u5176\u4ed6\u7b97\u4e66<br>\n\u7b2c\u4e09\u8282 \u7b79\u73e0\u5e76\u7528\u7684\u6570\u5b66\u5bb6\u548c\u6570\u5b66\u8457\u4f5c<br>\n\u4e00 \u5434\u656c\u53ca\u5176\u300a\u4e5d\u7ae0\u7b97\u6cd5\u6bd4\u7c7b\u5927\u5168\u300b<br>\n\u4e8c \u738b\u6587\u7d20\u53ca\u5176\u300a\u7b97\u5b66\u5b9d\u9274\u300b<br>\n\u4e09 \u5176\u4ed6\u7b97\u4e66<br>\n\u7b2c\u56db\u8282 \u7406\u8bba\u6570\u5b66\u7814\u7a76\u7684\u4f59\u7eea<br>\n\u4e00 \u5510\u987a\u4e4b\u53ca\u5176\u300a\u6570\u8bba\u300b\u516d\u7bc7<br>\n\u4e8c \u987e\u5e94\u7965\u53ca\u5176\u56db\u90e8\u6570\u5b66\u8457\u4f5c<br>\n\u4e09 \u5468\u8ff0\u5b66\u53ca\u5176\u300a\u5386\u5b97\u7b97\u4f1a\u300b<br>\n\u56db \u6731\u8f7d\u5809\u53ca\u5176\u300a\u7b97\u5b66\u65b0\u8bf4\u300b\u548c\u300a\u5609\u91cf\u7b97\u7ecf\u300b<br>\n\u7b2c\u4e94\u8282 \u73e0\u7b97\u6570\u5b66\u5bb6\u548c\u6570\u5b66\u8457\u4f5c<br>\n\u4e00 \u300a\u7b97\u6cd5\u7edf\u5b97\u300b\u4ee5\u524d\u7684\u73e0\u7b97\u8457\u4f5c<br>\n\u4e8c \u7a0b\u5927\u4f4d\u53ca\u5176\u300a\u7b97\u6cd5\u7edf\u5b97\u300b\u548c\u300a\u7b97\u6cd5\u7e82\u8981\u300b<br>\n\u4e09 \u5176\u4ed6\u73e0\u7b97\u8457\u4f5c<br>\n\u7b2c\u4e8c\u5341\u56db\u7ae0 \u6570\u5b66\u7684\u6b4c\u8bc0\u5316\u4e0e\u73e0\u7b97\u7684\u666e\u53ca<br>\n\u7b2c\u4e00\u8282 \u6570\u5b66\u7684\u5b9e\u7528\u5316\u4e0e\u6b4c\u8bc0\u5316<br>\n\u4e00 \u6570\u5b66\u7684\u5b9e\u7528\u5316\u3001\u5927\u4f17\u5316\u4e0e\u5546\u4e1a\u5316<br>\n\u4e8c \u6570\u5b66\u7684\u6b4c\u8bc0\u5316<br>\n\u4e09 \u5143\u672b\u4ee5\u6765\u7684\u6570\u5b66\u6b4c\u8bc0\u5316\u7b97\u9898<br>\n\u7b2c\u4e8c\u8282 \u660e\u4ee3\u6570\u5b66\u4e2d\u7684\u5404\u79cd\u201c\u6742\u6cd5\u201d<br>\n\u7b2c\u4e09\u8282 \u73e0\u7b97\u7684\u53d1\u5c55\u4e0e\u666e\u53ca<br>\n\u4e00 \u5143\u660e\u65f6\u4ee3\u51e0\u9879\u73e0\u7b97\u53f2\u6599\u6240\u53cd\u6620\u7684\u60c5\u51b5<br>\n\u4e8c \u6570\u5b66\u8457\u4f5c\u4e2d\u5bf9\u73e0\u7b97\u7684\u53cd\u6620<br>\n\u4e09 \u73e0\u7b97\u7684\u666e\u53ca\u4e0e\u7b79\u7b97\u7684\u6d88\u5931<br>\n\u7b2c\u4e8c\u5341\u4e94\u7ae0 \u660e\u4ee3\u7684\u82e5\u5e72\u6570\u5b66\u5de5\u4f5c<br>\n\u7b2c\u4e00\u8282 \u5f00\u65b9\u53ca\u65b9\u7a0b\u7684\u6570\u503c\u89e3\u6cd5<br>\n\u4e00 \u5143\u4e2d\u540e\u671f\u7684\u589e\u4e58\u5f00\u65b9\u6cd5<\/p>\n<\/div>\n<div>\n<p>table of Contents<br>\nGeneral Preface Lu Jiaxi<br>\nForeword iii<\/p>\n<p>The first series of Chinese mathematics forms a subject<br>\n\u2013 Mathematics from the primitive society to the Western Zhou Dynasty<br>\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society<br>\nSection 1 The Formation of Graphic Concepts<br>\nThe emergence of a graphic concept<br>\nSecond, from the concept of orientation to see the concept of graphics<br>\nThree original drawing tools \u2013 rules and regulations<br>\nSection II The Formation of Number Concepts and Original Counting Methods<br>\nThe emergence of a number concept<br>\nTwo original counting methods<br>\nSection 3 The legendary mathematical figure<br>\nOne<br>\nSecond Yellow Emperor and Lishou<br>\nThree \u5c27, \u821c, \u79b9 and \u5015<br>\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society<br>\nChapter 2 Mathematics Forms a Discipline\u2014\u2014Mathematics of the Three Generations of Xia, Shang, and Xi Zhou<br>\nSection 1 Formation of Decimal Value Notation<br>\nA number in Oracle and Jinwen<br>\nTwo decimal value notation<br>\nSection 2 Mathematics Becomes a Discipline<br>\nThe need for social management and work and the development of mathematics<br>\nSecond Mathematics enters teaching subjects<br>\nIII Shang Gao and its mastered mathematics knowledge<\/p>\n<p>Part Two Establishment of Traditional Chinese Mathematical Framework<br>\n\u2013 Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty<br>\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty<br>\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period<br>\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background<br>\nThe Second Qin and Han Mathematics and Social and Cultural Background<br>\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period<br>\nAn integer number of four operations in the Spring and Autumn Period<br>\nSecond, the extensive use of scores, ratios and proportions<br>\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era\u2014\u2014\u201cNine Numbers\u201d<br>\nIV Other Mathematics Knowledge in Pre-Qin Period<br>\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period<br>\nA Mohist and Mathematics<br>\nTwo homes of mathematics<br>\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools<br>\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period<br>\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips<br>\nA Qin Jian \u201cNumbers\u201d<br>\nII. The style, expression and characteristics of the \u201cnumeric book\u201d<br>\nThree compilation of \u201ccalculus book\u201d<br>\nThe content of the \u201cnumerical book\u201d and its position in the history of Chinese mathematics<br>\nSection V. The Zhouyi Classics and Chen Zi<br>\nOne Zhouyi Calculation<br>\nTwo Chen Zi<br>\nSection VI: \u201cNine Chapters of Arithmetic\u201d and Zhang Cang, Yan Shouchang<br>\nThe content of \u201cChapter 9 Arithmetic\u201d<br>\nII. The Style and Compilation of Nine Chapters of Arithmetic<br>\nThree \u201carithmetic book\u201d and \u201cNine chapters of arithmetic\u201d<br>\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World<br>\nFive Versions of Nine Chapters of Arithmetic<br>\nSix Zhang Canghe Yu Shouchang<br>\nSection 7 Other Mathematicians and Mathematical Works<br>\nA dealer and \u201cBusiness Arithmetic\u201d and \u201cDu Zhong Arithmetic\u201d<br>\nSecond Yin Xianhe Liu Hao<br>\nThree Zhang Heng and Ma continued<br>\nChapter IV Insufficient scores, rates, and profits<br>\nSection 1 Scores and Its Four Principles<br>\nA score and its representation<br>\nTwo fractional four algorithm<br>\nSection II Surgery and Decline Surgery<br>\nNow there is surgery<br>\nSecond decline<br>\nThree transmission techniques<br>\nSection III Insufficiency<br>\nInsufficiency<br>\nThe Application of Insufficiency Technique in General Mathematical Problems<br>\nChapter V Area, Volume, Pythagoreanism, and Observation<br>\nSection 1 Area<br>\nA linear area<br>\nSecond curved area<br>\nThree round and square<br>\nFour curved surface area<br>\nSection 2 Volume<br>\na polyhedral volume<br>\nTwo round body volume<br>\nSection III Pythagorean Theorem and Unfolding Tacks<br>\nAn Pythagorean Theorem<br>\nThe second solution hook shape<br>\nThree Pythagorean arrays<br>\nThe fourth quarter<br>\nA tick share<br>\nTwo ticks<br>\nSection V<br>\nOne time<br>\nThe bud of the second difference<br>\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences<br>\nThe first section of the prescription<br>\nOpen square<br>\nTwo open cubes<br>\nSection II Equations and Positive and Negative Techniques<br>\nOne equation and equation<br>\nSecond profit and loss<br>\nThree positive and negative surgery<br>\nSection III Series<\/p>\n<p>Part III Completion of Chinese Traditional Mathematical Theory System<br>\n\u2013 Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty<br>\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty<br>\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty<br>\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory<br>\nII Society and Mathematics in the Southern and Northern Dynasties<br>\nThe Society and Mathematics in the Middle of Tang Dynasty<br>\nSection Two: Xu Yue\u2019s \u201cSurgical Relics\u201d and Zhao Shuang\u2019s \u201cZhou Shuo\u2019s Recounts\u201d<br>\nLiu Hong, Xu Yue, and The Record of the Numbers<br>\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu<br>\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera<br>\nAn Liu Hui<br>\nTwo \u201cNine chapters of arithmetic note\u201d<br>\nThree \u201cThe Island\u201d<br>\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties<br>\nA Study on \u201cNine Chapters of Arithmetic\u201d<br>\nSecond \u201cSun Tzu Classic\u201d<br>\nThree \u201cXiahou Yang calculations\u201d<br>\nFour \u201cZhang Qiu Jian Su Jing\u201d<br>\nV. Zu Chongzhi, Zu Yu\u2019s and \u201cFuzheng\u201d<br>\nSix books and their mathematical works<br>\nSeven other mathematicians<br>\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty<br>\nLiu Yi<br>\nII Wang Xiaotong and \u201cAncient Gujing\u201d<br>\nThe three Li Yufeng and other finishing ten calculations<br>\nFour Lines and \u201cDa Yan Li\u201d<br>\nFive Sides<br>\nSection 6 Sui Tang School of Mathematics and Accounting<br>\nA math school<br>\nSecond Accounting Division<br>\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools<br>\nA large number of methods<br>\nTwo Attempts to Improve Calculation Tools<br>\nChapter VIII Principles of rate and principle<br>\nSection 1 Definition and Nature of Rates<br>\nThe definition of probability<br>\nThe Method and Nature of Bivariate<br>\nSection II Today\u2019s Promotion and Principles of Surgery<br>\nThe current promotion of surgery<br>\nTwo principles<br>\nThe third section of the arithmetic and the least common multiple<br>\nAn arithmetic problem<br>\nII Solving Mathematical Problems Directly<br>\nApplication of the three greatest common divisors and the least common multiple<br>\nChapter Nine Pythagoreans, Observations, and Errors<br>\nSection 1 Demonstration of Formulas for Explaining Pyramids<br>\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui<br>\nII Zhao Shuang and Liu Hui\u2019s Proof of the Formulas of the Solution<br>\nThree Liu Hui\u2019s Proof of the Pythagorean Array Formula<br>\nIV Wang Xiaotong\u2019s Expansion of the Hexagonal Shape Problem<br>\nSection 2 Proof of Formulas and Formulas<br>\nOne with the proof of the principle of entry and completion<br>\nB. Proof of the Principle of Keeping Preference with Pythagoreanism<br>\nSection III Correction<br>\nOne difference in skill<br>\nTwo Drawings Six Body and Mathematics<br>\nSection IV Other Observation Problems<br>\nAn Observation Problem in Zhang Qi Jian Jian Su Jing<br>\nII. The Problem of Expectation in the \u201cSeveral Notes to the Book\u201d<br>\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations<br>\nSection 1 Geometric Explanation and Improvement of Alchemy<br>\nA Liu Hui\u2019s Geometry Explanation of the Alchemy<br>\nII Liu Hui and Wang Xiaotong\u2019s Creation of Opening Methods<br>\nThe improvement of the three prescriptions<br>\nIV Liu Hui\u2019s \u201cseeking micro-number\u201d and the approximate value of the root<br>\nV. Zu Chongzhi\u2019s opening power and opening difference<br>\nThe root formula of six lines<br>\nSection II Progress of Equations<br>\nLiu Hui\u2019s equation theory<br>\nTwo mutual multiplication and denomination<br>\nThree equations new surgery<br>\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing<br>\nSection III Indefinite issues<br>\nA total of five wells<br>\nTwo things do not know the problem<br>\nThree hundred chicken<br>\nSection 4 Arithmetic series and geometric series<br>\nAn arithmetic progression<br>\nTwo equal number arrays<br>\nChapter 11 Infinitely small segmentation and limit thinking<br>\nSection 1 Cutting<br>\nSection II Principle of Liu Hui<br>\nSection III Principles and volume of the ancestral hall<br>\nAn ancestral principle<br>\nTwo square cover and ball volume<br>\nSection IV The Application of Limit Ideas in Approximate Calculation<br>\na pi ratio<br>\nSecond round rate and square rate<br>\nArc field density<br>\nSection V Liu Hui\u2019s area and volume derivation system<br>\nLiu Hui\u2019s area derivation system<br>\nTwo proofs of the polyhedral volume formula<br>\nThree Liu Hui\u2019s volume derivation system<br>\nSection 6 Liu Hui\u2019s Limitation Thought in the History of Mathematics<br>\nThe Infinite Segmentation of Liu Hui\u2019s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists<br>\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece<br>\nChapter Twelve Liu Hui\u2019s Logic Thought and Mathematical Theory System<br>\nThe first section Liu Hui\u2019s resignation and reason, class, and therefore<br>\nOne reason<br>\nCategory II<br>\nThree<br>\nSection 2 Definition<br>\nSection III Analogy and Induction<br>\nAn analogy<br>\nInductive reasoning<br>\nSection IV Deductive Reasoning of Liu Hui<br>\nSyllogism and Relational Reasoning<br>\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning<br>\nThird, the prototype of mathematical induction<br>\nSection 5 Mathematical Proof<br>\nA comprehensive approach<br>\nB. Analysis and synthesis<br>\nIII Rebuttal and Liu Hui\u2019s mistakes<br>\nSection VI Liu Hui\u2019s Mathematical Theory System<br>\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties<br>\nSection 1 The Creative Transformation of the Sui and Tang Calendars<br>\nThe discovery of a letter and its significance<br>\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties<br>\nSection II Secondary interpolation algorithm<br>\nOne \u201cThe Imperial Calendar\u201d<br>\nLiu Liu\u2019s Quadratic Interpolation Algorithm and Its Algorithmic Analysis<br>\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar<br>\nFour-phase subtractive multiplication<br>\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties<br>\nLiu Xi\u2019s \u201cEmperor\u201d calendar algorithm<br>\nII Li Yingfeng\u2019s \u201cLin Lun Li\u201d image algorithm<br>\nThree-Line \u201cDai Yan Li\u201d Nine Shadows Algorithm<br>\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang\u2019s \u201cChong Xuan Li\u201d<br>\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties<br>\nSection 1 Mathematical Communication between China and North Korea<br>\nSection 2 Mathematics Exchange between China and Japan<br>\nA Chinese calendar was introduced into Japan<br>\nII Introduction of Early Learning Education System<br>\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties<br>\nSection 3 Mathematical Communication between China and India<br>\nAn Indian mathematics introduced to China<br>\nII The Influence of Chinese Mathematics on India<\/p>\n<p>Part IV The Climax of Chinese Traditional Mathematics<br>\n\u2014\u2014Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty<br>\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty<br>\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty<br>\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty<br>\nII Thoughtful easing is a necessary condition for the development of mathematics<br>\nIII Social needs are a powerful force for the development of mathematics<br>\nFourth Song and Yuan rulers attach importance to mathematics<br>\nFive Characteristics of Mathematics in the Song and Yuan Dynasties<br>\nThe second section of the book \u201cXiahou Yang calculations\u201d<br>\nA Biography of the Date and Content of the \u201cXiahou Yang Scripture\u201d<br>\nTwo versions of the \u201cXiahou Yang Calculator\u201d<br>\nThe third quarter Jia Xianhe\u2019s \u201cThe Yellow Emperor\u2019s Nine Chapters, The Scriptures\u201d<br>\nJia Xian and his teacher Chu Yan<br>\nTwo Most Existential Examinations of \u201cThe Yellow Emperor\u2019s Nine Chapters Calculating Caojing\u201d<br>\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor\u2019s Nine Chapters.<br>\nSection IV Liu Yihe\u2019s \u201cProposal on Ancient Roots\u201d<br>\nYi Liu Yi<br>\nSecond, \u201cA discussion of Gu Gen Yuan\u201d<br>\nSection Five Qin Jiulu and \u201cNumbers Chapter 9\u201d<br>\nThe life of Qin Jiuhao<br>\nSecond Qin Jiuyao character identification<br>\nThree \u201cNumbers Chapter 9\u201d<br>\nSection 6 Li Yehe\u2019s \u201cMeasurement of Circular Oceanscope\u201d and \u201cYigu Performance\u201d<br>\nYi Ye<br>\nThe two holes Jiurong and \u201cTest round sea mirror\u201d<br>\nThree \u201cYi Gu Ji\u201d and \u201cYi Gu Performance\u201d<br>\nSection 7 Yang Hui and \u201cDetailed Explanation of Chapter 9 Algorithm\u201d and \u201cYang Hui Algorithm\u201d<br>\nYihui Yang<br>\nSecond, \u201cDetailed Nine Chapter Algorithms\u201d<br>\nThree \u201cdaily algorithm\u201d and \u201cYang Hui algorithm\u201d<br>\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book<br>\nOne Zhu Shijie<br>\nTwo \u201cEducation Enlightenment\u201d<br>\nThree \u201cSiyuan Yujian\u201d<br>\nSection 9 Other Mathematicians and Mathematical Works<br>\nA Li Jihe\u2019s \u201cNine Chapters of Arithmetic and Meaning\u201d and \u201cZhou Ji\u2019s Calculation of Sound and Meaning\u201d<br>\nTwo \u201cXiecha Microcalculus\u201d<br>\nThree Shen Kuohe\u2019s Mathematical Achievements in \u201cMeng Xi Bi Tan\u201d<br>\nFour Wang Xi, Guo Shoujing, and \u201cTime History\u201d<br>\nFive Zhao Youqin and \u201cNew Elephant\u201d<br>\nSix Shakes and The River Defense Theory \u2022 Algorithm Gate<br>\nSeven Other Mathematicians and Mathematical Works<br>\nChapter 16 Improvements in Computing Technology and Invention of Abacus<br>\nSection 1 \u25cb and Decimal Decimals<br>\nOne and digital<br>\nTwo decimal places<br>\nSection II Improvements in Computing Technology<br>\nOne for the law, one for the addition, subtraction, multiplication and division<br>\nII Heading Multiplication and Nine Return and Elimination<br>\nSection 3 The birth of abacus<br>\nAbacus produces many<br>\nThe second abacus was born in the Song Dynasty at the latest<br>\nChapter 17 Going to Share Volume and Cutting Circles<br>\nSection 1 Check Stock Volume<br>\nOne<br>\nTwo round city schema<br>\nThree identification notes<br>\nSection 2 Cutting<br>\nA Shen Kuo\u2019s Tactics<br>\nTwo Sagittal Cuts in the Time of Time<br>\nThree Zhao Youqin\u2019s cutting<br>\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple<br>\nSection 1 Numerical Solution of High Order Equations<br>\nAn upright release method<br>\nSecond Jia Xian Triangle<br>\nThree increase open method<br>\nFour Benefits and Reductions<br>\nFive positive and negative open<br>\nSection II Tianyuan surgery<br>\nOne-day history of metaphysics<br>\nThe perfection and application of the two-day meta-technique<br>\nThe third quarter of four<br>\nThe historical development of a quadruple surgery<br>\nTwo-quaternary elimination<br>\nThree binary<br>\nFour triples<br>\nFive four yuan surgery<br>\nChapter 19 Hoarding, tricks<br>\nSection 1 Hoarding<br>\nSlot technique<br>\nII Hoarding<br>\nSection II tricks surgery<br>\nA trick of \u201cTime-giving Calendar\u201d<br>\nTwo tricks of \u201cSyuanyuanjian\u201d<br>\nChapter Twenty The total number of Da Yan and vertical and horizontal map<br>\nThe first quarter total number of surgery<br>\nThe origin of a major total<br>\nTotal number of major<br>\nSection II.<br>\nA river map, Luo book and vertical and horizontal map<br>\nSecond, Yang Hui, etc.<br>\nThree Ding Yidong\u2019s map<br>\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty<br>\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges<br>\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century<br>\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties<br>\nSection 2 Chinese Mathematical Biography<br>\nThe Impact of Chinese Mathematics on Islamic Countries<br>\nII The Influence of Chinese Mathematics on North Korea and Japan<br>\nSection III Introduction of Mathematics in Islamic Countries<br>\nThe introduction of a mathematical work<br>\nII Arabic Digital and Crosswords<br>\nThree soil disc algorithm and lattice operator<\/p>\n<p>Part V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus<br>\n\u2013 Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty<br>\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty<br>\nSection 1 The Social Background of Mathematics in the Ming Dynasty<br>\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty<br>\nA \u201cYongle Grand Ceremony \u2022 Calculation\u201d and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty<br>\nThe loss of the second ancient book<br>\nLoss of three mathematics results<br>\nSection III The Mainstream of Mathematics in the Ming Dynasty<br>\nA survey of mathematics books in the Ming Dynasty<br>\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui<br>\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty<br>\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period<br>\nOne<br>\nTwo Ding Ju and his Ding Ju algorithm<br>\nThree Jiaheng\u2019s \u201cAlgorithm Set\u201d<br>\nFour \u201cDetailed Algorithm\u201d<br>\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty<br>\nYan Gong and his \u201cTongyuan algorithm\u201d<br>\nLiu Shilong and his \u201cNine Chapters Tuning Algorithm\u201d<br>\nThree Xia Yuanze\u2019s \u201cspecified algorithm\u201d<br>\nFour other calculations<br>\nSection 3 Mathematical and Mathematical Writings<br>\nWu Jing and his \u201cNine Chapter Algorithms\u201d<br>\nII Wang Wensu and his \u201cEducational Poems\u201d<br>\nThree other books<br>\nSection IV: The Theory of Theoretical Mathematics<br>\nTang Shunzhi and his \u201cNumber Theory\u201d six<br>\nII Gu Yingxiang and his four books on mathematics<br>\nThree Weeks of Learning and Its \u201cEcco\u201d<br>\nIV Zhu Zaiyu and his \u201cNew Theory of Calculation\u201d and \u201cJi-Suan Su Jing Jing\u201d<br>\nSection V Abacus Mathematicians and Mathematical Works<br>\nA previous work on abacus<br>\nTwo-way Big Place and Its \u201cAnalysis of Algorithms\u201d and \u201cAnalysis of Algorithms\u201d<br>\nThree other abacus work<br>\nChapter 24 Songs of Mathematics and Popularization of Abacus<br>\nSection 1 Practicality and Songs of Mathematics<br>\nA practical, popular and commercialized mathematics<br>\nThe second song of mathematics<br>\nMathematical Songs Since the End of the Three Yuan<br>\nSection 2 Various \u201cmiscellaneous methods\u201d in mathematics of the Ming Dynasty<br>\nSection 3 Development and Popularization of Abacus<br>\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties<br>\nThe reflection of abacus in the second mathematic book<br>\nThe disappearance of the popularity and calculation of the three abacus<br>\nChapter 25 Some Mathematics Work in the Ming Dynasty<br>\nSection 1 Numerical Solution of Squares and Equations<br>\nOne-Mid-Year Growth and Opening Method<\/p>\n<\/div>\n<div id=\"wpbl-posttd-top-container\">\n\t<div id=\"wpbl-posttd-left-row\">\n\t\t<div id=\"wpbl-posttd-image\"><img decoding=\"async\" id=\"wpbl-posttd-img\" src=\"https:\/\/images-na.ssl-images-amazon.com\/images\/I\/31UbVabZroL.jpg\"><\/div>\n\t\t<div id=\"wpbl-posttd-details-div\"><p style=\"margin:0px;font-size:10px; font-variant:all-small-caps; margin-left:5px;\">Not Available<\/p><div><p class=\"wpbl-posttd-share-text\">Share This Book<\/p><div class=\"addthis_sharing_toolbox addthis_default_style\" style=\"cursor:pointer\"><a style=\"cursor:pointer;\" href=\"\" addthis:title=\"The Science and Technology in China: Mathematics Volume \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u53f2\u00b7\u6570\u5b66\u5377\" addthis:description=\"\u76ee\u5f55\n\u603b\u5e8f \u5362\u5609\u9521i\n\u524d\u8a00iii\n\n\u7b2c\u4e00\u7f16 \u4e2d\u56fd\u6570\u5b66\u4ece\u5174\u8d77\u5230\u5f62\u6210\u4e00\u95e8\u5b66\u79d1\n&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u5230\u897f\u5468\u65f6\u671f\u7684\u6570\u5b66\n\u7b2c\u4e00\u7ae0 \u4e2d\u56fd\u6570\u5b66\u7684\u5174\u8d77&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u56fe\u5f62\u89c2\u5ff5\u7684\u5f62\u6210\n\u4e00 \u56fe\u5f62\u89c2\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u4ece\u65b9\u4f4d\u89c2\u5ff5\u770b\u56fe\u5f62\u89c2\u5ff5\n\u4e09 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\u4f20\u7edf\u6570\u5b66\u8457\u4f5c\u7684\u6574\u7406\u548c\u6821\u52d8\n\u4e00 \u6234\u9707\u4e0e\u300a\u56db\u5e93\u5168\u4e66\u300b\u3001\u300a\u6b66\u82f1\u6bbf\u805a\u73cd\u7248\u4e1b\u4e66\u300b\u4e2d\u6240\u6536\u7b97\u4e66\n\u4e8c \u6e05\u4e2d\u53f6\u5bf9\u6c49\u5510\u7b97\u7ecf\u7684\u6821\u52d8\u4e0e\u7814\u7a76\n\u4e09 \u5b8b\u5143\u6570\u5b66\u4e66\u7684\u4f20\u523b\u4e0e\u7814\u7a76\n\u56db \u300a\u7574\u4eba\u4f20\u300b\u53ca\u5176\u7eed\u7f16\n\u7b2c\u4e09\u8282 \u4f20\u7edf\u6570\u5b66\u7684\u7814\u7a76\u4e0e\u53d1\u5c55\n\u4e00 \u8c08\u5929\u4e09\u53cb\u548c\u5176\u4ed6\u6570\u5b66\u5bb6\n\u4e8c \u65b9\u7a0b\u8bba\u7814\u7a76\n\u4e09 \u5176\u4ed6\u7814\u7a76\u5de5\u4f5c\n\u7b2c\u4e09\u5341\u7ae0 \u5e42\u7ea7\u6570\u5c55\u5f00\u5f0f\u7684\u7814\u7a76\n\u7b2c\u4e00\u8282 \u660e\u5b89\u56fe\u53ca\u5176\u300a\u5272\u571c\u5bc6\u7387\u6377\u6cd5\u300b\n\u4e00 \u660e\u5b89\u56fe\n\u4e8c \u300a\u5272\u571c\u5bc6\u7387\u6377\u6cd5\u300b\n\u7b2c\u4e8c\u8282 \u8463\u7950\u8bda\u3001\u9879\u540d\u8fbe\u3001\u6234\u7166\u7b49\u7684\u5de5\u4f5c\n\u4e00 \u8463\u7950\u8bda\u53ca\u5176\u300a\u5272\u571c\u8fde\u6bd4\u4f8b\u672f\u56fe\u89e3\u300b\n\u4e8c \u9879\u540d\u8fbe\u53ca\u5176\u300a\u8c61\u6570\u4e00\u539f\u300b\n\u4e09 \u6234\u7166\u53ca\u5176\u300a\u6c42\u8868\u6377\u672f\u300b\n\u7b2c\u4e09\u8282 \u674e\u5584\u5170\u53ca\u5176\u5c16\u9525\u672f\n\u4e00 \u674e\u5584\u5170\n\u4e8c \u5c16\u9525\u672f\n\u7b2c\u56db\u8282 \u5f90\u6709\u58ec\u3001\u987e\u89c2\u5149\u3001\u90b9\u4f2f\u5947\u7b49\u7684\u7814\u7a76\u5de5\u4f5c\n\u4e00 \u5f90\u6709\u58ec\u53ca\u5176\u300a\u5272\u5706\u516b\u7ebf\u7f00\u672f\u300b\n\u4e8c \u987e\u89c2\u5149\u3001\u90b9\u4f2f\u5947\u7684\u7814\u7a76\u5de5\u4f5c\n\u7b2c\u4e09\u5341\u4e00\u7ae0 \u6e05\u672b\u897f\u65b9\u6570\u5b66\u7684\u4f20\u5165\n\u7b2c\u4e00\u8282 \u6e05\u672b\u897f\u65b9\u6570\u5b66\u4f20\u5165\u6982\u51b5\n\u4e00 \u674e\u5584\u5170\u7684\u6570\u5b66\u7ffb\u8bd1\u5de5\u4f5c\n\u4e8c \u534e\u8605\u82b3\u53ca\u5176\u6570\u5b66\u7ffb\u8bd1\u7814\u7a76\n\u7b2c\u4e8c\u8282 \u51e0\u4f55\u3001\u4ee3\u6570\u548c\u4e09\u89d2\u5b66\u8457\u4f5c\u7684\u7ffb\u8bd1\n\u4e00 \u300a\u51e0\u4f55\u539f\u672c\u300b\n\u4e8c \u300a\u4ee3\u6570\u5b66\u300b\u548c\u300a\u4ee3\u6570\u672f\u300b\n\u4e09 \u300a\u4e09\u89d2\u6570\u7406\u300b\u53ca\u5176\u4ed6\n\u7b2c\u4e09\u8282 \u5fae\u79ef\u5206\u548c\u6982\u7387\u8bba\u8457\u4f5c\u7684\u7ffb\u8bd1\n\u4e00 \u300a\u4ee3\u5fae\u79ef\u62fe\u7ea7\u300b\n\u4e8c \u300a\u5fae\u79ef\u6eaf\u6e90\u300b\n\u4e09 \u5176\u4ed6\u6709\u5173\u5fae\u79ef\u5206\u7684\u8457\u4f5c\n\u56db \u300a\u51b3\u7591\u6570\u5b66\u300b\n\u7b2c\u4e09\u5341\u4e8c\u7ae0 \u6e05\u672b\u6570\u5b66\u7814\u7a76\n\u7b2c\u4e00\u8282 \u590f\u9e3e\u7fd4\u3001\u767d\u8299\u5802\u8bf8\u5b50\u548c\u5176\u4ed6\u6570\u5b66\u5bb6\n\u4e00 \u590f\u9e3e\u7fd4\u53ca\u5176\u6570\u5b66\u8457\u4f5c\n\u4e8c \u767d\u8299\u5802\u8bf8\u5b50\u53ca\u5176\u6570\u5b66\u8457\u4f5c\n\u4e09 \u5218\u5f5d\u7a0b\u53ca\u5176\u6570\u5b66\u8457\u4f5c\n\u56db \u9648\u5fd7\u575a\u3001\u5468\u8fbe\u53ca\u5176\u6570\u5b66\u8457\u4f5c\n\u7b2c\u4e8c\u8282 \u6570\u8bba\u7684\u7814\u7a76\n\u4e00 \u7d20\u6570\u7684\u7814\u7a76\n\u4e8c \u6574\u6570\u52fe\u80a1\u5f62\u7684\u7814\u7a76\n\u4e09 \u767e\u9e21\u672f\u548c\u5927\u884d\u603b\u6570\u672f\u7684\u7814\u7a76\n\u7b2c\u4e09\u8282 \u579b\u79ef\u672f\u4e0e\u62db\u5dee\u672f\u7684\u7814\u7a76\n\u4e00 \u674e\u5584\u5170\u7684\u579b\u79ef\u672f\n\u4e8c \u590f\u9e3e\u7fd4\u7684\u579b\u79ef\u62db\u5dee\u7814\u7a76 \n\u4e09 \u5218\u5f5d\u7a0b\u7684\u579b\u79ef\u672f\u7814\u7a76\n\u7b2c\u56db\u8282 \u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e00 \u590f\u9e3e\u7fd4\u5bf9\u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e8c \u534e\u8605\u82b3\u7684\u6570\u6839\u5f00\u65b9\u672f\u4e0e\u79ef\u8f83\u5f00\u65b9\u672f\n\u7b2c\u4e94\u8282 \u5bf9\u5706\u9525\u66f2\u7ebf\u548c\u5fae\u79ef\u5206\u7684\u7814\u7a76\n\u4e00 \u5706\u9525\u66f2\u7ebf\u4f5c\u56fe\n\u4e8c \u4e8c\u6b21\u66f2\u7ebf\u6c42\u79ef\u95ee\u9898\n\u4e09 \u5e73\u5706\u5bb9\u5207\u4e0e\u7d2f\u5706\n\u7b2c\u4e09\u5341\u4e09\u7ae0 \u6e05\u672b\u6570\u5b66\u6559\u80b2\n\u7b2c\u4e00\u8282 \u6e05\u672b\u6570\u5b66\u6559\u80b2\u6982\u8ff0\n\u4e00 \u6570\u5b66\u6559\u80b2\u7684\u53d8\u9769\n\u4e8c \u6e05\u672b\u7684\u6570\u5b66\u6559\u80b2\u89c2\u5ff5\n\u4e09 \u6e05\u672b\u7684\u7559\u5b66\u6d3b\u52a8\u4e0e\u6570\u5b66\u7559\u5b66\u751f\n\u7b2c\u4e8c\u8282 \u665a\u6e05\u6570\u5b66\u6559\u80b2\n\u4e00 \u6d0b\u52a1\u5b66\u5802\u7684\u6570\u5b66\u6559\u80b2\n\u4e8c \u4e66\u9662\u7684\u53d8\u9769\u4e0e\u6570\u5b66\u6559\u80b2\n\u4e09 \u6559\u4f1a\u5b66\u6821\u7684\u6570\u5b66\u6559\u79d1\u4e66\n\u56db \u7678\u536f\u5b66\u5236\u7684\u6570\u5b66\u8bfe\u7a0b\n\u7b2c\u4e09\u8282 \u6570\u5b66\u4e1b\u4e66\u3001\u6570\u5b66\u793e\u56e2\u4e0e\u520a\u7269\n\u4e00 \u6570\u5b66\u4e1b\u4e66\u7684\u7f16\u7e82\n\u4e8c \u6570\u5b66\u793e\u56e2\n\u4e09 \u6570\u5b66\u520a\u7269\n\n\u4e3b\u8981\u53c2\u8003\u6587\u732e\n\u540e\u8bb0\n\u603b\u8dcb\n\ntable of Contents\nGeneral Preface Lu Jiaxi\nForeword iii\n\nThe first series of Chinese mathematics forms a subject\n- Mathematics from the primitive society to the Western Zhou Dynasty\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society\nSection 1 The Formation of Graphic Concepts\nThe emergence of a graphic concept\nSecond, from the concept of orientation to see the concept of graphics\nThree original drawing tools - rules and regulations\nSection II The Formation of Number Concepts and Original Counting Methods\nThe emergence of a number concept\nTwo original counting methods\nSection 3 The legendary mathematical figure\nOne\nSecond Yellow Emperor and Lishou\nThree \u5c27, \u821c, \u79b9 and \u5015\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society\nChapter 2 Mathematics Forms a Discipline&amp;mdash;&amp;mdash;Mathematics of the Three Generations of Xia, Shang, and Xi Zhou\nSection 1 Formation of Decimal Value Notation\nA number in Oracle and Jinwen\nTwo decimal value notation\nSection 2 Mathematics Becomes a Discipline\nThe need for social management and work and the development of mathematics\nSecond Mathematics enters teaching subjects\nIII Shang Gao and its mastered mathematics knowledge\n\nPart Two Establishment of Traditional Chinese Mathematical Framework\n- Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background\nThe Second Qin and Han Mathematics and Social and Cultural Background\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period\nAn integer number of four operations in the Spring and Autumn Period\nSecond, the extensive use of scores, ratios and proportions\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era&amp;mdash;&amp;mdash;&amp;ldquo;Nine Numbers&amp;rdquo;\nIV Other Mathematics Knowledge in Pre-Qin Period\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period\nA Mohist and Mathematics\nTwo homes of mathematics\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips\nA Qin Jian \\\\&amp;quot;Numbers\\\\&amp;quot;\nII. The style, expression and characteristics of the \\\\&amp;quot;numeric book\\\\&amp;quot;\nThree compilation of \\\\&amp;quot;calculus book\\\\&amp;quot;\nThe content of the \\\\&amp;quot;numerical book\\\\&amp;quot; and its position in the history of Chinese mathematics\nSection V. The Zhouyi Classics and Chen Zi\nOne Zhouyi Calculation\nTwo Chen Zi\nSection VI: \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot; and Zhang Cang, Yan Shouchang\nThe content of \\\\&amp;quot;Chapter 9 Arithmetic\\\\&amp;quot;\nII. The Style and Compilation of Nine Chapters of Arithmetic\nThree \\\\&amp;quot;arithmetic book\\\\&amp;quot; and \\\\&amp;quot;Nine chapters of arithmetic\\\\&amp;quot;\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World\nFive Versions of Nine Chapters of Arithmetic\nSix Zhang Canghe Yu Shouchang\nSection 7 Other Mathematicians and Mathematical Works\nA dealer and \\\\&amp;quot;Business Arithmetic\\\\&amp;quot; and \\\\&amp;quot;Du Zhong Arithmetic\\\\&amp;quot;\nSecond Yin Xianhe Liu Hao\nThree Zhang Heng and Ma continued\nChapter IV Insufficient scores, rates, and profits\nSection 1 Scores and Its Four Principles\nA score and its representation\nTwo fractional four algorithm\nSection II Surgery and Decline Surgery\nNow there is surgery\nSecond decline\nThree transmission techniques\nSection III Insufficiency\nInsufficiency\nThe Application of Insufficiency Technique in General Mathematical Problems\nChapter V Area, Volume, Pythagoreanism, and Observation\nSection 1 Area\nA linear area\nSecond curved area\nThree round and square\nFour curved surface area\nSection 2 Volume\na polyhedral volume\nTwo round body volume\nSection III Pythagorean Theorem and Unfolding Tacks\nAn Pythagorean Theorem\nThe second solution hook shape\nThree Pythagorean arrays\nThe fourth quarter\nA tick share\nTwo ticks\nSection V\nOne time\nThe bud of the second difference\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences\nThe first section of the prescription\nOpen square\nTwo open cubes\nSection II Equations and Positive and Negative Techniques\nOne equation and equation\nSecond profit and loss\nThree positive and negative surgery\nSection III Series\n\nPart III Completion of Chinese Traditional Mathematical Theory System\n- Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory\nII Society and Mathematics in the Southern and Northern Dynasties\nThe Society and Mathematics in the Middle of Tang Dynasty\nSection Two: Xu Yue\\\\&amp;#39;s \\\\&amp;quot;Surgical Relics\\\\&amp;quot; and Zhao Shuang\\\\&amp;#39;s \\\\&amp;quot;Zhou Shuo\\\\&amp;#39;s Recounts\\\\&amp;quot;\nLiu Hong, Xu Yue, and The Record of the Numbers\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera\nAn Liu Hui\nTwo \\\\&amp;quot;Nine chapters of arithmetic note\\\\&amp;quot;\nThree \\\\&amp;quot;The Island\\\\&amp;quot;\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties\nA Study on \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot;\nSecond \\\\&amp;quot;Sun Tzu Classic\\\\&amp;quot;\nThree \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nFour \\\\&amp;quot;Zhang Qiu Jian Su Jing\\\\&amp;quot;\nV. Zu Chongzhi, Zu Yu\\\\&amp;#39;s and \\\\&amp;quot;Fuzheng\\\\&amp;quot;\nSix books and their mathematical works\nSeven other mathematicians\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty\nLiu Yi\nII Wang Xiaotong and \\\\&amp;quot;Ancient Gujing\\\\&amp;quot;\nThe three Li Yufeng and other finishing ten calculations\nFour Lines and \\\\&amp;quot;Da Yan Li\\\\&amp;quot;\nFive Sides\nSection 6 Sui Tang School of Mathematics and Accounting\nA math school\nSecond Accounting Division\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools\nA large number of methods\nTwo Attempts to Improve Calculation Tools\nChapter VIII Principles of rate and principle\nSection 1 Definition and Nature of Rates\nThe definition of probability\nThe Method and Nature of Bivariate\nSection II Today\\\\&amp;#39;s Promotion and Principles of Surgery\nThe current promotion of surgery\nTwo principles\nThe third section of the arithmetic and the least common multiple\nAn arithmetic problem\nII Solving Mathematical Problems Directly\nApplication of the three greatest common divisors and the least common multiple\nChapter Nine Pythagoreans, Observations, and Errors\nSection 1 Demonstration of Formulas for Explaining Pyramids\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui\nII Zhao Shuang and Liu Hui\\\\&amp;#39;s Proof of the Formulas of the Solution\nThree Liu Hui\\\\&amp;#39;s Proof of the Pythagorean Array Formula\nIV Wang Xiaotong\\\\&amp;#39;s Expansion of the Hexagonal Shape Problem\nSection 2 Proof of Formulas and Formulas\nOne with the proof of the principle of entry and completion\nB. Proof of the Principle of Keeping Preference with Pythagoreanism\nSection III Correction\nOne difference in skill\nTwo Drawings Six Body and Mathematics\nSection IV Other Observation Problems\nAn Observation Problem in Zhang Qi Jian Jian Su Jing\nII. The Problem of Expectation in the \\\\&amp;quot;Several Notes to the Book\\\\&amp;quot;\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations\nSection 1 Geometric Explanation and Improvement of Alchemy\nA Liu Hui\\\\&amp;#39;s Geometry Explanation of the Alchemy\nII Liu Hui and Wang Xiaotong\\\\&amp;#39;s Creation of Opening Methods\nThe improvement of the three prescriptions\nIV Liu Hui\\\\&amp;#39;s \\\\&amp;quot;seeking micro-number\\\\&amp;quot; and the approximate value of the root\nV. Zu Chongzhi\\\\&amp;#39;s opening power and opening difference\nThe root formula of six lines\nSection II Progress of Equations\nLiu Hui\\\\&amp;#39;s equation theory\nTwo mutual multiplication and denomination\nThree equations new surgery\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing\nSection III Indefinite issues\nA total of five wells\nTwo things do not know the problem\nThree hundred chicken\nSection 4 Arithmetic series and geometric series\nAn arithmetic progression\nTwo equal number arrays\nChapter 11 Infinitely small segmentation and limit thinking\nSection 1 Cutting\nSection II Principle of Liu Hui\nSection III Principles and volume of the ancestral hall\nAn ancestral principle\nTwo square cover and ball volume\nSection IV The Application of Limit Ideas in Approximate Calculation\na pi ratio\nSecond round rate and square rate\nArc field density\nSection V Liu Hui\\\\&amp;#39;s area and volume derivation system\nLiu Hui\\\\&amp;#39;s area derivation system\nTwo proofs of the polyhedral volume formula\nThree Liu Hui\\\\&amp;#39;s volume derivation system\nSection 6 Liu Hui\\\\&amp;#39;s Limitation Thought in the History of Mathematics\nThe Infinite Segmentation of Liu Hui\\\\&amp;#39;s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece\nChapter Twelve Liu Hui\\\\&amp;#39;s Logic Thought and Mathematical Theory System\nThe first section Liu Hui\\\\&amp;#39;s resignation and reason, class, and therefore\nOne reason\nCategory II\nThree\nSection 2 Definition\nSection III Analogy and Induction\nAn analogy\nInductive reasoning\nSection IV Deductive Reasoning of Liu Hui\nSyllogism and Relational Reasoning\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning\nThird, the prototype of mathematical induction\nSection 5 Mathematical Proof\nA comprehensive approach\nB. Analysis and synthesis\nIII Rebuttal and Liu Hui\\\\&amp;#39;s mistakes\nSection VI Liu Hui\\\\&amp;#39;s Mathematical Theory System\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nSection 1 The Creative Transformation of the Sui and Tang Calendars\nThe discovery of a letter and its significance\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties\nSection II Secondary interpolation algorithm\nOne \\\\&amp;quot;The Imperial Calendar\\\\&amp;quot;\nLiu Liu\\\\&amp;#39;s Quadratic Interpolation Algorithm and Its Algorithmic Analysis\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar\nFour-phase subtractive multiplication\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nLiu Xi\\\\&amp;#39;s \\\\&amp;quot;Emperor\\\\&amp;quot; calendar algorithm\nII Li Yingfeng\\\\&amp;#39;s \\\\&amp;quot;Lin Lun Li\\\\&amp;quot; image algorithm\nThree-Line \\\\&amp;quot;Dai Yan Li\\\\&amp;quot; Nine Shadows Algorithm\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang\\\\&amp;#39;s \\\\&amp;quot;Chong Xuan Li\\\\&amp;quot;\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties\nSection 1 Mathematical Communication between China and North Korea\nSection 2 Mathematics Exchange between China and Japan\nA Chinese calendar was introduced into Japan\nII Introduction of Early Learning Education System\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties\nSection 3 Mathematical Communication between China and India\nAn Indian mathematics introduced to China\nII The Influence of Chinese Mathematics on India\n\nPart IV The Climax of Chinese Traditional Mathematics\n&amp;mdash;&amp;mdash;Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty\nII Thoughtful easing is a necessary condition for the development of mathematics\nIII Social needs are a powerful force for the development of mathematics\nFourth Song and Yuan rulers attach importance to mathematics\nFive Characteristics of Mathematics in the Song and Yuan Dynasties\nThe second section of the book \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nA Biography of the Date and Content of the \\\\&amp;quot;Xiahou Yang Scripture\\\\&amp;quot;\nTwo versions of the \\\\&amp;quot;Xiahou Yang Calculator\\\\&amp;quot;\nThe third quarter Jia Xianhe\\\\&amp;#39;s \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters, The Scriptures\\\\&amp;quot;\nJia Xian and his teacher Chu Yan\nTwo Most Existential Examinations of \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters Calculating Caojing\\\\&amp;quot;\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor\\\\&amp;#39;s Nine Chapters.\nSection IV Liu Yihe\\\\&amp;#39;s \\\\&amp;quot;Proposal on Ancient Roots\\\\&amp;quot;\nYi Liu Yi\nSecond, \\\\&amp;quot;A discussion of Gu Gen Yuan\\\\&amp;quot;\nSection Five Qin Jiulu and \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nThe life of Qin Jiuhao\nSecond Qin Jiuyao character identification\nThree \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nSection 6 Li Yehe\\\\&amp;#39;s \\\\&amp;quot;Measurement of Circular Oceanscope\\\\&amp;quot; and \\\\&amp;quot;Yigu Performance\\\\&amp;quot;\nYi Ye\nThe two holes Jiurong and \\\\&amp;quot;Test round sea mirror\\\\&amp;quot;\nThree \\\\&amp;quot;Yi Gu Ji\\\\&amp;quot; and \\\\&amp;quot;Yi Gu Performance\\\\&amp;quot;\nSection 7 Yang Hui and \\\\&amp;quot;Detailed Explanation of Chapter 9 Algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui Algorithm\\\\&amp;quot;\nYihui Yang\nSecond, \\\\&amp;quot;Detailed Nine Chapter Algorithms\\\\&amp;quot;\nThree \\\\&amp;quot;daily algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui algorithm\\\\&amp;quot;\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book\nOne Zhu Shijie\nTwo \\\\&amp;quot;Education Enlightenment\\\\&amp;quot;\nThree \\\\&amp;quot;Siyuan Yujian\\\\&amp;quot;\nSection 9 Other Mathematicians and Mathematical Works\nA Li Jihe\\\\&amp;#39;s \\\\&amp;quot;Nine Chapters of Arithmetic and Meaning\\\\&amp;quot; and \\\\&amp;quot;Zhou Ji\\\\&amp;#39;s Calculation of Sound and Meaning\\\\&amp;quot;\nTwo \\\\&amp;quot;Xiecha Microcalculus\\\\&amp;quot;\nThree Shen Kuohe\\\\&amp;#39;s Mathematical Achievements in \\\\&amp;quot;Meng Xi Bi Tan\\\\&amp;quot;\nFour Wang Xi, Guo Shoujing, and \\\\&amp;quot;Time History\\\\&amp;quot;\nFive Zhao Youqin and \\\\&amp;quot;New Elephant\\\\&amp;quot;\nSix Shakes and The River Defense Theory &amp;bull; Algorithm Gate\nSeven Other Mathematicians and Mathematical Works\nChapter 16 Improvements in Computing Technology and Invention of Abacus\nSection 1 \u25cb and Decimal Decimals\nOne and digital\nTwo decimal places\nSection II Improvements in Computing Technology\nOne for the law, one for the addition, subtraction, multiplication and division\nII Heading Multiplication and Nine Return and Elimination\nSection 3 The birth of abacus\nAbacus produces many\nThe second abacus was born in the Song Dynasty at the latest\nChapter 17 Going to Share Volume and Cutting Circles\nSection 1 Check Stock Volume\nOne\nTwo round city schema\nThree identification notes\nSection 2 Cutting\nA Shen Kuo&amp;rsquo;s Tactics\nTwo Sagittal Cuts in the Time of Time\nThree Zhao Youqin\\\\&amp;#39;s cutting\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple\nSection 1 Numerical Solution of High Order Equations\nAn upright release method\nSecond Jia Xian Triangle\nThree increase open method\nFour Benefits and Reductions\nFive positive and negative open\nSection II Tianyuan surgery\nOne-day history of metaphysics\nThe perfection and application of the two-day meta-technique\nThe third quarter of four\nThe historical development of a quadruple surgery\nTwo-quaternary elimination\nThree binary\nFour triples\nFive four yuan surgery\nChapter 19 Hoarding, tricks\nSection 1 Hoarding\nSlot technique\nII Hoarding\nSection II tricks surgery\nA trick of &amp;ldquo;Time-giving Calendar&amp;rdquo;\nTwo tricks of \\\\&amp;quot;Syuanyuanjian\\\\&amp;quot;\nChapter Twenty The total number of Da Yan and vertical and horizontal map\nThe first quarter total number of surgery\nThe origin of a major total\nTotal number of major\nSection II.\nA river map, Luo book and vertical and horizontal map\nSecond, Yang Hui, etc.\nThree Ding Yidong\\\\&amp;#39;s map\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties\nSection 2 Chinese Mathematical Biography\nThe Impact of Chinese Mathematics on Islamic Countries\nII The Influence of Chinese Mathematics on North Korea and Japan\nSection III Introduction of Mathematics in Islamic Countries\nThe introduction of a mathematical work\nII Arabic Digital and Crosswords\nThree soil disc algorithm and lattice operator\n\nPart V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus\n- Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty\nSection 1 The Social Background of Mathematics in the Ming Dynasty\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty\nA \\\\&amp;quot;Yongle Grand Ceremony &amp;bull; Calculation\\\\&amp;quot; and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty\nThe loss of the second ancient book\nLoss of three mathematics results\nSection III The Mainstream of Mathematics in the Ming Dynasty\nA survey of mathematics books in the Ming Dynasty\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period\nOne\nTwo Ding Ju and his Ding Ju algorithm\nThree Jiaheng\\\\&amp;#39;s \\\\&amp;quot;Algorithm Set\\\\&amp;quot;\nFour \\\\&amp;quot;Detailed Algorithm\\\\&amp;quot;\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty\nYan Gong and his \\\\&amp;quot;Tongyuan algorithm\\\\&amp;quot;\nLiu Shilong and his \\\\&amp;quot;Nine Chapters Tuning Algorithm\\\\&amp;quot;\nThree Xia Yuanze\\\\&amp;#39;s \\\\&amp;quot;specified algorithm\\\\&amp;quot;\nFour other calculations\nSection 3 Mathematical and Mathematical Writings\nWu Jing and his \\\\&amp;quot;Nine Chapter Algorithms\\\\&amp;quot;\nII Wang Wensu and his \\\\&amp;quot;Educational Poems\\\\&amp;quot;\nThree other books\nSection IV: The Theory of Theoretical Mathematics\nTang Shunzhi and his \\\\&amp;quot;Number Theory\\\\&amp;quot; six\nII Gu Yingxiang and his four books on mathematics\nThree Weeks of Learning and Its \\\\&amp;quot;Ecco\\\\&amp;quot;\nIV Zhu Zaiyu and his &amp;ldquo;New Theory of Calculation&amp;rdquo; and &amp;ldquo;Ji-Suan Su Jing Jing&amp;rdquo;\nSection V Abacus Mathematicians and Mathematical Works\nA previous work on abacus\nTwo-way Big Place and Its \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot; and \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot;\nThree other abacus work\nChapter 24 Songs of Mathematics and Popularization of Abacus\nSection 1 Practicality and Songs of Mathematics\nA practical, popular and commercialized mathematics\nThe second song of mathematics\nMathematical Songs Since the End of the Three Yuan\nSection 2 Various \\\\&amp;quot;miscellaneous methods\\\\&amp;quot; in mathematics of the Ming Dynasty\nSection 3 Development and Popularization of Abacus\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties\nThe reflection of abacus in the second mathematic book\nThe disappearance of the popularity and calculation of the three abacus\nChapter 25 Some Mathematics Work in the Ming Dynasty\nSection 1 Numerical Solution of Squares and Equations\nOne-Mid-Year Growth and Opening Method\" addthis:url=\"https:\/\/www.amazon.com\/Mathematics-History-Science-Technology-CHUN\/dp\/7030290534?SubscriptionId=AKIAJCI3DJTKR6N4LR2A&amp;&amp;linkCode=xm2&amp;camp=2025&amp;creative=165953&amp;creativeASIN=7030290534\" class=\"addthis_button_facebook\"><\/a><\/div><div class=\"addthis_sharing_toolbox addthis_default_style\" style=\"cursor:pointer\"><a style=\"cursor:pointer;\" href=\"\" addthis:title=\"The Science and Technology in China: Mathematics Volume \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u53f2\u00b7\u6570\u5b66\u5377\" addthis:description=\"\u76ee\u5f55\n\u603b\u5e8f \u5362\u5609\u9521i\n\u524d\u8a00iii\n\n\u7b2c\u4e00\u7f16 \u4e2d\u56fd\u6570\u5b66\u4ece\u5174\u8d77\u5230\u5f62\u6210\u4e00\u95e8\u5b66\u79d1\n&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u5230\u897f\u5468\u65f6\u671f\u7684\u6570\u5b66\n\u7b2c\u4e00\u7ae0 \u4e2d\u56fd\u6570\u5b66\u7684\u5174\u8d77&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u56fe\u5f62\u89c2\u5ff5\u7684\u5f62\u6210\n\u4e00 \u56fe\u5f62\u89c2\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u4ece\u65b9\u4f4d\u89c2\u5ff5\u770b\u56fe\u5f62\u89c2\u5ff5\n\u4e09 \u539f\u59cb\u7684\u4f5c\u56fe\u5de5\u5177&amp;mdash;&amp;mdash;\u89c4\u77e9\u51c6\u7ef3\n\u7b2c\u4e8c\u8282 \u6570\u6982\u5ff5\u7684\u5f62\u6210\u4e0e\u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u4e00 \u6570\u6982\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u7b2c\u4e09\u8282 \u4f20\u8bf4\u4e2d\u7684\u6570\u5b66\u4eba\u7269\n\u4e00 \u4f0f\u7fb2\n\u4e8c \u9ec4\u5e1d\u548c\u96b6\u9996\n\u4e09 \u5c27\u3001\u821c\u3001\u79b9\u548c\u5015\n\u7b2c\u56db\u8282 \u4ece\u539f\u59cb\u793e\u4f1a\u665a\u671f\u7684\u793e\u4f1a\u7ed3\u6784\u770b\u5f53\u65f6\u6570\u5b66\u7684\u53d1\u5c55\n\u7b2c\u4e8c\u7ae0 \u6570\u5b66\u5f62\u6210\u4e00\u95e8\u5b66\u79d1&amp;mdash;&amp;mdash;\u590f\u3001\u5546\u3001\u897f\u5468\u4e09\u4ee3\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\u7684\u5f62\u6210\n\u4e00 \u7532\u9aa8\u6587\u548c\u91d1\u6587\u4e2d\u7684\u6570\u5b57\n\u4e8c \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\n\u7b2c\u4e8c\u8282 \u6570\u5b66\u6210\u4e3a\u4e00\u95e8\u5b66\u79d1\n\u4e00 \u793e\u4f1a\u7ba1\u7406\u548c\u5de5\u4f5c\u7684\u9700\u8981\u4e0e\u6570\u5b66\u7684\u53d1\u5c55\n\u4e8c \u6570\u5b66\u8fdb\u5165\u6559\u5b66\u79d1\u76ee\n\u4e09 \u5546\u9ad8\u53ca\u5176\u6240\u638c\u63e1\u7684\u6570\u5b66\u77e5\u8bc6\n\n\u7b2c\u4e8c\u7f16 \u4e2d\u56fd\u4f20\u7edf\u6570\u5b66\u6846\u67b6\u7684\u786e\u7acb\n&amp;mdash;&amp;mdash;\u6625\u79cb\u81f3\u4e1c\u6c49\u4e2d\u671f\u7684\u6570\u5b66\n\u7b2c\u4e09\u7ae0 \u6625\u79cb\u81f3\u6c49\u4ee3\u6570\u5b66\u6982\u8bba\n\u7b2c\u4e00\u8282 \u6625\u79cb\u6218\u56fd\u79e6\u6c49\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e00 \u6625\u79cb\u6218\u56fd\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e8c \u79e6\u6c49\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u7b2c\u4e8c\u8282 \u7b97\u6cd5\u5f0f\u6570\u5b66\u5728\u6625\u79cb\u6218\u56fd\u65f6\u671f\u8fbe\u5230\u9ad8\u5cf0\n\u4e00 \u6574\u6570\u56db\u5219\u8fd0\u7b97\u5728\u6625\u79cb\u65f6\u671f\u7684\u666e\u53ca\n\u4e8c \u5206\u6570\u3001\u6bd4\u548c\u6bd4\u4f8b\u7684\u5e7f\u6cdb\u4f7f\u7528\n\u4e09 \u4ece\u5148\u79e6\u6587\u732e\u770b\u6625\u79cb\u6218\u56fd\u65f6\u4ee3\u7684\u7b97\u6cd5\u5316\u6570\u5b66&amp;mdash;&amp;mdash;&amp;ldquo;\u4e5d\u6570&amp;rdquo;\n\u56db \u5148\u79e6\u65f6\u671f\u7684\u5176\u4ed6\u6570\u5b66\u77e5\u8bc6\n\u7b2c\u4e09\u8282 \u7406\u8bba\u601d\u8fa8\u503e\u5411&amp;mdash;&amp;mdash;\u6625\u79cb\u6218\u56fd\u6570\u5b66\u7684\u65b0\u52a8\u5411\n\u4e00 \u58a8\u5bb6\u4e0e\u6570\u5b66\n\u4e8c \u540d\u5bb6\u7684\u6570\u5b66\u601d\u60f3\n\u4e09 \u5148\u79e6\u9053\u5bb6\u7b49\u5b66\u6d3e\u7684\u65e0\u9650\u601d\u60f3\n\u56db 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\u5218\u5f5d\u7a0b\u7684\u579b\u79ef\u672f\u7814\u7a76\n\u7b2c\u56db\u8282 \u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e00 \u590f\u9e3e\u7fd4\u5bf9\u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e8c \u534e\u8605\u82b3\u7684\u6570\u6839\u5f00\u65b9\u672f\u4e0e\u79ef\u8f83\u5f00\u65b9\u672f\n\u7b2c\u4e94\u8282 \u5bf9\u5706\u9525\u66f2\u7ebf\u548c\u5fae\u79ef\u5206\u7684\u7814\u7a76\n\u4e00 \u5706\u9525\u66f2\u7ebf\u4f5c\u56fe\n\u4e8c \u4e8c\u6b21\u66f2\u7ebf\u6c42\u79ef\u95ee\u9898\n\u4e09 \u5e73\u5706\u5bb9\u5207\u4e0e\u7d2f\u5706\n\u7b2c\u4e09\u5341\u4e09\u7ae0 \u6e05\u672b\u6570\u5b66\u6559\u80b2\n\u7b2c\u4e00\u8282 \u6e05\u672b\u6570\u5b66\u6559\u80b2\u6982\u8ff0\n\u4e00 \u6570\u5b66\u6559\u80b2\u7684\u53d8\u9769\n\u4e8c \u6e05\u672b\u7684\u6570\u5b66\u6559\u80b2\u89c2\u5ff5\n\u4e09 \u6e05\u672b\u7684\u7559\u5b66\u6d3b\u52a8\u4e0e\u6570\u5b66\u7559\u5b66\u751f\n\u7b2c\u4e8c\u8282 \u665a\u6e05\u6570\u5b66\u6559\u80b2\n\u4e00 \u6d0b\u52a1\u5b66\u5802\u7684\u6570\u5b66\u6559\u80b2\n\u4e8c \u4e66\u9662\u7684\u53d8\u9769\u4e0e\u6570\u5b66\u6559\u80b2\n\u4e09 \u6559\u4f1a\u5b66\u6821\u7684\u6570\u5b66\u6559\u79d1\u4e66\n\u56db \u7678\u536f\u5b66\u5236\u7684\u6570\u5b66\u8bfe\u7a0b\n\u7b2c\u4e09\u8282 \u6570\u5b66\u4e1b\u4e66\u3001\u6570\u5b66\u793e\u56e2\u4e0e\u520a\u7269\n\u4e00 \u6570\u5b66\u4e1b\u4e66\u7684\u7f16\u7e82\n\u4e8c \u6570\u5b66\u793e\u56e2\n\u4e09 \u6570\u5b66\u520a\u7269\n\n\u4e3b\u8981\u53c2\u8003\u6587\u732e\n\u540e\u8bb0\n\u603b\u8dcb\n\ntable of Contents\nGeneral Preface Lu Jiaxi\nForeword iii\n\nThe first series of Chinese mathematics forms a subject\n- Mathematics from the primitive society to the Western Zhou Dynasty\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society\nSection 1 The Formation of Graphic Concepts\nThe emergence of a graphic concept\nSecond, from the concept of orientation to see the concept of graphics\nThree original drawing tools - rules and regulations\nSection II The Formation of Number Concepts and Original Counting Methods\nThe emergence of a number concept\nTwo original counting methods\nSection 3 The legendary mathematical figure\nOne\nSecond Yellow Emperor and Lishou\nThree \u5c27, \u821c, \u79b9 and \u5015\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society\nChapter 2 Mathematics Forms a Discipline&amp;mdash;&amp;mdash;Mathematics of the Three Generations of Xia, Shang, and Xi Zhou\nSection 1 Formation of Decimal Value Notation\nA number in Oracle and Jinwen\nTwo decimal value notation\nSection 2 Mathematics Becomes a Discipline\nThe need for social management and work and the development of mathematics\nSecond Mathematics enters teaching subjects\nIII Shang Gao and its mastered mathematics knowledge\n\nPart Two Establishment of Traditional Chinese Mathematical Framework\n- Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background\nThe Second Qin and Han Mathematics and Social and Cultural Background\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period\nAn integer number of four operations in the Spring and Autumn Period\nSecond, the extensive use of scores, ratios and proportions\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era&amp;mdash;&amp;mdash;&amp;ldquo;Nine Numbers&amp;rdquo;\nIV Other Mathematics Knowledge in Pre-Qin Period\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period\nA Mohist and Mathematics\nTwo homes of mathematics\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips\nA Qin Jian \\\\&amp;quot;Numbers\\\\&amp;quot;\nII. The style, expression and characteristics of the \\\\&amp;quot;numeric book\\\\&amp;quot;\nThree compilation of \\\\&amp;quot;calculus book\\\\&amp;quot;\nThe content of the \\\\&amp;quot;numerical book\\\\&amp;quot; and its position in the history of Chinese mathematics\nSection V. The Zhouyi Classics and Chen Zi\nOne Zhouyi Calculation\nTwo Chen Zi\nSection VI: \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot; and Zhang Cang, Yan Shouchang\nThe content of \\\\&amp;quot;Chapter 9 Arithmetic\\\\&amp;quot;\nII. The Style and Compilation of Nine Chapters of Arithmetic\nThree \\\\&amp;quot;arithmetic book\\\\&amp;quot; and \\\\&amp;quot;Nine chapters of arithmetic\\\\&amp;quot;\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World\nFive Versions of Nine Chapters of Arithmetic\nSix Zhang Canghe Yu Shouchang\nSection 7 Other Mathematicians and Mathematical Works\nA dealer and \\\\&amp;quot;Business Arithmetic\\\\&amp;quot; and \\\\&amp;quot;Du Zhong Arithmetic\\\\&amp;quot;\nSecond Yin Xianhe Liu Hao\nThree Zhang Heng and Ma continued\nChapter IV Insufficient scores, rates, and profits\nSection 1 Scores and Its Four Principles\nA score and its representation\nTwo fractional four algorithm\nSection II Surgery and Decline Surgery\nNow there is surgery\nSecond decline\nThree transmission techniques\nSection III Insufficiency\nInsufficiency\nThe Application of Insufficiency Technique in General Mathematical Problems\nChapter V Area, Volume, Pythagoreanism, and Observation\nSection 1 Area\nA linear area\nSecond curved area\nThree round and square\nFour curved surface area\nSection 2 Volume\na polyhedral volume\nTwo round body volume\nSection III Pythagorean Theorem and Unfolding Tacks\nAn Pythagorean Theorem\nThe second solution hook shape\nThree Pythagorean arrays\nThe fourth quarter\nA tick share\nTwo ticks\nSection V\nOne time\nThe bud of the second difference\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences\nThe first section of the prescription\nOpen square\nTwo open cubes\nSection II Equations and Positive and Negative Techniques\nOne equation and equation\nSecond profit and loss\nThree positive and negative surgery\nSection III Series\n\nPart III Completion of Chinese Traditional Mathematical Theory System\n- Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory\nII Society and Mathematics in the Southern and Northern Dynasties\nThe Society and Mathematics in the Middle of Tang Dynasty\nSection Two: Xu Yue\\\\&amp;#39;s \\\\&amp;quot;Surgical Relics\\\\&amp;quot; and Zhao Shuang\\\\&amp;#39;s \\\\&amp;quot;Zhou Shuo\\\\&amp;#39;s Recounts\\\\&amp;quot;\nLiu Hong, Xu Yue, and The Record of the Numbers\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera\nAn Liu Hui\nTwo \\\\&amp;quot;Nine chapters of arithmetic note\\\\&amp;quot;\nThree \\\\&amp;quot;The Island\\\\&amp;quot;\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties\nA Study on \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot;\nSecond \\\\&amp;quot;Sun Tzu Classic\\\\&amp;quot;\nThree \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nFour \\\\&amp;quot;Zhang Qiu Jian Su Jing\\\\&amp;quot;\nV. Zu Chongzhi, Zu Yu\\\\&amp;#39;s and \\\\&amp;quot;Fuzheng\\\\&amp;quot;\nSix books and their mathematical works\nSeven other mathematicians\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty\nLiu Yi\nII Wang Xiaotong and \\\\&amp;quot;Ancient Gujing\\\\&amp;quot;\nThe three Li Yufeng and other finishing ten calculations\nFour Lines and \\\\&amp;quot;Da Yan Li\\\\&amp;quot;\nFive Sides\nSection 6 Sui Tang School of Mathematics and Accounting\nA math school\nSecond Accounting Division\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools\nA large number of methods\nTwo Attempts to Improve Calculation Tools\nChapter VIII Principles of rate and principle\nSection 1 Definition and Nature of Rates\nThe definition of probability\nThe Method and Nature of Bivariate\nSection II Today\\\\&amp;#39;s Promotion and Principles of Surgery\nThe current promotion of surgery\nTwo principles\nThe third section of the arithmetic and the least common multiple\nAn arithmetic problem\nII Solving Mathematical Problems Directly\nApplication of the three greatest common divisors and the least common multiple\nChapter Nine Pythagoreans, Observations, and Errors\nSection 1 Demonstration of Formulas for Explaining Pyramids\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui\nII Zhao Shuang and Liu Hui\\\\&amp;#39;s Proof of the Formulas of the Solution\nThree Liu Hui\\\\&amp;#39;s Proof of the Pythagorean Array Formula\nIV Wang Xiaotong\\\\&amp;#39;s Expansion of the Hexagonal Shape Problem\nSection 2 Proof of Formulas and Formulas\nOne with the proof of the principle of entry and completion\nB. Proof of the Principle of Keeping Preference with Pythagoreanism\nSection III Correction\nOne difference in skill\nTwo Drawings Six Body and Mathematics\nSection IV Other Observation Problems\nAn Observation Problem in Zhang Qi Jian Jian Su Jing\nII. The Problem of Expectation in the \\\\&amp;quot;Several Notes to the Book\\\\&amp;quot;\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations\nSection 1 Geometric Explanation and Improvement of Alchemy\nA Liu Hui\\\\&amp;#39;s Geometry Explanation of the Alchemy\nII Liu Hui and Wang Xiaotong\\\\&amp;#39;s Creation of Opening Methods\nThe improvement of the three prescriptions\nIV Liu Hui\\\\&amp;#39;s \\\\&amp;quot;seeking micro-number\\\\&amp;quot; and the approximate value of the root\nV. Zu Chongzhi\\\\&amp;#39;s opening power and opening difference\nThe root formula of six lines\nSection II Progress of Equations\nLiu Hui\\\\&amp;#39;s equation theory\nTwo mutual multiplication and denomination\nThree equations new surgery\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing\nSection III Indefinite issues\nA total of five wells\nTwo things do not know the problem\nThree hundred chicken\nSection 4 Arithmetic series and geometric series\nAn arithmetic progression\nTwo equal number arrays\nChapter 11 Infinitely small segmentation and limit thinking\nSection 1 Cutting\nSection II Principle of Liu Hui\nSection III Principles and volume of the ancestral hall\nAn ancestral principle\nTwo square cover and ball volume\nSection IV The Application of Limit Ideas in Approximate Calculation\na pi ratio\nSecond round rate and square rate\nArc field density\nSection V Liu Hui\\\\&amp;#39;s area and volume derivation system\nLiu Hui\\\\&amp;#39;s area derivation system\nTwo proofs of the polyhedral volume formula\nThree Liu Hui\\\\&amp;#39;s volume derivation system\nSection 6 Liu Hui\\\\&amp;#39;s Limitation Thought in the History of Mathematics\nThe Infinite Segmentation of Liu Hui\\\\&amp;#39;s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece\nChapter Twelve Liu Hui\\\\&amp;#39;s Logic Thought and Mathematical Theory System\nThe first section Liu Hui\\\\&amp;#39;s resignation and reason, class, and therefore\nOne reason\nCategory II\nThree\nSection 2 Definition\nSection III Analogy and Induction\nAn analogy\nInductive reasoning\nSection IV Deductive Reasoning of Liu Hui\nSyllogism and Relational Reasoning\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning\nThird, the prototype of mathematical induction\nSection 5 Mathematical Proof\nA comprehensive approach\nB. Analysis and synthesis\nIII Rebuttal and Liu Hui\\\\&amp;#39;s mistakes\nSection VI Liu Hui\\\\&amp;#39;s Mathematical Theory System\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nSection 1 The Creative Transformation of the Sui and Tang Calendars\nThe discovery of a letter and its significance\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties\nSection II Secondary interpolation algorithm\nOne \\\\&amp;quot;The Imperial Calendar\\\\&amp;quot;\nLiu Liu\\\\&amp;#39;s Quadratic Interpolation Algorithm and Its Algorithmic Analysis\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar\nFour-phase subtractive multiplication\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nLiu Xi\\\\&amp;#39;s \\\\&amp;quot;Emperor\\\\&amp;quot; calendar algorithm\nII Li Yingfeng\\\\&amp;#39;s \\\\&amp;quot;Lin Lun Li\\\\&amp;quot; image algorithm\nThree-Line \\\\&amp;quot;Dai Yan Li\\\\&amp;quot; Nine Shadows Algorithm\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang\\\\&amp;#39;s \\\\&amp;quot;Chong Xuan Li\\\\&amp;quot;\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties\nSection 1 Mathematical Communication between China and North Korea\nSection 2 Mathematics Exchange between China and Japan\nA Chinese calendar was introduced into Japan\nII Introduction of Early Learning Education System\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties\nSection 3 Mathematical Communication between China and India\nAn Indian mathematics introduced to China\nII The Influence of Chinese Mathematics on India\n\nPart IV The Climax of Chinese Traditional Mathematics\n&amp;mdash;&amp;mdash;Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty\nII Thoughtful easing is a necessary condition for the development of mathematics\nIII Social needs are a powerful force for the development of mathematics\nFourth Song and Yuan rulers attach importance to mathematics\nFive Characteristics of Mathematics in the Song and Yuan Dynasties\nThe second section of the book \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nA Biography of the Date and Content of the \\\\&amp;quot;Xiahou Yang Scripture\\\\&amp;quot;\nTwo versions of the \\\\&amp;quot;Xiahou Yang Calculator\\\\&amp;quot;\nThe third quarter Jia Xianhe\\\\&amp;#39;s \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters, The Scriptures\\\\&amp;quot;\nJia Xian and his teacher Chu Yan\nTwo Most Existential Examinations of \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters Calculating Caojing\\\\&amp;quot;\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor\\\\&amp;#39;s Nine Chapters.\nSection IV Liu Yihe\\\\&amp;#39;s \\\\&amp;quot;Proposal on Ancient Roots\\\\&amp;quot;\nYi Liu Yi\nSecond, \\\\&amp;quot;A discussion of Gu Gen Yuan\\\\&amp;quot;\nSection Five Qin Jiulu and \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nThe life of Qin Jiuhao\nSecond Qin Jiuyao character identification\nThree \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nSection 6 Li Yehe\\\\&amp;#39;s \\\\&amp;quot;Measurement of Circular Oceanscope\\\\&amp;quot; and \\\\&amp;quot;Yigu Performance\\\\&amp;quot;\nYi Ye\nThe two holes Jiurong and \\\\&amp;quot;Test round sea mirror\\\\&amp;quot;\nThree \\\\&amp;quot;Yi Gu Ji\\\\&amp;quot; and \\\\&amp;quot;Yi Gu Performance\\\\&amp;quot;\nSection 7 Yang Hui and \\\\&amp;quot;Detailed Explanation of Chapter 9 Algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui Algorithm\\\\&amp;quot;\nYihui Yang\nSecond, \\\\&amp;quot;Detailed Nine Chapter Algorithms\\\\&amp;quot;\nThree \\\\&amp;quot;daily algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui algorithm\\\\&amp;quot;\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book\nOne Zhu Shijie\nTwo \\\\&amp;quot;Education Enlightenment\\\\&amp;quot;\nThree \\\\&amp;quot;Siyuan Yujian\\\\&amp;quot;\nSection 9 Other Mathematicians and Mathematical Works\nA Li Jihe\\\\&amp;#39;s \\\\&amp;quot;Nine Chapters of Arithmetic and Meaning\\\\&amp;quot; and \\\\&amp;quot;Zhou Ji\\\\&amp;#39;s Calculation of Sound and Meaning\\\\&amp;quot;\nTwo \\\\&amp;quot;Xiecha Microcalculus\\\\&amp;quot;\nThree Shen Kuohe\\\\&amp;#39;s Mathematical Achievements in \\\\&amp;quot;Meng Xi Bi Tan\\\\&amp;quot;\nFour Wang Xi, Guo Shoujing, and \\\\&amp;quot;Time History\\\\&amp;quot;\nFive Zhao Youqin and \\\\&amp;quot;New Elephant\\\\&amp;quot;\nSix Shakes and The River Defense Theory &amp;bull; Algorithm Gate\nSeven Other Mathematicians and Mathematical Works\nChapter 16 Improvements in Computing Technology and Invention of Abacus\nSection 1 \u25cb and Decimal Decimals\nOne and digital\nTwo decimal places\nSection II Improvements in Computing Technology\nOne for the law, one for the addition, subtraction, multiplication and division\nII Heading Multiplication and Nine Return and Elimination\nSection 3 The birth of abacus\nAbacus produces many\nThe second abacus was born in the Song Dynasty at the latest\nChapter 17 Going to Share Volume and Cutting Circles\nSection 1 Check Stock Volume\nOne\nTwo round city schema\nThree identification notes\nSection 2 Cutting\nA Shen Kuo&amp;rsquo;s Tactics\nTwo Sagittal Cuts in the Time of Time\nThree Zhao Youqin\\\\&amp;#39;s cutting\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple\nSection 1 Numerical Solution of High Order Equations\nAn upright release method\nSecond Jia Xian Triangle\nThree increase open method\nFour Benefits and Reductions\nFive positive and negative open\nSection II Tianyuan surgery\nOne-day history of metaphysics\nThe perfection and application of the two-day meta-technique\nThe third quarter of four\nThe historical development of a quadruple surgery\nTwo-quaternary elimination\nThree binary\nFour triples\nFive four yuan surgery\nChapter 19 Hoarding, tricks\nSection 1 Hoarding\nSlot technique\nII Hoarding\nSection II tricks surgery\nA trick of &amp;ldquo;Time-giving Calendar&amp;rdquo;\nTwo tricks of \\\\&amp;quot;Syuanyuanjian\\\\&amp;quot;\nChapter Twenty The total number of Da Yan and vertical and horizontal map\nThe first quarter total number of surgery\nThe origin of a major total\nTotal number of major\nSection II.\nA river map, Luo book and vertical and horizontal map\nSecond, Yang Hui, etc.\nThree Ding Yidong\\\\&amp;#39;s map\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties\nSection 2 Chinese Mathematical Biography\nThe Impact of Chinese Mathematics on Islamic Countries\nII The Influence of Chinese Mathematics on North Korea and Japan\nSection III Introduction of Mathematics in Islamic Countries\nThe introduction of a mathematical work\nII Arabic Digital and Crosswords\nThree soil disc algorithm and lattice operator\n\nPart V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus\n- Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty\nSection 1 The Social Background of Mathematics in the Ming Dynasty\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty\nA \\\\&amp;quot;Yongle Grand Ceremony &amp;bull; Calculation\\\\&amp;quot; and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty\nThe loss of the second ancient book\nLoss of three mathematics results\nSection III The Mainstream of Mathematics in the Ming Dynasty\nA survey of mathematics books in the Ming Dynasty\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period\nOne\nTwo Ding Ju and his Ding Ju algorithm\nThree Jiaheng\\\\&amp;#39;s \\\\&amp;quot;Algorithm Set\\\\&amp;quot;\nFour \\\\&amp;quot;Detailed Algorithm\\\\&amp;quot;\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty\nYan Gong and his \\\\&amp;quot;Tongyuan algorithm\\\\&amp;quot;\nLiu Shilong and his \\\\&amp;quot;Nine Chapters Tuning Algorithm\\\\&amp;quot;\nThree Xia Yuanze\\\\&amp;#39;s \\\\&amp;quot;specified algorithm\\\\&amp;quot;\nFour other calculations\nSection 3 Mathematical and Mathematical Writings\nWu Jing and his \\\\&amp;quot;Nine Chapter Algorithms\\\\&amp;quot;\nII Wang Wensu and his \\\\&amp;quot;Educational Poems\\\\&amp;quot;\nThree other books\nSection IV: The Theory of Theoretical Mathematics\nTang Shunzhi and his \\\\&amp;quot;Number Theory\\\\&amp;quot; six\nII Gu Yingxiang and his four books on mathematics\nThree Weeks of Learning and Its \\\\&amp;quot;Ecco\\\\&amp;quot;\nIV Zhu Zaiyu and his &amp;ldquo;New Theory of Calculation&amp;rdquo; and &amp;ldquo;Ji-Suan Su Jing Jing&amp;rdquo;\nSection V Abacus Mathematicians and Mathematical Works\nA previous work on abacus\nTwo-way Big Place and Its \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot; and \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot;\nThree other abacus work\nChapter 24 Songs of Mathematics and Popularization of Abacus\nSection 1 Practicality and Songs of Mathematics\nA practical, popular and commercialized mathematics\nThe second song of mathematics\nMathematical Songs Since the End of the Three Yuan\nSection 2 Various \\\\&amp;quot;miscellaneous methods\\\\&amp;quot; in mathematics of the Ming Dynasty\nSection 3 Development and Popularization of Abacus\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties\nThe reflection of abacus in the second mathematic book\nThe disappearance of the popularity and calculation of the three abacus\nChapter 25 Some Mathematics Work in the Ming Dynasty\nSection 1 Numerical Solution of Squares and Equations\nOne-Mid-Year Growth and Opening Method\" addthis:url=\"https:\/\/www.amazon.com\/Mathematics-History-Science-Technology-CHUN\/dp\/7030290534?SubscriptionId=AKIAJCI3DJTKR6N4LR2A&amp;&amp;linkCode=xm2&amp;camp=2025&amp;creative=165953&amp;creativeASIN=7030290534\" class=\"addthis_button_twitter\"><\/a><\/div><div class=\"addthis_sharing_toolbox addthis_default_style\" style=\"cursor:pointer\"><a style=\"cursor:pointer;\" href=\"\" addthis:title=\"The Science and Technology in China: Mathematics Volume \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u53f2\u00b7\u6570\u5b66\u5377\" addthis:description=\"\u76ee\u5f55\n\u603b\u5e8f \u5362\u5609\u9521i\n\u524d\u8a00iii\n\n\u7b2c\u4e00\u7f16 \u4e2d\u56fd\u6570\u5b66\u4ece\u5174\u8d77\u5230\u5f62\u6210\u4e00\u95e8\u5b66\u79d1\n&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u5230\u897f\u5468\u65f6\u671f\u7684\u6570\u5b66\n\u7b2c\u4e00\u7ae0 \u4e2d\u56fd\u6570\u5b66\u7684\u5174\u8d77&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u56fe\u5f62\u89c2\u5ff5\u7684\u5f62\u6210\n\u4e00 \u56fe\u5f62\u89c2\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u4ece\u65b9\u4f4d\u89c2\u5ff5\u770b\u56fe\u5f62\u89c2\u5ff5\n\u4e09 \u539f\u59cb\u7684\u4f5c\u56fe\u5de5\u5177&amp;mdash;&amp;mdash;\u89c4\u77e9\u51c6\u7ef3\n\u7b2c\u4e8c\u8282 \u6570\u6982\u5ff5\u7684\u5f62\u6210\u4e0e\u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u4e00 \u6570\u6982\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u7b2c\u4e09\u8282 \u4f20\u8bf4\u4e2d\u7684\u6570\u5b66\u4eba\u7269\n\u4e00 \u4f0f\u7fb2\n\u4e8c \u9ec4\u5e1d\u548c\u96b6\u9996\n\u4e09 \u5c27\u3001\u821c\u3001\u79b9\u548c\u5015\n\u7b2c\u56db\u8282 \u4ece\u539f\u59cb\u793e\u4f1a\u665a\u671f\u7684\u793e\u4f1a\u7ed3\u6784\u770b\u5f53\u65f6\u6570\u5b66\u7684\u53d1\u5c55\n\u7b2c\u4e8c\u7ae0 \u6570\u5b66\u5f62\u6210\u4e00\u95e8\u5b66\u79d1&amp;mdash;&amp;mdash;\u590f\u3001\u5546\u3001\u897f\u5468\u4e09\u4ee3\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\u7684\u5f62\u6210\n\u4e00 \u7532\u9aa8\u6587\u548c\u91d1\u6587\u4e2d\u7684\u6570\u5b57\n\u4e8c \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\n\u7b2c\u4e8c\u8282 \u6570\u5b66\u6210\u4e3a\u4e00\u95e8\u5b66\u79d1\n\u4e00 \u793e\u4f1a\u7ba1\u7406\u548c\u5de5\u4f5c\u7684\u9700\u8981\u4e0e\u6570\u5b66\u7684\u53d1\u5c55\n\u4e8c \u6570\u5b66\u8fdb\u5165\u6559\u5b66\u79d1\u76ee\n\u4e09 \u5546\u9ad8\u53ca\u5176\u6240\u638c\u63e1\u7684\u6570\u5b66\u77e5\u8bc6\n\n\u7b2c\u4e8c\u7f16 \u4e2d\u56fd\u4f20\u7edf\u6570\u5b66\u6846\u67b6\u7684\u786e\u7acb\n&amp;mdash;&amp;mdash;\u6625\u79cb\u81f3\u4e1c\u6c49\u4e2d\u671f\u7684\u6570\u5b66\n\u7b2c\u4e09\u7ae0 \u6625\u79cb\u81f3\u6c49\u4ee3\u6570\u5b66\u6982\u8bba\n\u7b2c\u4e00\u8282 \u6625\u79cb\u6218\u56fd\u79e6\u6c49\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e00 \u6625\u79cb\u6218\u56fd\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e8c \u79e6\u6c49\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u7b2c\u4e8c\u8282 \u7b97\u6cd5\u5f0f\u6570\u5b66\u5728\u6625\u79cb\u6218\u56fd\u65f6\u671f\u8fbe\u5230\u9ad8\u5cf0\n\u4e00 \u6574\u6570\u56db\u5219\u8fd0\u7b97\u5728\u6625\u79cb\u65f6\u671f\u7684\u666e\u53ca\n\u4e8c \u5206\u6570\u3001\u6bd4\u548c\u6bd4\u4f8b\u7684\u5e7f\u6cdb\u4f7f\u7528\n\u4e09 \u4ece\u5148\u79e6\u6587\u732e\u770b\u6625\u79cb\u6218\u56fd\u65f6\u4ee3\u7684\u7b97\u6cd5\u5316\u6570\u5b66&amp;mdash;&amp;mdash;&amp;ldquo;\u4e5d\u6570&amp;rdquo;\n\u56db \u5148\u79e6\u65f6\u671f\u7684\u5176\u4ed6\u6570\u5b66\u77e5\u8bc6\n\u7b2c\u4e09\u8282 \u7406\u8bba\u601d\u8fa8\u503e\u5411&amp;mdash;&amp;mdash;\u6625\u79cb\u6218\u56fd\u6570\u5b66\u7684\u65b0\u52a8\u5411\n\u4e00 \u58a8\u5bb6\u4e0e\u6570\u5b66\n\u4e8c \u540d\u5bb6\u7684\u6570\u5b66\u601d\u60f3\n\u4e09 \u5148\u79e6\u9053\u5bb6\u7b49\u5b66\u6d3e\u7684\u65e0\u9650\u601d\u60f3\n\u56db 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\u5218\u5f5d\u7a0b\u7684\u579b\u79ef\u672f\u7814\u7a76\n\u7b2c\u56db\u8282 \u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e00 \u590f\u9e3e\u7fd4\u5bf9\u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e8c \u534e\u8605\u82b3\u7684\u6570\u6839\u5f00\u65b9\u672f\u4e0e\u79ef\u8f83\u5f00\u65b9\u672f\n\u7b2c\u4e94\u8282 \u5bf9\u5706\u9525\u66f2\u7ebf\u548c\u5fae\u79ef\u5206\u7684\u7814\u7a76\n\u4e00 \u5706\u9525\u66f2\u7ebf\u4f5c\u56fe\n\u4e8c \u4e8c\u6b21\u66f2\u7ebf\u6c42\u79ef\u95ee\u9898\n\u4e09 \u5e73\u5706\u5bb9\u5207\u4e0e\u7d2f\u5706\n\u7b2c\u4e09\u5341\u4e09\u7ae0 \u6e05\u672b\u6570\u5b66\u6559\u80b2\n\u7b2c\u4e00\u8282 \u6e05\u672b\u6570\u5b66\u6559\u80b2\u6982\u8ff0\n\u4e00 \u6570\u5b66\u6559\u80b2\u7684\u53d8\u9769\n\u4e8c \u6e05\u672b\u7684\u6570\u5b66\u6559\u80b2\u89c2\u5ff5\n\u4e09 \u6e05\u672b\u7684\u7559\u5b66\u6d3b\u52a8\u4e0e\u6570\u5b66\u7559\u5b66\u751f\n\u7b2c\u4e8c\u8282 \u665a\u6e05\u6570\u5b66\u6559\u80b2\n\u4e00 \u6d0b\u52a1\u5b66\u5802\u7684\u6570\u5b66\u6559\u80b2\n\u4e8c \u4e66\u9662\u7684\u53d8\u9769\u4e0e\u6570\u5b66\u6559\u80b2\n\u4e09 \u6559\u4f1a\u5b66\u6821\u7684\u6570\u5b66\u6559\u79d1\u4e66\n\u56db \u7678\u536f\u5b66\u5236\u7684\u6570\u5b66\u8bfe\u7a0b\n\u7b2c\u4e09\u8282 \u6570\u5b66\u4e1b\u4e66\u3001\u6570\u5b66\u793e\u56e2\u4e0e\u520a\u7269\n\u4e00 \u6570\u5b66\u4e1b\u4e66\u7684\u7f16\u7e82\n\u4e8c \u6570\u5b66\u793e\u56e2\n\u4e09 \u6570\u5b66\u520a\u7269\n\n\u4e3b\u8981\u53c2\u8003\u6587\u732e\n\u540e\u8bb0\n\u603b\u8dcb\n\ntable of Contents\nGeneral Preface Lu Jiaxi\nForeword iii\n\nThe first series of Chinese mathematics forms a subject\n- Mathematics from the primitive society to the Western Zhou Dynasty\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society\nSection 1 The Formation of Graphic Concepts\nThe emergence of a graphic concept\nSecond, from the concept of orientation to see the concept of graphics\nThree original drawing tools - rules and regulations\nSection II The Formation of Number Concepts and Original Counting Methods\nThe emergence of a number concept\nTwo original counting methods\nSection 3 The legendary mathematical figure\nOne\nSecond Yellow Emperor and Lishou\nThree \u5c27, \u821c, \u79b9 and \u5015\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society\nChapter 2 Mathematics Forms a Discipline&amp;mdash;&amp;mdash;Mathematics of the Three Generations of Xia, Shang, and Xi Zhou\nSection 1 Formation of Decimal Value Notation\nA number in Oracle and Jinwen\nTwo decimal value notation\nSection 2 Mathematics Becomes a Discipline\nThe need for social management and work and the development of mathematics\nSecond Mathematics enters teaching subjects\nIII Shang Gao and its mastered mathematics knowledge\n\nPart Two Establishment of Traditional Chinese Mathematical Framework\n- Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background\nThe Second Qin and Han Mathematics and Social and Cultural Background\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period\nAn integer number of four operations in the Spring and Autumn Period\nSecond, the extensive use of scores, ratios and proportions\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era&amp;mdash;&amp;mdash;&amp;ldquo;Nine Numbers&amp;rdquo;\nIV Other Mathematics Knowledge in Pre-Qin Period\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period\nA Mohist and Mathematics\nTwo homes of mathematics\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips\nA Qin Jian \\\\&amp;quot;Numbers\\\\&amp;quot;\nII. The style, expression and characteristics of the \\\\&amp;quot;numeric book\\\\&amp;quot;\nThree compilation of \\\\&amp;quot;calculus book\\\\&amp;quot;\nThe content of the \\\\&amp;quot;numerical book\\\\&amp;quot; and its position in the history of Chinese mathematics\nSection V. The Zhouyi Classics and Chen Zi\nOne Zhouyi Calculation\nTwo Chen Zi\nSection VI: \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot; and Zhang Cang, Yan Shouchang\nThe content of \\\\&amp;quot;Chapter 9 Arithmetic\\\\&amp;quot;\nII. The Style and Compilation of Nine Chapters of Arithmetic\nThree \\\\&amp;quot;arithmetic book\\\\&amp;quot; and \\\\&amp;quot;Nine chapters of arithmetic\\\\&amp;quot;\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World\nFive Versions of Nine Chapters of Arithmetic\nSix Zhang Canghe Yu Shouchang\nSection 7 Other Mathematicians and Mathematical Works\nA dealer and \\\\&amp;quot;Business Arithmetic\\\\&amp;quot; and \\\\&amp;quot;Du Zhong Arithmetic\\\\&amp;quot;\nSecond Yin Xianhe Liu Hao\nThree Zhang Heng and Ma continued\nChapter IV Insufficient scores, rates, and profits\nSection 1 Scores and Its Four Principles\nA score and its representation\nTwo fractional four algorithm\nSection II Surgery and Decline Surgery\nNow there is surgery\nSecond decline\nThree transmission techniques\nSection III Insufficiency\nInsufficiency\nThe Application of Insufficiency Technique in General Mathematical Problems\nChapter V Area, Volume, Pythagoreanism, and Observation\nSection 1 Area\nA linear area\nSecond curved area\nThree round and square\nFour curved surface area\nSection 2 Volume\na polyhedral volume\nTwo round body volume\nSection III Pythagorean Theorem and Unfolding Tacks\nAn Pythagorean Theorem\nThe second solution hook shape\nThree Pythagorean arrays\nThe fourth quarter\nA tick share\nTwo ticks\nSection V\nOne time\nThe bud of the second difference\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences\nThe first section of the prescription\nOpen square\nTwo open cubes\nSection II Equations and Positive and Negative Techniques\nOne equation and equation\nSecond profit and loss\nThree positive and negative surgery\nSection III Series\n\nPart III Completion of Chinese Traditional Mathematical Theory System\n- Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory\nII Society and Mathematics in the Southern and Northern Dynasties\nThe Society and Mathematics in the Middle of Tang Dynasty\nSection Two: Xu Yue\\\\&amp;#39;s \\\\&amp;quot;Surgical Relics\\\\&amp;quot; and Zhao Shuang\\\\&amp;#39;s \\\\&amp;quot;Zhou Shuo\\\\&amp;#39;s Recounts\\\\&amp;quot;\nLiu Hong, Xu Yue, and The Record of the Numbers\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera\nAn Liu Hui\nTwo \\\\&amp;quot;Nine chapters of arithmetic note\\\\&amp;quot;\nThree \\\\&amp;quot;The Island\\\\&amp;quot;\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties\nA Study on \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot;\nSecond \\\\&amp;quot;Sun Tzu Classic\\\\&amp;quot;\nThree \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nFour \\\\&amp;quot;Zhang Qiu Jian Su Jing\\\\&amp;quot;\nV. Zu Chongzhi, Zu Yu\\\\&amp;#39;s and \\\\&amp;quot;Fuzheng\\\\&amp;quot;\nSix books and their mathematical works\nSeven other mathematicians\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty\nLiu Yi\nII Wang Xiaotong and \\\\&amp;quot;Ancient Gujing\\\\&amp;quot;\nThe three Li Yufeng and other finishing ten calculations\nFour Lines and \\\\&amp;quot;Da Yan Li\\\\&amp;quot;\nFive Sides\nSection 6 Sui Tang School of Mathematics and Accounting\nA math school\nSecond Accounting Division\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools\nA large number of methods\nTwo Attempts to Improve Calculation Tools\nChapter VIII Principles of rate and principle\nSection 1 Definition and Nature of Rates\nThe definition of probability\nThe Method and Nature of Bivariate\nSection II Today\\\\&amp;#39;s Promotion and Principles of Surgery\nThe current promotion of surgery\nTwo principles\nThe third section of the arithmetic and the least common multiple\nAn arithmetic problem\nII Solving Mathematical Problems Directly\nApplication of the three greatest common divisors and the least common multiple\nChapter Nine Pythagoreans, Observations, and Errors\nSection 1 Demonstration of Formulas for Explaining Pyramids\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui\nII Zhao Shuang and Liu Hui\\\\&amp;#39;s Proof of the Formulas of the Solution\nThree Liu Hui\\\\&amp;#39;s Proof of the Pythagorean Array Formula\nIV Wang Xiaotong\\\\&amp;#39;s Expansion of the Hexagonal Shape Problem\nSection 2 Proof of Formulas and Formulas\nOne with the proof of the principle of entry and completion\nB. Proof of the Principle of Keeping Preference with Pythagoreanism\nSection III Correction\nOne difference in skill\nTwo Drawings Six Body and Mathematics\nSection IV Other Observation Problems\nAn Observation Problem in Zhang Qi Jian Jian Su Jing\nII. The Problem of Expectation in the \\\\&amp;quot;Several Notes to the Book\\\\&amp;quot;\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations\nSection 1 Geometric Explanation and Improvement of Alchemy\nA Liu Hui\\\\&amp;#39;s Geometry Explanation of the Alchemy\nII Liu Hui and Wang Xiaotong\\\\&amp;#39;s Creation of Opening Methods\nThe improvement of the three prescriptions\nIV Liu Hui\\\\&amp;#39;s \\\\&amp;quot;seeking micro-number\\\\&amp;quot; and the approximate value of the root\nV. Zu Chongzhi\\\\&amp;#39;s opening power and opening difference\nThe root formula of six lines\nSection II Progress of Equations\nLiu Hui\\\\&amp;#39;s equation theory\nTwo mutual multiplication and denomination\nThree equations new surgery\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing\nSection III Indefinite issues\nA total of five wells\nTwo things do not know the problem\nThree hundred chicken\nSection 4 Arithmetic series and geometric series\nAn arithmetic progression\nTwo equal number arrays\nChapter 11 Infinitely small segmentation and limit thinking\nSection 1 Cutting\nSection II Principle of Liu Hui\nSection III Principles and volume of the ancestral hall\nAn ancestral principle\nTwo square cover and ball volume\nSection IV The Application of Limit Ideas in Approximate Calculation\na pi ratio\nSecond round rate and square rate\nArc field density\nSection V Liu Hui\\\\&amp;#39;s area and volume derivation system\nLiu Hui\\\\&amp;#39;s area derivation system\nTwo proofs of the polyhedral volume formula\nThree Liu Hui\\\\&amp;#39;s volume derivation system\nSection 6 Liu Hui\\\\&amp;#39;s Limitation Thought in the History of Mathematics\nThe Infinite Segmentation of Liu Hui\\\\&amp;#39;s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece\nChapter Twelve Liu Hui\\\\&amp;#39;s Logic Thought and Mathematical Theory System\nThe first section Liu Hui\\\\&amp;#39;s resignation and reason, class, and therefore\nOne reason\nCategory II\nThree\nSection 2 Definition\nSection III Analogy and Induction\nAn analogy\nInductive reasoning\nSection IV Deductive Reasoning of Liu Hui\nSyllogism and Relational Reasoning\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning\nThird, the prototype of mathematical induction\nSection 5 Mathematical Proof\nA comprehensive approach\nB. Analysis and synthesis\nIII Rebuttal and Liu Hui\\\\&amp;#39;s mistakes\nSection VI Liu Hui\\\\&amp;#39;s Mathematical Theory System\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nSection 1 The Creative Transformation of the Sui and Tang Calendars\nThe discovery of a letter and its significance\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties\nSection II Secondary interpolation algorithm\nOne \\\\&amp;quot;The Imperial Calendar\\\\&amp;quot;\nLiu Liu\\\\&amp;#39;s Quadratic Interpolation Algorithm and Its Algorithmic Analysis\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar\nFour-phase subtractive multiplication\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nLiu Xi\\\\&amp;#39;s \\\\&amp;quot;Emperor\\\\&amp;quot; calendar algorithm\nII Li Yingfeng\\\\&amp;#39;s \\\\&amp;quot;Lin Lun Li\\\\&amp;quot; image algorithm\nThree-Line \\\\&amp;quot;Dai Yan Li\\\\&amp;quot; Nine Shadows Algorithm\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang\\\\&amp;#39;s \\\\&amp;quot;Chong Xuan Li\\\\&amp;quot;\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties\nSection 1 Mathematical Communication between China and North Korea\nSection 2 Mathematics Exchange between China and Japan\nA Chinese calendar was introduced into Japan\nII Introduction of Early Learning Education System\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties\nSection 3 Mathematical Communication between China and India\nAn Indian mathematics introduced to China\nII The Influence of Chinese Mathematics on India\n\nPart IV The Climax of Chinese Traditional Mathematics\n&amp;mdash;&amp;mdash;Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty\nII Thoughtful easing is a necessary condition for the development of mathematics\nIII Social needs are a powerful force for the development of mathematics\nFourth Song and Yuan rulers attach importance to mathematics\nFive Characteristics of Mathematics in the Song and Yuan Dynasties\nThe second section of the book \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nA Biography of the Date and Content of the \\\\&amp;quot;Xiahou Yang Scripture\\\\&amp;quot;\nTwo versions of the \\\\&amp;quot;Xiahou Yang Calculator\\\\&amp;quot;\nThe third quarter Jia Xianhe\\\\&amp;#39;s \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters, The Scriptures\\\\&amp;quot;\nJia Xian and his teacher Chu Yan\nTwo Most Existential Examinations of \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters Calculating Caojing\\\\&amp;quot;\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor\\\\&amp;#39;s Nine Chapters.\nSection IV Liu Yihe\\\\&amp;#39;s \\\\&amp;quot;Proposal on Ancient Roots\\\\&amp;quot;\nYi Liu Yi\nSecond, \\\\&amp;quot;A discussion of Gu Gen Yuan\\\\&amp;quot;\nSection Five Qin Jiulu and \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nThe life of Qin Jiuhao\nSecond Qin Jiuyao character identification\nThree \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nSection 6 Li Yehe\\\\&amp;#39;s \\\\&amp;quot;Measurement of Circular Oceanscope\\\\&amp;quot; and \\\\&amp;quot;Yigu Performance\\\\&amp;quot;\nYi Ye\nThe two holes Jiurong and \\\\&amp;quot;Test round sea mirror\\\\&amp;quot;\nThree \\\\&amp;quot;Yi Gu Ji\\\\&amp;quot; and \\\\&amp;quot;Yi Gu Performance\\\\&amp;quot;\nSection 7 Yang Hui and \\\\&amp;quot;Detailed Explanation of Chapter 9 Algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui Algorithm\\\\&amp;quot;\nYihui Yang\nSecond, \\\\&amp;quot;Detailed Nine Chapter Algorithms\\\\&amp;quot;\nThree \\\\&amp;quot;daily algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui algorithm\\\\&amp;quot;\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book\nOne Zhu Shijie\nTwo \\\\&amp;quot;Education Enlightenment\\\\&amp;quot;\nThree \\\\&amp;quot;Siyuan Yujian\\\\&amp;quot;\nSection 9 Other Mathematicians and Mathematical Works\nA Li Jihe\\\\&amp;#39;s \\\\&amp;quot;Nine Chapters of Arithmetic and Meaning\\\\&amp;quot; and \\\\&amp;quot;Zhou Ji\\\\&amp;#39;s Calculation of Sound and Meaning\\\\&amp;quot;\nTwo \\\\&amp;quot;Xiecha Microcalculus\\\\&amp;quot;\nThree Shen Kuohe\\\\&amp;#39;s Mathematical Achievements in \\\\&amp;quot;Meng Xi Bi Tan\\\\&amp;quot;\nFour Wang Xi, Guo Shoujing, and \\\\&amp;quot;Time History\\\\&amp;quot;\nFive Zhao Youqin and \\\\&amp;quot;New Elephant\\\\&amp;quot;\nSix Shakes and The River Defense Theory &amp;bull; Algorithm Gate\nSeven Other Mathematicians and Mathematical Works\nChapter 16 Improvements in Computing Technology and Invention of Abacus\nSection 1 \u25cb and Decimal Decimals\nOne and digital\nTwo decimal places\nSection II Improvements in Computing Technology\nOne for the law, one for the addition, subtraction, multiplication and division\nII Heading Multiplication and Nine Return and Elimination\nSection 3 The birth of abacus\nAbacus produces many\nThe second abacus was born in the Song Dynasty at the latest\nChapter 17 Going to Share Volume and Cutting Circles\nSection 1 Check Stock Volume\nOne\nTwo round city schema\nThree identification notes\nSection 2 Cutting\nA Shen Kuo&amp;rsquo;s Tactics\nTwo Sagittal Cuts in the Time of Time\nThree Zhao Youqin\\\\&amp;#39;s cutting\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple\nSection 1 Numerical Solution of High Order Equations\nAn upright release method\nSecond Jia Xian Triangle\nThree increase open method\nFour Benefits and Reductions\nFive positive and negative open\nSection II Tianyuan surgery\nOne-day history of metaphysics\nThe perfection and application of the two-day meta-technique\nThe third quarter of four\nThe historical development of a quadruple surgery\nTwo-quaternary elimination\nThree binary\nFour triples\nFive four yuan surgery\nChapter 19 Hoarding, tricks\nSection 1 Hoarding\nSlot technique\nII Hoarding\nSection II tricks surgery\nA trick of &amp;ldquo;Time-giving Calendar&amp;rdquo;\nTwo tricks of \\\\&amp;quot;Syuanyuanjian\\\\&amp;quot;\nChapter Twenty The total number of Da Yan and vertical and horizontal map\nThe first quarter total number of surgery\nThe origin of a major total\nTotal number of major\nSection II.\nA river map, Luo book and vertical and horizontal map\nSecond, Yang Hui, etc.\nThree Ding Yidong\\\\&amp;#39;s map\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties\nSection 2 Chinese Mathematical Biography\nThe Impact of Chinese Mathematics on Islamic Countries\nII The Influence of Chinese Mathematics on North Korea and Japan\nSection III Introduction of Mathematics in Islamic Countries\nThe introduction of a mathematical work\nII Arabic Digital and Crosswords\nThree soil disc algorithm and lattice operator\n\nPart V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus\n- Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty\nSection 1 The Social Background of Mathematics in the Ming Dynasty\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty\nA \\\\&amp;quot;Yongle Grand Ceremony &amp;bull; Calculation\\\\&amp;quot; and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty\nThe loss of the second ancient book\nLoss of three mathematics results\nSection III The Mainstream of Mathematics in the Ming Dynasty\nA survey of mathematics books in the Ming Dynasty\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period\nOne\nTwo Ding Ju and his Ding Ju algorithm\nThree Jiaheng\\\\&amp;#39;s \\\\&amp;quot;Algorithm Set\\\\&amp;quot;\nFour \\\\&amp;quot;Detailed Algorithm\\\\&amp;quot;\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty\nYan Gong and his \\\\&amp;quot;Tongyuan algorithm\\\\&amp;quot;\nLiu Shilong and his \\\\&amp;quot;Nine Chapters Tuning Algorithm\\\\&amp;quot;\nThree Xia Yuanze\\\\&amp;#39;s \\\\&amp;quot;specified algorithm\\\\&amp;quot;\nFour other calculations\nSection 3 Mathematical and Mathematical Writings\nWu Jing and his \\\\&amp;quot;Nine Chapter Algorithms\\\\&amp;quot;\nII Wang Wensu and his \\\\&amp;quot;Educational Poems\\\\&amp;quot;\nThree other books\nSection IV: The Theory of Theoretical Mathematics\nTang Shunzhi and his \\\\&amp;quot;Number Theory\\\\&amp;quot; six\nII Gu Yingxiang and his four books on mathematics\nThree Weeks of Learning and Its \\\\&amp;quot;Ecco\\\\&amp;quot;\nIV Zhu Zaiyu and his &amp;ldquo;New Theory of Calculation&amp;rdquo; and &amp;ldquo;Ji-Suan Su Jing Jing&amp;rdquo;\nSection V Abacus Mathematicians and Mathematical Works\nA previous work on abacus\nTwo-way Big Place and Its \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot; and \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot;\nThree other abacus work\nChapter 24 Songs of Mathematics and Popularization of Abacus\nSection 1 Practicality and Songs of Mathematics\nA practical, popular and commercialized mathematics\nThe second song of mathematics\nMathematical Songs Since the End of the Three Yuan\nSection 2 Various \\\\&amp;quot;miscellaneous methods\\\\&amp;quot; in mathematics of the Ming Dynasty\nSection 3 Development and Popularization of Abacus\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties\nThe reflection of abacus in the second mathematic book\nThe disappearance of the popularity and calculation of the three abacus\nChapter 25 Some Mathematics Work in the Ming Dynasty\nSection 1 Numerical Solution of Squares and Equations\nOne-Mid-Year Growth and Opening Method\" addthis:url=\"https:\/\/www.amazon.com\/Mathematics-History-Science-Technology-CHUN\/dp\/7030290534?SubscriptionId=AKIAJCI3DJTKR6N4LR2A&amp;&amp;linkCode=xm2&amp;camp=2025&amp;creative=165953&amp;creativeASIN=7030290534\" class=\"addthis_button_google_plusone_share\"><\/a><\/div><div class=\"addthis_sharing_toolbox addthis_default_style\" style=\"cursor:pointer\"><a style=\"cursor:pointer;\" href=\"\" addthis:title=\"The Science and Technology in China: Mathematics Volume \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u53f2\u00b7\u6570\u5b66\u5377\" addthis:description=\"\u76ee\u5f55\n\u603b\u5e8f \u5362\u5609\u9521i\n\u524d\u8a00iii\n\n\u7b2c\u4e00\u7f16 \u4e2d\u56fd\u6570\u5b66\u4ece\u5174\u8d77\u5230\u5f62\u6210\u4e00\u95e8\u5b66\u79d1\n&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u5230\u897f\u5468\u65f6\u671f\u7684\u6570\u5b66\n\u7b2c\u4e00\u7ae0 \u4e2d\u56fd\u6570\u5b66\u7684\u5174\u8d77&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u56fe\u5f62\u89c2\u5ff5\u7684\u5f62\u6210\n\u4e00 \u56fe\u5f62\u89c2\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u4ece\u65b9\u4f4d\u89c2\u5ff5\u770b\u56fe\u5f62\u89c2\u5ff5\n\u4e09 \u539f\u59cb\u7684\u4f5c\u56fe\u5de5\u5177&amp;mdash;&amp;mdash;\u89c4\u77e9\u51c6\u7ef3\n\u7b2c\u4e8c\u8282 \u6570\u6982\u5ff5\u7684\u5f62\u6210\u4e0e\u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u4e00 \u6570\u6982\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u7b2c\u4e09\u8282 \u4f20\u8bf4\u4e2d\u7684\u6570\u5b66\u4eba\u7269\n\u4e00 \u4f0f\u7fb2\n\u4e8c \u9ec4\u5e1d\u548c\u96b6\u9996\n\u4e09 \u5c27\u3001\u821c\u3001\u79b9\u548c\u5015\n\u7b2c\u56db\u8282 \u4ece\u539f\u59cb\u793e\u4f1a\u665a\u671f\u7684\u793e\u4f1a\u7ed3\u6784\u770b\u5f53\u65f6\u6570\u5b66\u7684\u53d1\u5c55\n\u7b2c\u4e8c\u7ae0 \u6570\u5b66\u5f62\u6210\u4e00\u95e8\u5b66\u79d1&amp;mdash;&amp;mdash;\u590f\u3001\u5546\u3001\u897f\u5468\u4e09\u4ee3\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\u7684\u5f62\u6210\n\u4e00 \u7532\u9aa8\u6587\u548c\u91d1\u6587\u4e2d\u7684\u6570\u5b57\n\u4e8c \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\n\u7b2c\u4e8c\u8282 \u6570\u5b66\u6210\u4e3a\u4e00\u95e8\u5b66\u79d1\n\u4e00 \u793e\u4f1a\u7ba1\u7406\u548c\u5de5\u4f5c\u7684\u9700\u8981\u4e0e\u6570\u5b66\u7684\u53d1\u5c55\n\u4e8c \u6570\u5b66\u8fdb\u5165\u6559\u5b66\u79d1\u76ee\n\u4e09 \u5546\u9ad8\u53ca\u5176\u6240\u638c\u63e1\u7684\u6570\u5b66\u77e5\u8bc6\n\n\u7b2c\u4e8c\u7f16 \u4e2d\u56fd\u4f20\u7edf\u6570\u5b66\u6846\u67b6\u7684\u786e\u7acb\n&amp;mdash;&amp;mdash;\u6625\u79cb\u81f3\u4e1c\u6c49\u4e2d\u671f\u7684\u6570\u5b66\n\u7b2c\u4e09\u7ae0 \u6625\u79cb\u81f3\u6c49\u4ee3\u6570\u5b66\u6982\u8bba\n\u7b2c\u4e00\u8282 \u6625\u79cb\u6218\u56fd\u79e6\u6c49\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e00 \u6625\u79cb\u6218\u56fd\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e8c \u79e6\u6c49\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u7b2c\u4e8c\u8282 \u7b97\u6cd5\u5f0f\u6570\u5b66\u5728\u6625\u79cb\u6218\u56fd\u65f6\u671f\u8fbe\u5230\u9ad8\u5cf0\n\u4e00 \u6574\u6570\u56db\u5219\u8fd0\u7b97\u5728\u6625\u79cb\u65f6\u671f\u7684\u666e\u53ca\n\u4e8c \u5206\u6570\u3001\u6bd4\u548c\u6bd4\u4f8b\u7684\u5e7f\u6cdb\u4f7f\u7528\n\u4e09 \u4ece\u5148\u79e6\u6587\u732e\u770b\u6625\u79cb\u6218\u56fd\u65f6\u4ee3\u7684\u7b97\u6cd5\u5316\u6570\u5b66&amp;mdash;&amp;mdash;&amp;ldquo;\u4e5d\u6570&amp;rdquo;\n\u56db \u5148\u79e6\u65f6\u671f\u7684\u5176\u4ed6\u6570\u5b66\u77e5\u8bc6\n\u7b2c\u4e09\u8282 \u7406\u8bba\u601d\u8fa8\u503e\u5411&amp;mdash;&amp;mdash;\u6625\u79cb\u6218\u56fd\u6570\u5b66\u7684\u65b0\u52a8\u5411\n\u4e00 \u58a8\u5bb6\u4e0e\u6570\u5b66\n\u4e8c \u540d\u5bb6\u7684\u6570\u5b66\u601d\u60f3\n\u4e09 \u5148\u79e6\u9053\u5bb6\u7b49\u5b66\u6d3e\u7684\u65e0\u9650\u601d\u60f3\n\u56db 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\u5218\u5f5d\u7a0b\u7684\u579b\u79ef\u672f\u7814\u7a76\n\u7b2c\u56db\u8282 \u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e00 \u590f\u9e3e\u7fd4\u5bf9\u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e8c \u534e\u8605\u82b3\u7684\u6570\u6839\u5f00\u65b9\u672f\u4e0e\u79ef\u8f83\u5f00\u65b9\u672f\n\u7b2c\u4e94\u8282 \u5bf9\u5706\u9525\u66f2\u7ebf\u548c\u5fae\u79ef\u5206\u7684\u7814\u7a76\n\u4e00 \u5706\u9525\u66f2\u7ebf\u4f5c\u56fe\n\u4e8c \u4e8c\u6b21\u66f2\u7ebf\u6c42\u79ef\u95ee\u9898\n\u4e09 \u5e73\u5706\u5bb9\u5207\u4e0e\u7d2f\u5706\n\u7b2c\u4e09\u5341\u4e09\u7ae0 \u6e05\u672b\u6570\u5b66\u6559\u80b2\n\u7b2c\u4e00\u8282 \u6e05\u672b\u6570\u5b66\u6559\u80b2\u6982\u8ff0\n\u4e00 \u6570\u5b66\u6559\u80b2\u7684\u53d8\u9769\n\u4e8c \u6e05\u672b\u7684\u6570\u5b66\u6559\u80b2\u89c2\u5ff5\n\u4e09 \u6e05\u672b\u7684\u7559\u5b66\u6d3b\u52a8\u4e0e\u6570\u5b66\u7559\u5b66\u751f\n\u7b2c\u4e8c\u8282 \u665a\u6e05\u6570\u5b66\u6559\u80b2\n\u4e00 \u6d0b\u52a1\u5b66\u5802\u7684\u6570\u5b66\u6559\u80b2\n\u4e8c \u4e66\u9662\u7684\u53d8\u9769\u4e0e\u6570\u5b66\u6559\u80b2\n\u4e09 \u6559\u4f1a\u5b66\u6821\u7684\u6570\u5b66\u6559\u79d1\u4e66\n\u56db \u7678\u536f\u5b66\u5236\u7684\u6570\u5b66\u8bfe\u7a0b\n\u7b2c\u4e09\u8282 \u6570\u5b66\u4e1b\u4e66\u3001\u6570\u5b66\u793e\u56e2\u4e0e\u520a\u7269\n\u4e00 \u6570\u5b66\u4e1b\u4e66\u7684\u7f16\u7e82\n\u4e8c \u6570\u5b66\u793e\u56e2\n\u4e09 \u6570\u5b66\u520a\u7269\n\n\u4e3b\u8981\u53c2\u8003\u6587\u732e\n\u540e\u8bb0\n\u603b\u8dcb\n\ntable of Contents\nGeneral Preface Lu Jiaxi\nForeword iii\n\nThe first series of Chinese mathematics forms a subject\n- Mathematics from the primitive society to the Western Zhou Dynasty\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society\nSection 1 The Formation of Graphic Concepts\nThe emergence of a graphic concept\nSecond, from the concept of orientation to see the concept of graphics\nThree original drawing tools - rules and regulations\nSection II The Formation of Number Concepts and Original Counting Methods\nThe emergence of a number concept\nTwo original counting methods\nSection 3 The legendary mathematical figure\nOne\nSecond Yellow Emperor and Lishou\nThree \u5c27, \u821c, \u79b9 and \u5015\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society\nChapter 2 Mathematics Forms a Discipline&amp;mdash;&amp;mdash;Mathematics of the Three Generations of Xia, Shang, and Xi Zhou\nSection 1 Formation of Decimal Value Notation\nA number in Oracle and Jinwen\nTwo decimal value notation\nSection 2 Mathematics Becomes a Discipline\nThe need for social management and work and the development of mathematics\nSecond Mathematics enters teaching subjects\nIII Shang Gao and its mastered mathematics knowledge\n\nPart Two Establishment of Traditional Chinese Mathematical Framework\n- Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background\nThe Second Qin and Han Mathematics and Social and Cultural Background\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period\nAn integer number of four operations in the Spring and Autumn Period\nSecond, the extensive use of scores, ratios and proportions\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era&amp;mdash;&amp;mdash;&amp;ldquo;Nine Numbers&amp;rdquo;\nIV Other Mathematics Knowledge in Pre-Qin Period\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period\nA Mohist and Mathematics\nTwo homes of mathematics\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips\nA Qin Jian \\\\&amp;quot;Numbers\\\\&amp;quot;\nII. The style, expression and characteristics of the \\\\&amp;quot;numeric book\\\\&amp;quot;\nThree compilation of \\\\&amp;quot;calculus book\\\\&amp;quot;\nThe content of the \\\\&amp;quot;numerical book\\\\&amp;quot; and its position in the history of Chinese mathematics\nSection V. The Zhouyi Classics and Chen Zi\nOne Zhouyi Calculation\nTwo Chen Zi\nSection VI: \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot; and Zhang Cang, Yan Shouchang\nThe content of \\\\&amp;quot;Chapter 9 Arithmetic\\\\&amp;quot;\nII. The Style and Compilation of Nine Chapters of Arithmetic\nThree \\\\&amp;quot;arithmetic book\\\\&amp;quot; and \\\\&amp;quot;Nine chapters of arithmetic\\\\&amp;quot;\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World\nFive Versions of Nine Chapters of Arithmetic\nSix Zhang Canghe Yu Shouchang\nSection 7 Other Mathematicians and Mathematical Works\nA dealer and \\\\&amp;quot;Business Arithmetic\\\\&amp;quot; and \\\\&amp;quot;Du Zhong Arithmetic\\\\&amp;quot;\nSecond Yin Xianhe Liu Hao\nThree Zhang Heng and Ma continued\nChapter IV Insufficient scores, rates, and profits\nSection 1 Scores and Its Four Principles\nA score and its representation\nTwo fractional four algorithm\nSection II Surgery and Decline Surgery\nNow there is surgery\nSecond decline\nThree transmission techniques\nSection III Insufficiency\nInsufficiency\nThe Application of Insufficiency Technique in General Mathematical Problems\nChapter V Area, Volume, Pythagoreanism, and Observation\nSection 1 Area\nA linear area\nSecond curved area\nThree round and square\nFour curved surface area\nSection 2 Volume\na polyhedral volume\nTwo round body volume\nSection III Pythagorean Theorem and Unfolding Tacks\nAn Pythagorean Theorem\nThe second solution hook shape\nThree Pythagorean arrays\nThe fourth quarter\nA tick share\nTwo ticks\nSection V\nOne time\nThe bud of the second difference\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences\nThe first section of the prescription\nOpen square\nTwo open cubes\nSection II Equations and Positive and Negative Techniques\nOne equation and equation\nSecond profit and loss\nThree positive and negative surgery\nSection III Series\n\nPart III Completion of Chinese Traditional Mathematical Theory System\n- Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory\nII Society and Mathematics in the Southern and Northern Dynasties\nThe Society and Mathematics in the Middle of Tang Dynasty\nSection Two: Xu Yue\\\\&amp;#39;s \\\\&amp;quot;Surgical Relics\\\\&amp;quot; and Zhao Shuang\\\\&amp;#39;s \\\\&amp;quot;Zhou Shuo\\\\&amp;#39;s Recounts\\\\&amp;quot;\nLiu Hong, Xu Yue, and The Record of the Numbers\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera\nAn Liu Hui\nTwo \\\\&amp;quot;Nine chapters of arithmetic note\\\\&amp;quot;\nThree \\\\&amp;quot;The Island\\\\&amp;quot;\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties\nA Study on \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot;\nSecond \\\\&amp;quot;Sun Tzu Classic\\\\&amp;quot;\nThree \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nFour \\\\&amp;quot;Zhang Qiu Jian Su Jing\\\\&amp;quot;\nV. Zu Chongzhi, Zu Yu\\\\&amp;#39;s and \\\\&amp;quot;Fuzheng\\\\&amp;quot;\nSix books and their mathematical works\nSeven other mathematicians\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty\nLiu Yi\nII Wang Xiaotong and \\\\&amp;quot;Ancient Gujing\\\\&amp;quot;\nThe three Li Yufeng and other finishing ten calculations\nFour Lines and \\\\&amp;quot;Da Yan Li\\\\&amp;quot;\nFive Sides\nSection 6 Sui Tang School of Mathematics and Accounting\nA math school\nSecond Accounting Division\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools\nA large number of methods\nTwo Attempts to Improve Calculation Tools\nChapter VIII Principles of rate and principle\nSection 1 Definition and Nature of Rates\nThe definition of probability\nThe Method and Nature of Bivariate\nSection II Today\\\\&amp;#39;s Promotion and Principles of Surgery\nThe current promotion of surgery\nTwo principles\nThe third section of the arithmetic and the least common multiple\nAn arithmetic problem\nII Solving Mathematical Problems Directly\nApplication of the three greatest common divisors and the least common multiple\nChapter Nine Pythagoreans, Observations, and Errors\nSection 1 Demonstration of Formulas for Explaining Pyramids\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui\nII Zhao Shuang and Liu Hui\\\\&amp;#39;s Proof of the Formulas of the Solution\nThree Liu Hui\\\\&amp;#39;s Proof of the Pythagorean Array Formula\nIV Wang Xiaotong\\\\&amp;#39;s Expansion of the Hexagonal Shape Problem\nSection 2 Proof of Formulas and Formulas\nOne with the proof of the principle of entry and completion\nB. Proof of the Principle of Keeping Preference with Pythagoreanism\nSection III Correction\nOne difference in skill\nTwo Drawings Six Body and Mathematics\nSection IV Other Observation Problems\nAn Observation Problem in Zhang Qi Jian Jian Su Jing\nII. The Problem of Expectation in the \\\\&amp;quot;Several Notes to the Book\\\\&amp;quot;\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations\nSection 1 Geometric Explanation and Improvement of Alchemy\nA Liu Hui\\\\&amp;#39;s Geometry Explanation of the Alchemy\nII Liu Hui and Wang Xiaotong\\\\&amp;#39;s Creation of Opening Methods\nThe improvement of the three prescriptions\nIV Liu Hui\\\\&amp;#39;s \\\\&amp;quot;seeking micro-number\\\\&amp;quot; and the approximate value of the root\nV. Zu Chongzhi\\\\&amp;#39;s opening power and opening difference\nThe root formula of six lines\nSection II Progress of Equations\nLiu Hui\\\\&amp;#39;s equation theory\nTwo mutual multiplication and denomination\nThree equations new surgery\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing\nSection III Indefinite issues\nA total of five wells\nTwo things do not know the problem\nThree hundred chicken\nSection 4 Arithmetic series and geometric series\nAn arithmetic progression\nTwo equal number arrays\nChapter 11 Infinitely small segmentation and limit thinking\nSection 1 Cutting\nSection II Principle of Liu Hui\nSection III Principles and volume of the ancestral hall\nAn ancestral principle\nTwo square cover and ball volume\nSection IV The Application of Limit Ideas in Approximate Calculation\na pi ratio\nSecond round rate and square rate\nArc field density\nSection V Liu Hui\\\\&amp;#39;s area and volume derivation system\nLiu Hui\\\\&amp;#39;s area derivation system\nTwo proofs of the polyhedral volume formula\nThree Liu Hui\\\\&amp;#39;s volume derivation system\nSection 6 Liu Hui\\\\&amp;#39;s Limitation Thought in the History of Mathematics\nThe Infinite Segmentation of Liu Hui\\\\&amp;#39;s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece\nChapter Twelve Liu Hui\\\\&amp;#39;s Logic Thought and Mathematical Theory System\nThe first section Liu Hui\\\\&amp;#39;s resignation and reason, class, and therefore\nOne reason\nCategory II\nThree\nSection 2 Definition\nSection III Analogy and Induction\nAn analogy\nInductive reasoning\nSection IV Deductive Reasoning of Liu Hui\nSyllogism and Relational Reasoning\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning\nThird, the prototype of mathematical induction\nSection 5 Mathematical Proof\nA comprehensive approach\nB. Analysis and synthesis\nIII Rebuttal and Liu Hui\\\\&amp;#39;s mistakes\nSection VI Liu Hui\\\\&amp;#39;s Mathematical Theory System\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nSection 1 The Creative Transformation of the Sui and Tang Calendars\nThe discovery of a letter and its significance\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties\nSection II Secondary interpolation algorithm\nOne \\\\&amp;quot;The Imperial Calendar\\\\&amp;quot;\nLiu Liu\\\\&amp;#39;s Quadratic Interpolation Algorithm and Its Algorithmic Analysis\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar\nFour-phase subtractive multiplication\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nLiu Xi\\\\&amp;#39;s \\\\&amp;quot;Emperor\\\\&amp;quot; calendar algorithm\nII Li Yingfeng\\\\&amp;#39;s \\\\&amp;quot;Lin Lun Li\\\\&amp;quot; image algorithm\nThree-Line \\\\&amp;quot;Dai Yan Li\\\\&amp;quot; Nine Shadows Algorithm\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang\\\\&amp;#39;s \\\\&amp;quot;Chong Xuan Li\\\\&amp;quot;\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties\nSection 1 Mathematical Communication between China and North Korea\nSection 2 Mathematics Exchange between China and Japan\nA Chinese calendar was introduced into Japan\nII Introduction of Early Learning Education System\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties\nSection 3 Mathematical Communication between China and India\nAn Indian mathematics introduced to China\nII The Influence of Chinese Mathematics on India\n\nPart IV The Climax of Chinese Traditional Mathematics\n&amp;mdash;&amp;mdash;Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty\nII Thoughtful easing is a necessary condition for the development of mathematics\nIII Social needs are a powerful force for the development of mathematics\nFourth Song and Yuan rulers attach importance to mathematics\nFive Characteristics of Mathematics in the Song and Yuan Dynasties\nThe second section of the book \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nA Biography of the Date and Content of the \\\\&amp;quot;Xiahou Yang Scripture\\\\&amp;quot;\nTwo versions of the \\\\&amp;quot;Xiahou Yang Calculator\\\\&amp;quot;\nThe third quarter Jia Xianhe\\\\&amp;#39;s \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters, The Scriptures\\\\&amp;quot;\nJia Xian and his teacher Chu Yan\nTwo Most Existential Examinations of \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters Calculating Caojing\\\\&amp;quot;\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor\\\\&amp;#39;s Nine Chapters.\nSection IV Liu Yihe\\\\&amp;#39;s \\\\&amp;quot;Proposal on Ancient Roots\\\\&amp;quot;\nYi Liu Yi\nSecond, \\\\&amp;quot;A discussion of Gu Gen Yuan\\\\&amp;quot;\nSection Five Qin Jiulu and \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nThe life of Qin Jiuhao\nSecond Qin Jiuyao character identification\nThree \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nSection 6 Li Yehe\\\\&amp;#39;s \\\\&amp;quot;Measurement of Circular Oceanscope\\\\&amp;quot; and \\\\&amp;quot;Yigu Performance\\\\&amp;quot;\nYi Ye\nThe two holes Jiurong and \\\\&amp;quot;Test round sea mirror\\\\&amp;quot;\nThree \\\\&amp;quot;Yi Gu Ji\\\\&amp;quot; and \\\\&amp;quot;Yi Gu Performance\\\\&amp;quot;\nSection 7 Yang Hui and \\\\&amp;quot;Detailed Explanation of Chapter 9 Algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui Algorithm\\\\&amp;quot;\nYihui Yang\nSecond, \\\\&amp;quot;Detailed Nine Chapter Algorithms\\\\&amp;quot;\nThree \\\\&amp;quot;daily algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui algorithm\\\\&amp;quot;\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book\nOne Zhu Shijie\nTwo \\\\&amp;quot;Education Enlightenment\\\\&amp;quot;\nThree \\\\&amp;quot;Siyuan Yujian\\\\&amp;quot;\nSection 9 Other Mathematicians and Mathematical Works\nA Li Jihe\\\\&amp;#39;s \\\\&amp;quot;Nine Chapters of Arithmetic and Meaning\\\\&amp;quot; and \\\\&amp;quot;Zhou Ji\\\\&amp;#39;s Calculation of Sound and Meaning\\\\&amp;quot;\nTwo \\\\&amp;quot;Xiecha Microcalculus\\\\&amp;quot;\nThree Shen Kuohe\\\\&amp;#39;s Mathematical Achievements in \\\\&amp;quot;Meng Xi Bi Tan\\\\&amp;quot;\nFour Wang Xi, Guo Shoujing, and \\\\&amp;quot;Time History\\\\&amp;quot;\nFive Zhao Youqin and \\\\&amp;quot;New Elephant\\\\&amp;quot;\nSix Shakes and The River Defense Theory &amp;bull; Algorithm Gate\nSeven Other Mathematicians and Mathematical Works\nChapter 16 Improvements in Computing Technology and Invention of Abacus\nSection 1 \u25cb and Decimal Decimals\nOne and digital\nTwo decimal places\nSection II Improvements in Computing Technology\nOne for the law, one for the addition, subtraction, multiplication and division\nII Heading Multiplication and Nine Return and Elimination\nSection 3 The birth of abacus\nAbacus produces many\nThe second abacus was born in the Song Dynasty at the latest\nChapter 17 Going to Share Volume and Cutting Circles\nSection 1 Check Stock Volume\nOne\nTwo round city schema\nThree identification notes\nSection 2 Cutting\nA Shen Kuo&amp;rsquo;s Tactics\nTwo Sagittal Cuts in the Time of Time\nThree Zhao Youqin\\\\&amp;#39;s cutting\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple\nSection 1 Numerical Solution of High Order Equations\nAn upright release method\nSecond Jia Xian Triangle\nThree increase open method\nFour Benefits and Reductions\nFive positive and negative open\nSection II Tianyuan surgery\nOne-day history of metaphysics\nThe perfection and application of the two-day meta-technique\nThe third quarter of four\nThe historical development of a quadruple surgery\nTwo-quaternary elimination\nThree binary\nFour triples\nFive four yuan surgery\nChapter 19 Hoarding, tricks\nSection 1 Hoarding\nSlot technique\nII Hoarding\nSection II tricks surgery\nA trick of &amp;ldquo;Time-giving Calendar&amp;rdquo;\nTwo tricks of \\\\&amp;quot;Syuanyuanjian\\\\&amp;quot;\nChapter Twenty The total number of Da Yan and vertical and horizontal map\nThe first quarter total number of surgery\nThe origin of a major total\nTotal number of major\nSection II.\nA river map, Luo book and vertical and horizontal map\nSecond, Yang Hui, etc.\nThree Ding Yidong\\\\&amp;#39;s map\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties\nSection 2 Chinese Mathematical Biography\nThe Impact of Chinese Mathematics on Islamic Countries\nII The Influence of Chinese Mathematics on North Korea and Japan\nSection III Introduction of Mathematics in Islamic Countries\nThe introduction of a mathematical work\nII Arabic Digital and Crosswords\nThree soil disc algorithm and lattice operator\n\nPart V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus\n- Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty\nSection 1 The Social Background of Mathematics in the Ming Dynasty\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty\nA \\\\&amp;quot;Yongle Grand Ceremony &amp;bull; Calculation\\\\&amp;quot; and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty\nThe loss of the second ancient book\nLoss of three mathematics results\nSection III The Mainstream of Mathematics in the Ming Dynasty\nA survey of mathematics books in the Ming Dynasty\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period\nOne\nTwo Ding Ju and his Ding Ju algorithm\nThree Jiaheng\\\\&amp;#39;s \\\\&amp;quot;Algorithm Set\\\\&amp;quot;\nFour \\\\&amp;quot;Detailed Algorithm\\\\&amp;quot;\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty\nYan Gong and his \\\\&amp;quot;Tongyuan algorithm\\\\&amp;quot;\nLiu Shilong and his \\\\&amp;quot;Nine Chapters Tuning Algorithm\\\\&amp;quot;\nThree Xia Yuanze\\\\&amp;#39;s \\\\&amp;quot;specified algorithm\\\\&amp;quot;\nFour other calculations\nSection 3 Mathematical and Mathematical Writings\nWu Jing and his \\\\&amp;quot;Nine Chapter Algorithms\\\\&amp;quot;\nII Wang Wensu and his \\\\&amp;quot;Educational Poems\\\\&amp;quot;\nThree other books\nSection IV: The Theory of Theoretical Mathematics\nTang Shunzhi and his \\\\&amp;quot;Number Theory\\\\&amp;quot; six\nII Gu Yingxiang and his four books on mathematics\nThree Weeks of Learning and Its \\\\&amp;quot;Ecco\\\\&amp;quot;\nIV Zhu Zaiyu and his &amp;ldquo;New Theory of Calculation&amp;rdquo; and &amp;ldquo;Ji-Suan Su Jing Jing&amp;rdquo;\nSection V Abacus Mathematicians and Mathematical Works\nA previous work on abacus\nTwo-way Big Place and Its \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot; and \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot;\nThree other abacus work\nChapter 24 Songs of Mathematics and Popularization of Abacus\nSection 1 Practicality and Songs of Mathematics\nA practical, popular and commercialized mathematics\nThe second song of mathematics\nMathematical Songs Since the End of the Three Yuan\nSection 2 Various \\\\&amp;quot;miscellaneous methods\\\\&amp;quot; in mathematics of the Ming Dynasty\nSection 3 Development and Popularization of Abacus\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties\nThe reflection of abacus in the second mathematic book\nThe disappearance of the popularity and calculation of the three abacus\nChapter 25 Some Mathematics Work in the Ming Dynasty\nSection 1 Numerical Solution of Squares and Equations\nOne-Mid-Year Growth and Opening Method\" addthis:url=\"https:\/\/www.amazon.com\/Mathematics-History-Science-Technology-CHUN\/dp\/7030290534?SubscriptionId=AKIAJCI3DJTKR6N4LR2A&amp;&amp;linkCode=xm2&amp;camp=2025&amp;creative=165953&amp;creativeASIN=7030290534\" class=\"addthis_button_messenger\"><\/a><\/div><div class=\"addthis_sharing_toolbox addthis_default_style\" style=\"cursor:pointer\"><a style=\"cursor:pointer;\" href=\"\" addthis:title=\"The Science and Technology in China: Mathematics Volume \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u53f2\u00b7\u6570\u5b66\u5377\" addthis:description=\"\u76ee\u5f55\n\u603b\u5e8f \u5362\u5609\u9521i\n\u524d\u8a00iii\n\n\u7b2c\u4e00\u7f16 \u4e2d\u56fd\u6570\u5b66\u4ece\u5174\u8d77\u5230\u5f62\u6210\u4e00\u95e8\u5b66\u79d1\n&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u5230\u897f\u5468\u65f6\u671f\u7684\u6570\u5b66\n\u7b2c\u4e00\u7ae0 \u4e2d\u56fd\u6570\u5b66\u7684\u5174\u8d77&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u56fe\u5f62\u89c2\u5ff5\u7684\u5f62\u6210\n\u4e00 \u56fe\u5f62\u89c2\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u4ece\u65b9\u4f4d\u89c2\u5ff5\u770b\u56fe\u5f62\u89c2\u5ff5\n\u4e09 \u539f\u59cb\u7684\u4f5c\u56fe\u5de5\u5177&amp;mdash;&amp;mdash;\u89c4\u77e9\u51c6\u7ef3\n\u7b2c\u4e8c\u8282 \u6570\u6982\u5ff5\u7684\u5f62\u6210\u4e0e\u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u4e00 \u6570\u6982\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u7b2c\u4e09\u8282 \u4f20\u8bf4\u4e2d\u7684\u6570\u5b66\u4eba\u7269\n\u4e00 \u4f0f\u7fb2\n\u4e8c \u9ec4\u5e1d\u548c\u96b6\u9996\n\u4e09 \u5c27\u3001\u821c\u3001\u79b9\u548c\u5015\n\u7b2c\u56db\u8282 \u4ece\u539f\u59cb\u793e\u4f1a\u665a\u671f\u7684\u793e\u4f1a\u7ed3\u6784\u770b\u5f53\u65f6\u6570\u5b66\u7684\u53d1\u5c55\n\u7b2c\u4e8c\u7ae0 \u6570\u5b66\u5f62\u6210\u4e00\u95e8\u5b66\u79d1&amp;mdash;&amp;mdash;\u590f\u3001\u5546\u3001\u897f\u5468\u4e09\u4ee3\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\u7684\u5f62\u6210\n\u4e00 \u7532\u9aa8\u6587\u548c\u91d1\u6587\u4e2d\u7684\u6570\u5b57\n\u4e8c \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\n\u7b2c\u4e8c\u8282 \u6570\u5b66\u6210\u4e3a\u4e00\u95e8\u5b66\u79d1\n\u4e00 \u793e\u4f1a\u7ba1\u7406\u548c\u5de5\u4f5c\u7684\u9700\u8981\u4e0e\u6570\u5b66\u7684\u53d1\u5c55\n\u4e8c \u6570\u5b66\u8fdb\u5165\u6559\u5b66\u79d1\u76ee\n\u4e09 \u5546\u9ad8\u53ca\u5176\u6240\u638c\u63e1\u7684\u6570\u5b66\u77e5\u8bc6\n\n\u7b2c\u4e8c\u7f16 \u4e2d\u56fd\u4f20\u7edf\u6570\u5b66\u6846\u67b6\u7684\u786e\u7acb\n&amp;mdash;&amp;mdash;\u6625\u79cb\u81f3\u4e1c\u6c49\u4e2d\u671f\u7684\u6570\u5b66\n\u7b2c\u4e09\u7ae0 \u6625\u79cb\u81f3\u6c49\u4ee3\u6570\u5b66\u6982\u8bba\n\u7b2c\u4e00\u8282 \u6625\u79cb\u6218\u56fd\u79e6\u6c49\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e00 \u6625\u79cb\u6218\u56fd\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e8c 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\u5218\u5f5d\u7a0b\u7684\u579b\u79ef\u672f\u7814\u7a76\n\u7b2c\u56db\u8282 \u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e00 \u590f\u9e3e\u7fd4\u5bf9\u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e8c \u534e\u8605\u82b3\u7684\u6570\u6839\u5f00\u65b9\u672f\u4e0e\u79ef\u8f83\u5f00\u65b9\u672f\n\u7b2c\u4e94\u8282 \u5bf9\u5706\u9525\u66f2\u7ebf\u548c\u5fae\u79ef\u5206\u7684\u7814\u7a76\n\u4e00 \u5706\u9525\u66f2\u7ebf\u4f5c\u56fe\n\u4e8c \u4e8c\u6b21\u66f2\u7ebf\u6c42\u79ef\u95ee\u9898\n\u4e09 \u5e73\u5706\u5bb9\u5207\u4e0e\u7d2f\u5706\n\u7b2c\u4e09\u5341\u4e09\u7ae0 \u6e05\u672b\u6570\u5b66\u6559\u80b2\n\u7b2c\u4e00\u8282 \u6e05\u672b\u6570\u5b66\u6559\u80b2\u6982\u8ff0\n\u4e00 \u6570\u5b66\u6559\u80b2\u7684\u53d8\u9769\n\u4e8c \u6e05\u672b\u7684\u6570\u5b66\u6559\u80b2\u89c2\u5ff5\n\u4e09 \u6e05\u672b\u7684\u7559\u5b66\u6d3b\u52a8\u4e0e\u6570\u5b66\u7559\u5b66\u751f\n\u7b2c\u4e8c\u8282 \u665a\u6e05\u6570\u5b66\u6559\u80b2\n\u4e00 \u6d0b\u52a1\u5b66\u5802\u7684\u6570\u5b66\u6559\u80b2\n\u4e8c \u4e66\u9662\u7684\u53d8\u9769\u4e0e\u6570\u5b66\u6559\u80b2\n\u4e09 \u6559\u4f1a\u5b66\u6821\u7684\u6570\u5b66\u6559\u79d1\u4e66\n\u56db \u7678\u536f\u5b66\u5236\u7684\u6570\u5b66\u8bfe\u7a0b\n\u7b2c\u4e09\u8282 \u6570\u5b66\u4e1b\u4e66\u3001\u6570\u5b66\u793e\u56e2\u4e0e\u520a\u7269\n\u4e00 \u6570\u5b66\u4e1b\u4e66\u7684\u7f16\u7e82\n\u4e8c \u6570\u5b66\u793e\u56e2\n\u4e09 \u6570\u5b66\u520a\u7269\n\n\u4e3b\u8981\u53c2\u8003\u6587\u732e\n\u540e\u8bb0\n\u603b\u8dcb\n\ntable of Contents\nGeneral Preface Lu Jiaxi\nForeword iii\n\nThe first series of Chinese mathematics forms a subject\n- Mathematics from the primitive society to the Western Zhou Dynasty\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society\nSection 1 The Formation of Graphic Concepts\nThe emergence of a graphic concept\nSecond, from the concept of orientation to see the concept of graphics\nThree original drawing tools - rules and regulations\nSection II The Formation of Number Concepts and Original Counting Methods\nThe emergence of a number concept\nTwo original counting methods\nSection 3 The legendary mathematical figure\nOne\nSecond Yellow Emperor and Lishou\nThree \u5c27, \u821c, \u79b9 and \u5015\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society\nChapter 2 Mathematics Forms a Discipline&amp;mdash;&amp;mdash;Mathematics of the Three Generations of Xia, Shang, and Xi Zhou\nSection 1 Formation of Decimal Value Notation\nA number in Oracle and Jinwen\nTwo decimal value notation\nSection 2 Mathematics Becomes a Discipline\nThe need for social management and work and the development of mathematics\nSecond Mathematics enters teaching subjects\nIII Shang Gao and its mastered mathematics knowledge\n\nPart Two Establishment of Traditional Chinese Mathematical Framework\n- Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background\nThe Second Qin and Han Mathematics and Social and Cultural Background\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period\nAn integer number of four operations in the Spring and Autumn Period\nSecond, the extensive use of scores, ratios and proportions\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era&amp;mdash;&amp;mdash;&amp;ldquo;Nine Numbers&amp;rdquo;\nIV Other Mathematics Knowledge in Pre-Qin Period\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period\nA Mohist and Mathematics\nTwo homes of mathematics\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips\nA Qin Jian \\\\&amp;quot;Numbers\\\\&amp;quot;\nII. The style, expression and characteristics of the \\\\&amp;quot;numeric book\\\\&amp;quot;\nThree compilation of \\\\&amp;quot;calculus book\\\\&amp;quot;\nThe content of the \\\\&amp;quot;numerical book\\\\&amp;quot; and its position in the history of Chinese mathematics\nSection V. The Zhouyi Classics and Chen Zi\nOne Zhouyi Calculation\nTwo Chen Zi\nSection VI: \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot; and Zhang Cang, Yan Shouchang\nThe content of \\\\&amp;quot;Chapter 9 Arithmetic\\\\&amp;quot;\nII. The Style and Compilation of Nine Chapters of Arithmetic\nThree \\\\&amp;quot;arithmetic book\\\\&amp;quot; and \\\\&amp;quot;Nine chapters of arithmetic\\\\&amp;quot;\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World\nFive Versions of Nine Chapters of Arithmetic\nSix Zhang Canghe Yu Shouchang\nSection 7 Other Mathematicians and Mathematical Works\nA dealer and \\\\&amp;quot;Business Arithmetic\\\\&amp;quot; and \\\\&amp;quot;Du Zhong Arithmetic\\\\&amp;quot;\nSecond Yin Xianhe Liu Hao\nThree Zhang Heng and Ma continued\nChapter IV Insufficient scores, rates, and profits\nSection 1 Scores and Its Four Principles\nA score and its representation\nTwo fractional four algorithm\nSection II Surgery and Decline Surgery\nNow there is surgery\nSecond decline\nThree transmission techniques\nSection III Insufficiency\nInsufficiency\nThe Application of Insufficiency Technique in General Mathematical Problems\nChapter V Area, Volume, Pythagoreanism, and Observation\nSection 1 Area\nA linear area\nSecond curved area\nThree round and square\nFour curved surface area\nSection 2 Volume\na polyhedral volume\nTwo round body volume\nSection III Pythagorean Theorem and Unfolding Tacks\nAn Pythagorean Theorem\nThe second solution hook shape\nThree Pythagorean arrays\nThe fourth quarter\nA tick share\nTwo ticks\nSection V\nOne time\nThe bud of the second difference\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences\nThe first section of the prescription\nOpen square\nTwo open cubes\nSection II Equations and Positive and Negative Techniques\nOne equation and equation\nSecond profit and loss\nThree positive and negative surgery\nSection III Series\n\nPart III Completion of Chinese Traditional Mathematical Theory System\n- Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory\nII Society and Mathematics in the Southern and Northern Dynasties\nThe Society and Mathematics in the Middle of Tang Dynasty\nSection Two: Xu Yue\\\\&amp;#39;s \\\\&amp;quot;Surgical Relics\\\\&amp;quot; and Zhao Shuang\\\\&amp;#39;s \\\\&amp;quot;Zhou Shuo\\\\&amp;#39;s Recounts\\\\&amp;quot;\nLiu Hong, Xu Yue, and The Record of the Numbers\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera\nAn Liu Hui\nTwo \\\\&amp;quot;Nine chapters of arithmetic note\\\\&amp;quot;\nThree \\\\&amp;quot;The Island\\\\&amp;quot;\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties\nA Study on \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot;\nSecond \\\\&amp;quot;Sun Tzu Classic\\\\&amp;quot;\nThree \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nFour \\\\&amp;quot;Zhang Qiu Jian Su Jing\\\\&amp;quot;\nV. Zu Chongzhi, Zu Yu\\\\&amp;#39;s and \\\\&amp;quot;Fuzheng\\\\&amp;quot;\nSix books and their mathematical works\nSeven other mathematicians\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty\nLiu Yi\nII Wang Xiaotong and \\\\&amp;quot;Ancient Gujing\\\\&amp;quot;\nThe three Li Yufeng and other finishing ten calculations\nFour Lines and \\\\&amp;quot;Da Yan Li\\\\&amp;quot;\nFive Sides\nSection 6 Sui Tang School of Mathematics and Accounting\nA math school\nSecond Accounting Division\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools\nA large number of methods\nTwo Attempts to Improve Calculation Tools\nChapter VIII Principles of rate and principle\nSection 1 Definition and Nature of Rates\nThe definition of probability\nThe Method and Nature of Bivariate\nSection II Today\\\\&amp;#39;s Promotion and Principles of Surgery\nThe current promotion of surgery\nTwo principles\nThe third section of the arithmetic and the least common multiple\nAn arithmetic problem\nII Solving Mathematical Problems Directly\nApplication of the three greatest common divisors and the least common multiple\nChapter Nine Pythagoreans, Observations, and Errors\nSection 1 Demonstration of Formulas for Explaining Pyramids\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui\nII Zhao Shuang and Liu Hui\\\\&amp;#39;s Proof of the Formulas of the Solution\nThree Liu Hui\\\\&amp;#39;s Proof of the Pythagorean Array Formula\nIV Wang Xiaotong\\\\&amp;#39;s Expansion of the Hexagonal Shape Problem\nSection 2 Proof of Formulas and Formulas\nOne with the proof of the principle of entry and completion\nB. Proof of the Principle of Keeping Preference with Pythagoreanism\nSection III Correction\nOne difference in skill\nTwo Drawings Six Body and Mathematics\nSection IV Other Observation Problems\nAn Observation Problem in Zhang Qi Jian Jian Su Jing\nII. The Problem of Expectation in the \\\\&amp;quot;Several Notes to the Book\\\\&amp;quot;\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations\nSection 1 Geometric Explanation and Improvement of Alchemy\nA Liu Hui\\\\&amp;#39;s Geometry Explanation of the Alchemy\nII Liu Hui and Wang Xiaotong\\\\&amp;#39;s Creation of Opening Methods\nThe improvement of the three prescriptions\nIV Liu Hui\\\\&amp;#39;s \\\\&amp;quot;seeking micro-number\\\\&amp;quot; and the approximate value of the root\nV. Zu Chongzhi\\\\&amp;#39;s opening power and opening difference\nThe root formula of six lines\nSection II Progress of Equations\nLiu Hui\\\\&amp;#39;s equation theory\nTwo mutual multiplication and denomination\nThree equations new surgery\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing\nSection III Indefinite issues\nA total of five wells\nTwo things do not know the problem\nThree hundred chicken\nSection 4 Arithmetic series and geometric series\nAn arithmetic progression\nTwo equal number arrays\nChapter 11 Infinitely small segmentation and limit thinking\nSection 1 Cutting\nSection II Principle of Liu Hui\nSection III Principles and volume of the ancestral hall\nAn ancestral principle\nTwo square cover and ball volume\nSection IV The Application of Limit Ideas in Approximate Calculation\na pi ratio\nSecond round rate and square rate\nArc field density\nSection V Liu Hui\\\\&amp;#39;s area and volume derivation system\nLiu Hui\\\\&amp;#39;s area derivation system\nTwo proofs of the polyhedral volume formula\nThree Liu Hui\\\\&amp;#39;s volume derivation system\nSection 6 Liu Hui\\\\&amp;#39;s Limitation Thought in the History of Mathematics\nThe Infinite Segmentation of Liu Hui\\\\&amp;#39;s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece\nChapter Twelve Liu Hui\\\\&amp;#39;s Logic Thought and Mathematical Theory System\nThe first section Liu Hui\\\\&amp;#39;s resignation and reason, class, and therefore\nOne reason\nCategory II\nThree\nSection 2 Definition\nSection III Analogy and Induction\nAn analogy\nInductive reasoning\nSection IV Deductive Reasoning of Liu Hui\nSyllogism and Relational Reasoning\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning\nThird, the prototype of mathematical induction\nSection 5 Mathematical Proof\nA comprehensive approach\nB. Analysis and synthesis\nIII Rebuttal and Liu Hui\\\\&amp;#39;s mistakes\nSection VI Liu Hui\\\\&amp;#39;s Mathematical Theory System\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nSection 1 The Creative Transformation of the Sui and Tang Calendars\nThe discovery of a letter and its significance\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties\nSection II Secondary interpolation algorithm\nOne \\\\&amp;quot;The Imperial Calendar\\\\&amp;quot;\nLiu Liu\\\\&amp;#39;s Quadratic Interpolation Algorithm and Its Algorithmic Analysis\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar\nFour-phase subtractive multiplication\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nLiu Xi\\\\&amp;#39;s \\\\&amp;quot;Emperor\\\\&amp;quot; calendar algorithm\nII Li Yingfeng\\\\&amp;#39;s \\\\&amp;quot;Lin Lun Li\\\\&amp;quot; image algorithm\nThree-Line \\\\&amp;quot;Dai Yan Li\\\\&amp;quot; Nine Shadows Algorithm\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang\\\\&amp;#39;s \\\\&amp;quot;Chong Xuan Li\\\\&amp;quot;\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties\nSection 1 Mathematical Communication between China and North Korea\nSection 2 Mathematics Exchange between China and Japan\nA Chinese calendar was introduced into Japan\nII Introduction of Early Learning Education System\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties\nSection 3 Mathematical Communication between China and India\nAn Indian mathematics introduced to China\nII The Influence of Chinese Mathematics on India\n\nPart IV The Climax of Chinese Traditional Mathematics\n&amp;mdash;&amp;mdash;Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty\nII Thoughtful easing is a necessary condition for the development of mathematics\nIII Social needs are a powerful force for the development of mathematics\nFourth Song and Yuan rulers attach importance to mathematics\nFive Characteristics of Mathematics in the Song and Yuan Dynasties\nThe second section of the book \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nA Biography of the Date and Content of the \\\\&amp;quot;Xiahou Yang Scripture\\\\&amp;quot;\nTwo versions of the \\\\&amp;quot;Xiahou Yang Calculator\\\\&amp;quot;\nThe third quarter Jia Xianhe\\\\&amp;#39;s \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters, The Scriptures\\\\&amp;quot;\nJia Xian and his teacher Chu Yan\nTwo Most Existential Examinations of \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters Calculating Caojing\\\\&amp;quot;\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor\\\\&amp;#39;s Nine Chapters.\nSection IV Liu Yihe\\\\&amp;#39;s \\\\&amp;quot;Proposal on Ancient Roots\\\\&amp;quot;\nYi Liu Yi\nSecond, \\\\&amp;quot;A discussion of Gu Gen Yuan\\\\&amp;quot;\nSection Five Qin Jiulu and \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nThe life of Qin Jiuhao\nSecond Qin Jiuyao character identification\nThree \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nSection 6 Li Yehe\\\\&amp;#39;s \\\\&amp;quot;Measurement of Circular Oceanscope\\\\&amp;quot; and \\\\&amp;quot;Yigu Performance\\\\&amp;quot;\nYi Ye\nThe two holes Jiurong and \\\\&amp;quot;Test round sea mirror\\\\&amp;quot;\nThree \\\\&amp;quot;Yi Gu Ji\\\\&amp;quot; and \\\\&amp;quot;Yi Gu Performance\\\\&amp;quot;\nSection 7 Yang Hui and \\\\&amp;quot;Detailed Explanation of Chapter 9 Algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui Algorithm\\\\&amp;quot;\nYihui Yang\nSecond, \\\\&amp;quot;Detailed Nine Chapter Algorithms\\\\&amp;quot;\nThree \\\\&amp;quot;daily algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui algorithm\\\\&amp;quot;\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book\nOne Zhu Shijie\nTwo \\\\&amp;quot;Education Enlightenment\\\\&amp;quot;\nThree \\\\&amp;quot;Siyuan Yujian\\\\&amp;quot;\nSection 9 Other Mathematicians and Mathematical Works\nA Li Jihe\\\\&amp;#39;s \\\\&amp;quot;Nine Chapters of Arithmetic and Meaning\\\\&amp;quot; and \\\\&amp;quot;Zhou Ji\\\\&amp;#39;s Calculation of Sound and Meaning\\\\&amp;quot;\nTwo \\\\&amp;quot;Xiecha Microcalculus\\\\&amp;quot;\nThree Shen Kuohe\\\\&amp;#39;s Mathematical Achievements in \\\\&amp;quot;Meng Xi Bi Tan\\\\&amp;quot;\nFour Wang Xi, Guo Shoujing, and \\\\&amp;quot;Time History\\\\&amp;quot;\nFive Zhao Youqin and \\\\&amp;quot;New Elephant\\\\&amp;quot;\nSix Shakes and The River Defense Theory &amp;bull; Algorithm Gate\nSeven Other Mathematicians and Mathematical Works\nChapter 16 Improvements in Computing Technology and Invention of Abacus\nSection 1 \u25cb and Decimal Decimals\nOne and digital\nTwo decimal places\nSection II Improvements in Computing Technology\nOne for the law, one for the addition, subtraction, multiplication and division\nII Heading Multiplication and Nine Return and Elimination\nSection 3 The birth of abacus\nAbacus produces many\nThe second abacus was born in the Song Dynasty at the latest\nChapter 17 Going to Share Volume and Cutting Circles\nSection 1 Check Stock Volume\nOne\nTwo round city schema\nThree identification notes\nSection 2 Cutting\nA Shen Kuo&amp;rsquo;s Tactics\nTwo Sagittal Cuts in the Time of Time\nThree Zhao Youqin\\\\&amp;#39;s cutting\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple\nSection 1 Numerical Solution of High Order Equations\nAn upright release method\nSecond Jia Xian Triangle\nThree increase open method\nFour Benefits and Reductions\nFive positive and negative open\nSection II Tianyuan surgery\nOne-day history of metaphysics\nThe perfection and application of the two-day meta-technique\nThe third quarter of four\nThe historical development of a quadruple surgery\nTwo-quaternary elimination\nThree binary\nFour triples\nFive four yuan surgery\nChapter 19 Hoarding, tricks\nSection 1 Hoarding\nSlot technique\nII Hoarding\nSection II tricks surgery\nA trick of &amp;ldquo;Time-giving Calendar&amp;rdquo;\nTwo tricks of \\\\&amp;quot;Syuanyuanjian\\\\&amp;quot;\nChapter Twenty The total number of Da Yan and vertical and horizontal map\nThe first quarter total number of surgery\nThe origin of a major total\nTotal number of major\nSection II.\nA river map, Luo book and vertical and horizontal map\nSecond, Yang Hui, etc.\nThree Ding Yidong\\\\&amp;#39;s map\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties\nSection 2 Chinese Mathematical Biography\nThe Impact of Chinese Mathematics on Islamic Countries\nII The Influence of Chinese Mathematics on North Korea and Japan\nSection III Introduction of Mathematics in Islamic Countries\nThe introduction of a mathematical work\nII Arabic Digital and Crosswords\nThree soil disc algorithm and lattice operator\n\nPart V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus\n- Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty\nSection 1 The Social Background of Mathematics in the Ming Dynasty\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty\nA \\\\&amp;quot;Yongle Grand Ceremony &amp;bull; Calculation\\\\&amp;quot; and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty\nThe loss of the second ancient book\nLoss of three mathematics results\nSection III The Mainstream of Mathematics in the Ming Dynasty\nA survey of mathematics books in the Ming Dynasty\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period\nOne\nTwo Ding Ju and his Ding Ju algorithm\nThree Jiaheng\\\\&amp;#39;s \\\\&amp;quot;Algorithm Set\\\\&amp;quot;\nFour \\\\&amp;quot;Detailed Algorithm\\\\&amp;quot;\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty\nYan Gong and his \\\\&amp;quot;Tongyuan algorithm\\\\&amp;quot;\nLiu Shilong and his \\\\&amp;quot;Nine Chapters Tuning Algorithm\\\\&amp;quot;\nThree Xia Yuanze\\\\&amp;#39;s \\\\&amp;quot;specified algorithm\\\\&amp;quot;\nFour other calculations\nSection 3 Mathematical and Mathematical Writings\nWu Jing and his \\\\&amp;quot;Nine Chapter Algorithms\\\\&amp;quot;\nII Wang Wensu and his \\\\&amp;quot;Educational Poems\\\\&amp;quot;\nThree other books\nSection IV: The Theory of Theoretical Mathematics\nTang Shunzhi and his \\\\&amp;quot;Number Theory\\\\&amp;quot; six\nII Gu Yingxiang and his four books on mathematics\nThree Weeks of Learning and Its \\\\&amp;quot;Ecco\\\\&amp;quot;\nIV Zhu Zaiyu and his &amp;ldquo;New Theory of Calculation&amp;rdquo; and &amp;ldquo;Ji-Suan Su Jing Jing&amp;rdquo;\nSection V Abacus Mathematicians and Mathematical Works\nA previous work on abacus\nTwo-way Big Place and Its \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot; and \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot;\nThree other abacus work\nChapter 24 Songs of Mathematics and Popularization of Abacus\nSection 1 Practicality and Songs of Mathematics\nA practical, popular and commercialized mathematics\nThe second song of mathematics\nMathematical Songs Since the End of the Three Yuan\nSection 2 Various \\\\&amp;quot;miscellaneous methods\\\\&amp;quot; in mathematics of the Ming Dynasty\nSection 3 Development and Popularization of Abacus\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties\nThe reflection of abacus in the second mathematic book\nThe disappearance of the popularity and calculation of the three abacus\nChapter 25 Some Mathematics Work in the Ming Dynasty\nSection 1 Numerical Solution of Squares and Equations\nOne-Mid-Year Growth and Opening Method\" addthis:url=\"https:\/\/www.amazon.com\/Mathematics-History-Science-Technology-CHUN\/dp\/7030290534?SubscriptionId=AKIAJCI3DJTKR6N4LR2A&amp;&amp;linkCode=xm2&amp;camp=2025&amp;creative=165953&amp;creativeASIN=7030290534\" class=\"addthis_button_pinterest_share\"><\/a><\/div><div class=\"addthis_sharing_toolbox addthis_default_style\" style=\"cursor:pointer\"><a style=\"cursor:pointer;\" href=\"\" addthis:title=\"The Science and Technology in China: Mathematics Volume \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u53f2\u00b7\u6570\u5b66\u5377\" addthis:description=\"\u76ee\u5f55\n\u603b\u5e8f \u5362\u5609\u9521i\n\u524d\u8a00iii\n\n\u7b2c\u4e00\u7f16 \u4e2d\u56fd\u6570\u5b66\u4ece\u5174\u8d77\u5230\u5f62\u6210\u4e00\u95e8\u5b66\u79d1\n&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u5230\u897f\u5468\u65f6\u671f\u7684\u6570\u5b66\n\u7b2c\u4e00\u7ae0 \u4e2d\u56fd\u6570\u5b66\u7684\u5174\u8d77&amp;mdash;&amp;mdash;\u539f\u59cb\u793e\u4f1a\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u56fe\u5f62\u89c2\u5ff5\u7684\u5f62\u6210\n\u4e00 \u56fe\u5f62\u89c2\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u4ece\u65b9\u4f4d\u89c2\u5ff5\u770b\u56fe\u5f62\u89c2\u5ff5\n\u4e09 \u539f\u59cb\u7684\u4f5c\u56fe\u5de5\u5177&amp;mdash;&amp;mdash;\u89c4\u77e9\u51c6\u7ef3\n\u7b2c\u4e8c\u8282 \u6570\u6982\u5ff5\u7684\u5f62\u6210\u4e0e\u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u4e00 \u6570\u6982\u5ff5\u7684\u4ea7\u751f\n\u4e8c \u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5\n\u7b2c\u4e09\u8282 \u4f20\u8bf4\u4e2d\u7684\u6570\u5b66\u4eba\u7269\n\u4e00 \u4f0f\u7fb2\n\u4e8c \u9ec4\u5e1d\u548c\u96b6\u9996\n\u4e09 \u5c27\u3001\u821c\u3001\u79b9\u548c\u5015\n\u7b2c\u56db\u8282 \u4ece\u539f\u59cb\u793e\u4f1a\u665a\u671f\u7684\u793e\u4f1a\u7ed3\u6784\u770b\u5f53\u65f6\u6570\u5b66\u7684\u53d1\u5c55\n\u7b2c\u4e8c\u7ae0 \u6570\u5b66\u5f62\u6210\u4e00\u95e8\u5b66\u79d1&amp;mdash;&amp;mdash;\u590f\u3001\u5546\u3001\u897f\u5468\u4e09\u4ee3\u7684\u6570\u5b66\n\u7b2c\u4e00\u8282 \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\u7684\u5f62\u6210\n\u4e00 \u7532\u9aa8\u6587\u548c\u91d1\u6587\u4e2d\u7684\u6570\u5b57\n\u4e8c \u5341\u8fdb\u4f4d\u503c\u5236\u8bb0\u6570\u6cd5\n\u7b2c\u4e8c\u8282 \u6570\u5b66\u6210\u4e3a\u4e00\u95e8\u5b66\u79d1\n\u4e00 \u793e\u4f1a\u7ba1\u7406\u548c\u5de5\u4f5c\u7684\u9700\u8981\u4e0e\u6570\u5b66\u7684\u53d1\u5c55\n\u4e8c \u6570\u5b66\u8fdb\u5165\u6559\u5b66\u79d1\u76ee\n\u4e09 \u5546\u9ad8\u53ca\u5176\u6240\u638c\u63e1\u7684\u6570\u5b66\u77e5\u8bc6\n\n\u7b2c\u4e8c\u7f16 \u4e2d\u56fd\u4f20\u7edf\u6570\u5b66\u6846\u67b6\u7684\u786e\u7acb\n&amp;mdash;&amp;mdash;\u6625\u79cb\u81f3\u4e1c\u6c49\u4e2d\u671f\u7684\u6570\u5b66\n\u7b2c\u4e09\u7ae0 \u6625\u79cb\u81f3\u6c49\u4ee3\u6570\u5b66\u6982\u8bba\n\u7b2c\u4e00\u8282 \u6625\u79cb\u6218\u56fd\u79e6\u6c49\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e00 \u6625\u79cb\u6218\u56fd\u6570\u5b66\u4e0e\u793e\u4f1a\u53ca\u6587\u5316\u80cc\u666f\n\u4e8c 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\u5218\u5f5d\u7a0b\u7684\u579b\u79ef\u672f\u7814\u7a76\n\u7b2c\u56db\u8282 \u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e00 \u590f\u9e3e\u7fd4\u5bf9\u5f00\u65b9\u672f\u7684\u7814\u7a76\n\u4e8c \u534e\u8605\u82b3\u7684\u6570\u6839\u5f00\u65b9\u672f\u4e0e\u79ef\u8f83\u5f00\u65b9\u672f\n\u7b2c\u4e94\u8282 \u5bf9\u5706\u9525\u66f2\u7ebf\u548c\u5fae\u79ef\u5206\u7684\u7814\u7a76\n\u4e00 \u5706\u9525\u66f2\u7ebf\u4f5c\u56fe\n\u4e8c \u4e8c\u6b21\u66f2\u7ebf\u6c42\u79ef\u95ee\u9898\n\u4e09 \u5e73\u5706\u5bb9\u5207\u4e0e\u7d2f\u5706\n\u7b2c\u4e09\u5341\u4e09\u7ae0 \u6e05\u672b\u6570\u5b66\u6559\u80b2\n\u7b2c\u4e00\u8282 \u6e05\u672b\u6570\u5b66\u6559\u80b2\u6982\u8ff0\n\u4e00 \u6570\u5b66\u6559\u80b2\u7684\u53d8\u9769\n\u4e8c \u6e05\u672b\u7684\u6570\u5b66\u6559\u80b2\u89c2\u5ff5\n\u4e09 \u6e05\u672b\u7684\u7559\u5b66\u6d3b\u52a8\u4e0e\u6570\u5b66\u7559\u5b66\u751f\n\u7b2c\u4e8c\u8282 \u665a\u6e05\u6570\u5b66\u6559\u80b2\n\u4e00 \u6d0b\u52a1\u5b66\u5802\u7684\u6570\u5b66\u6559\u80b2\n\u4e8c \u4e66\u9662\u7684\u53d8\u9769\u4e0e\u6570\u5b66\u6559\u80b2\n\u4e09 \u6559\u4f1a\u5b66\u6821\u7684\u6570\u5b66\u6559\u79d1\u4e66\n\u56db \u7678\u536f\u5b66\u5236\u7684\u6570\u5b66\u8bfe\u7a0b\n\u7b2c\u4e09\u8282 \u6570\u5b66\u4e1b\u4e66\u3001\u6570\u5b66\u793e\u56e2\u4e0e\u520a\u7269\n\u4e00 \u6570\u5b66\u4e1b\u4e66\u7684\u7f16\u7e82\n\u4e8c \u6570\u5b66\u793e\u56e2\n\u4e09 \u6570\u5b66\u520a\u7269\n\n\u4e3b\u8981\u53c2\u8003\u6587\u732e\n\u540e\u8bb0\n\u603b\u8dcb\n\ntable of Contents\nGeneral Preface Lu Jiaxi\nForeword iii\n\nThe first series of Chinese mathematics forms a subject\n- Mathematics from the primitive society to the Western Zhou Dynasty\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society\nSection 1 The Formation of Graphic Concepts\nThe emergence of a graphic concept\nSecond, from the concept of orientation to see the concept of graphics\nThree original drawing tools - rules and regulations\nSection II The Formation of Number Concepts and Original Counting Methods\nThe emergence of a number concept\nTwo original counting methods\nSection 3 The legendary mathematical figure\nOne\nSecond Yellow Emperor and Lishou\nThree \u5c27, \u821c, \u79b9 and \u5015\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society\nChapter 2 Mathematics Forms a Discipline&amp;mdash;&amp;mdash;Mathematics of the Three Generations of Xia, Shang, and Xi Zhou\nSection 1 Formation of Decimal Value Notation\nA number in Oracle and Jinwen\nTwo decimal value notation\nSection 2 Mathematics Becomes a Discipline\nThe need for social management and work and the development of mathematics\nSecond Mathematics enters teaching subjects\nIII Shang Gao and its mastered mathematics knowledge\n\nPart Two Establishment of Traditional Chinese Mathematical Framework\n- Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background\nThe Second Qin and Han Mathematics and Social and Cultural Background\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period\nAn integer number of four operations in the Spring and Autumn Period\nSecond, the extensive use of scores, ratios and proportions\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era&amp;mdash;&amp;mdash;&amp;ldquo;Nine Numbers&amp;rdquo;\nIV Other Mathematics Knowledge in Pre-Qin Period\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period\nA Mohist and Mathematics\nTwo homes of mathematics\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips\nA Qin Jian \\\\&amp;quot;Numbers\\\\&amp;quot;\nII. The style, expression and characteristics of the \\\\&amp;quot;numeric book\\\\&amp;quot;\nThree compilation of \\\\&amp;quot;calculus book\\\\&amp;quot;\nThe content of the \\\\&amp;quot;numerical book\\\\&amp;quot; and its position in the history of Chinese mathematics\nSection V. The Zhouyi Classics and Chen Zi\nOne Zhouyi Calculation\nTwo Chen Zi\nSection VI: \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot; and Zhang Cang, Yan Shouchang\nThe content of \\\\&amp;quot;Chapter 9 Arithmetic\\\\&amp;quot;\nII. The Style and Compilation of Nine Chapters of Arithmetic\nThree \\\\&amp;quot;arithmetic book\\\\&amp;quot; and \\\\&amp;quot;Nine chapters of arithmetic\\\\&amp;quot;\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World\nFive Versions of Nine Chapters of Arithmetic\nSix Zhang Canghe Yu Shouchang\nSection 7 Other Mathematicians and Mathematical Works\nA dealer and \\\\&amp;quot;Business Arithmetic\\\\&amp;quot; and \\\\&amp;quot;Du Zhong Arithmetic\\\\&amp;quot;\nSecond Yin Xianhe Liu Hao\nThree Zhang Heng and Ma continued\nChapter IV Insufficient scores, rates, and profits\nSection 1 Scores and Its Four Principles\nA score and its representation\nTwo fractional four algorithm\nSection II Surgery and Decline Surgery\nNow there is surgery\nSecond decline\nThree transmission techniques\nSection III Insufficiency\nInsufficiency\nThe Application of Insufficiency Technique in General Mathematical Problems\nChapter V Area, Volume, Pythagoreanism, and Observation\nSection 1 Area\nA linear area\nSecond curved area\nThree round and square\nFour curved surface area\nSection 2 Volume\na polyhedral volume\nTwo round body volume\nSection III Pythagorean Theorem and Unfolding Tacks\nAn Pythagorean Theorem\nThe second solution hook shape\nThree Pythagorean arrays\nThe fourth quarter\nA tick share\nTwo ticks\nSection V\nOne time\nThe bud of the second difference\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences\nThe first section of the prescription\nOpen square\nTwo open cubes\nSection II Equations and Positive and Negative Techniques\nOne equation and equation\nSecond profit and loss\nThree positive and negative surgery\nSection III Series\n\nPart III Completion of Chinese Traditional Mathematical Theory System\n- Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory\nII Society and Mathematics in the Southern and Northern Dynasties\nThe Society and Mathematics in the Middle of Tang Dynasty\nSection Two: Xu Yue\\\\&amp;#39;s \\\\&amp;quot;Surgical Relics\\\\&amp;quot; and Zhao Shuang\\\\&amp;#39;s \\\\&amp;quot;Zhou Shuo\\\\&amp;#39;s Recounts\\\\&amp;quot;\nLiu Hong, Xu Yue, and The Record of the Numbers\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera\nAn Liu Hui\nTwo \\\\&amp;quot;Nine chapters of arithmetic note\\\\&amp;quot;\nThree \\\\&amp;quot;The Island\\\\&amp;quot;\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties\nA Study on \\\\&amp;quot;Nine Chapters of Arithmetic\\\\&amp;quot;\nSecond \\\\&amp;quot;Sun Tzu Classic\\\\&amp;quot;\nThree \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nFour \\\\&amp;quot;Zhang Qiu Jian Su Jing\\\\&amp;quot;\nV. Zu Chongzhi, Zu Yu\\\\&amp;#39;s and \\\\&amp;quot;Fuzheng\\\\&amp;quot;\nSix books and their mathematical works\nSeven other mathematicians\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty\nLiu Yi\nII Wang Xiaotong and \\\\&amp;quot;Ancient Gujing\\\\&amp;quot;\nThe three Li Yufeng and other finishing ten calculations\nFour Lines and \\\\&amp;quot;Da Yan Li\\\\&amp;quot;\nFive Sides\nSection 6 Sui Tang School of Mathematics and Accounting\nA math school\nSecond Accounting Division\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools\nA large number of methods\nTwo Attempts to Improve Calculation Tools\nChapter VIII Principles of rate and principle\nSection 1 Definition and Nature of Rates\nThe definition of probability\nThe Method and Nature of Bivariate\nSection II Today\\\\&amp;#39;s Promotion and Principles of Surgery\nThe current promotion of surgery\nTwo principles\nThe third section of the arithmetic and the least common multiple\nAn arithmetic problem\nII Solving Mathematical Problems Directly\nApplication of the three greatest common divisors and the least common multiple\nChapter Nine Pythagoreans, Observations, and Errors\nSection 1 Demonstration of Formulas for Explaining Pyramids\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui\nII Zhao Shuang and Liu Hui\\\\&amp;#39;s Proof of the Formulas of the Solution\nThree Liu Hui\\\\&amp;#39;s Proof of the Pythagorean Array Formula\nIV Wang Xiaotong\\\\&amp;#39;s Expansion of the Hexagonal Shape Problem\nSection 2 Proof of Formulas and Formulas\nOne with the proof of the principle of entry and completion\nB. Proof of the Principle of Keeping Preference with Pythagoreanism\nSection III Correction\nOne difference in skill\nTwo Drawings Six Body and Mathematics\nSection IV Other Observation Problems\nAn Observation Problem in Zhang Qi Jian Jian Su Jing\nII. The Problem of Expectation in the \\\\&amp;quot;Several Notes to the Book\\\\&amp;quot;\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations\nSection 1 Geometric Explanation and Improvement of Alchemy\nA Liu Hui\\\\&amp;#39;s Geometry Explanation of the Alchemy\nII Liu Hui and Wang Xiaotong\\\\&amp;#39;s Creation of Opening Methods\nThe improvement of the three prescriptions\nIV Liu Hui\\\\&amp;#39;s \\\\&amp;quot;seeking micro-number\\\\&amp;quot; and the approximate value of the root\nV. Zu Chongzhi\\\\&amp;#39;s opening power and opening difference\nThe root formula of six lines\nSection II Progress of Equations\nLiu Hui\\\\&amp;#39;s equation theory\nTwo mutual multiplication and denomination\nThree equations new surgery\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing\nSection III Indefinite issues\nA total of five wells\nTwo things do not know the problem\nThree hundred chicken\nSection 4 Arithmetic series and geometric series\nAn arithmetic progression\nTwo equal number arrays\nChapter 11 Infinitely small segmentation and limit thinking\nSection 1 Cutting\nSection II Principle of Liu Hui\nSection III Principles and volume of the ancestral hall\nAn ancestral principle\nTwo square cover and ball volume\nSection IV The Application of Limit Ideas in Approximate Calculation\na pi ratio\nSecond round rate and square rate\nArc field density\nSection V Liu Hui\\\\&amp;#39;s area and volume derivation system\nLiu Hui\\\\&amp;#39;s area derivation system\nTwo proofs of the polyhedral volume formula\nThree Liu Hui\\\\&amp;#39;s volume derivation system\nSection 6 Liu Hui\\\\&amp;#39;s Limitation Thought in the History of Mathematics\nThe Infinite Segmentation of Liu Hui\\\\&amp;#39;s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece\nChapter Twelve Liu Hui\\\\&amp;#39;s Logic Thought and Mathematical Theory System\nThe first section Liu Hui\\\\&amp;#39;s resignation and reason, class, and therefore\nOne reason\nCategory II\nThree\nSection 2 Definition\nSection III Analogy and Induction\nAn analogy\nInductive reasoning\nSection IV Deductive Reasoning of Liu Hui\nSyllogism and Relational Reasoning\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning\nThird, the prototype of mathematical induction\nSection 5 Mathematical Proof\nA comprehensive approach\nB. Analysis and synthesis\nIII Rebuttal and Liu Hui\\\\&amp;#39;s mistakes\nSection VI Liu Hui\\\\&amp;#39;s Mathematical Theory System\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nSection 1 The Creative Transformation of the Sui and Tang Calendars\nThe discovery of a letter and its significance\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties\nSection II Secondary interpolation algorithm\nOne \\\\&amp;quot;The Imperial Calendar\\\\&amp;quot;\nLiu Liu\\\\&amp;#39;s Quadratic Interpolation Algorithm and Its Algorithmic Analysis\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar\nFour-phase subtractive multiplication\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nLiu Xi\\\\&amp;#39;s \\\\&amp;quot;Emperor\\\\&amp;quot; calendar algorithm\nII Li Yingfeng\\\\&amp;#39;s \\\\&amp;quot;Lin Lun Li\\\\&amp;quot; image algorithm\nThree-Line \\\\&amp;quot;Dai Yan Li\\\\&amp;quot; Nine Shadows Algorithm\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang\\\\&amp;#39;s \\\\&amp;quot;Chong Xuan Li\\\\&amp;quot;\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties\nSection 1 Mathematical Communication between China and North Korea\nSection 2 Mathematics Exchange between China and Japan\nA Chinese calendar was introduced into Japan\nII Introduction of Early Learning Education System\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties\nSection 3 Mathematical Communication between China and India\nAn Indian mathematics introduced to China\nII The Influence of Chinese Mathematics on India\n\nPart IV The Climax of Chinese Traditional Mathematics\n&amp;mdash;&amp;mdash;Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty\nII Thoughtful easing is a necessary condition for the development of mathematics\nIII Social needs are a powerful force for the development of mathematics\nFourth Song and Yuan rulers attach importance to mathematics\nFive Characteristics of Mathematics in the Song and Yuan Dynasties\nThe second section of the book \\\\&amp;quot;Xiahou Yang calculations\\\\&amp;quot;\nA Biography of the Date and Content of the \\\\&amp;quot;Xiahou Yang Scripture\\\\&amp;quot;\nTwo versions of the \\\\&amp;quot;Xiahou Yang Calculator\\\\&amp;quot;\nThe third quarter Jia Xianhe\\\\&amp;#39;s \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters, The Scriptures\\\\&amp;quot;\nJia Xian and his teacher Chu Yan\nTwo Most Existential Examinations of \\\\&amp;quot;The Yellow Emperor\\\\&amp;#39;s Nine Chapters Calculating Caojing\\\\&amp;quot;\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor\\\\&amp;#39;s Nine Chapters.\nSection IV Liu Yihe\\\\&amp;#39;s \\\\&amp;quot;Proposal on Ancient Roots\\\\&amp;quot;\nYi Liu Yi\nSecond, \\\\&amp;quot;A discussion of Gu Gen Yuan\\\\&amp;quot;\nSection Five Qin Jiulu and \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nThe life of Qin Jiuhao\nSecond Qin Jiuyao character identification\nThree \\\\&amp;quot;Numbers Chapter 9\\\\&amp;quot;\nSection 6 Li Yehe\\\\&amp;#39;s \\\\&amp;quot;Measurement of Circular Oceanscope\\\\&amp;quot; and \\\\&amp;quot;Yigu Performance\\\\&amp;quot;\nYi Ye\nThe two holes Jiurong and \\\\&amp;quot;Test round sea mirror\\\\&amp;quot;\nThree \\\\&amp;quot;Yi Gu Ji\\\\&amp;quot; and \\\\&amp;quot;Yi Gu Performance\\\\&amp;quot;\nSection 7 Yang Hui and \\\\&amp;quot;Detailed Explanation of Chapter 9 Algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui Algorithm\\\\&amp;quot;\nYihui Yang\nSecond, \\\\&amp;quot;Detailed Nine Chapter Algorithms\\\\&amp;quot;\nThree \\\\&amp;quot;daily algorithm\\\\&amp;quot; and \\\\&amp;quot;Yang Hui algorithm\\\\&amp;quot;\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book\nOne Zhu Shijie\nTwo \\\\&amp;quot;Education Enlightenment\\\\&amp;quot;\nThree \\\\&amp;quot;Siyuan Yujian\\\\&amp;quot;\nSection 9 Other Mathematicians and Mathematical Works\nA Li Jihe\\\\&amp;#39;s \\\\&amp;quot;Nine Chapters of Arithmetic and Meaning\\\\&amp;quot; and \\\\&amp;quot;Zhou Ji\\\\&amp;#39;s Calculation of Sound and Meaning\\\\&amp;quot;\nTwo \\\\&amp;quot;Xiecha Microcalculus\\\\&amp;quot;\nThree Shen Kuohe\\\\&amp;#39;s Mathematical Achievements in \\\\&amp;quot;Meng Xi Bi Tan\\\\&amp;quot;\nFour Wang Xi, Guo Shoujing, and \\\\&amp;quot;Time History\\\\&amp;quot;\nFive Zhao Youqin and \\\\&amp;quot;New Elephant\\\\&amp;quot;\nSix Shakes and The River Defense Theory &amp;bull; Algorithm Gate\nSeven Other Mathematicians and Mathematical Works\nChapter 16 Improvements in Computing Technology and Invention of Abacus\nSection 1 \u25cb and Decimal Decimals\nOne and digital\nTwo decimal places\nSection II Improvements in Computing Technology\nOne for the law, one for the addition, subtraction, multiplication and division\nII Heading Multiplication and Nine Return and Elimination\nSection 3 The birth of abacus\nAbacus produces many\nThe second abacus was born in the Song Dynasty at the latest\nChapter 17 Going to Share Volume and Cutting Circles\nSection 1 Check Stock Volume\nOne\nTwo round city schema\nThree identification notes\nSection 2 Cutting\nA Shen Kuo&amp;rsquo;s Tactics\nTwo Sagittal Cuts in the Time of Time\nThree Zhao Youqin\\\\&amp;#39;s cutting\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple\nSection 1 Numerical Solution of High Order Equations\nAn upright release method\nSecond Jia Xian Triangle\nThree increase open method\nFour Benefits and Reductions\nFive positive and negative open\nSection II Tianyuan surgery\nOne-day history of metaphysics\nThe perfection and application of the two-day meta-technique\nThe third quarter of four\nThe historical development of a quadruple surgery\nTwo-quaternary elimination\nThree binary\nFour triples\nFive four yuan surgery\nChapter 19 Hoarding, tricks\nSection 1 Hoarding\nSlot technique\nII Hoarding\nSection II tricks surgery\nA trick of &amp;ldquo;Time-giving Calendar&amp;rdquo;\nTwo tricks of \\\\&amp;quot;Syuanyuanjian\\\\&amp;quot;\nChapter Twenty The total number of Da Yan and vertical and horizontal map\nThe first quarter total number of surgery\nThe origin of a major total\nTotal number of major\nSection II.\nA river map, Luo book and vertical and horizontal map\nSecond, Yang Hui, etc.\nThree Ding Yidong\\\\&amp;#39;s map\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties\nSection 2 Chinese Mathematical Biography\nThe Impact of Chinese Mathematics on Islamic Countries\nII The Influence of Chinese Mathematics on North Korea and Japan\nSection III Introduction of Mathematics in Islamic Countries\nThe introduction of a mathematical work\nII Arabic Digital and Crosswords\nThree soil disc algorithm and lattice operator\n\nPart V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus\n- Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty\nSection 1 The Social Background of Mathematics in the Ming Dynasty\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty\nA \\\\&amp;quot;Yongle Grand Ceremony &amp;bull; Calculation\\\\&amp;quot; and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty\nThe loss of the second ancient book\nLoss of three mathematics results\nSection III The Mainstream of Mathematics in the Ming Dynasty\nA survey of mathematics books in the Ming Dynasty\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period\nOne\nTwo Ding Ju and his Ding Ju algorithm\nThree Jiaheng\\\\&amp;#39;s \\\\&amp;quot;Algorithm Set\\\\&amp;quot;\nFour \\\\&amp;quot;Detailed Algorithm\\\\&amp;quot;\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty\nYan Gong and his \\\\&amp;quot;Tongyuan algorithm\\\\&amp;quot;\nLiu Shilong and his \\\\&amp;quot;Nine Chapters Tuning Algorithm\\\\&amp;quot;\nThree Xia Yuanze\\\\&amp;#39;s \\\\&amp;quot;specified algorithm\\\\&amp;quot;\nFour other calculations\nSection 3 Mathematical and Mathematical Writings\nWu Jing and his \\\\&amp;quot;Nine Chapter Algorithms\\\\&amp;quot;\nII Wang Wensu and his \\\\&amp;quot;Educational Poems\\\\&amp;quot;\nThree other books\nSection IV: The Theory of Theoretical Mathematics\nTang Shunzhi and his \\\\&amp;quot;Number Theory\\\\&amp;quot; six\nII Gu Yingxiang and his four books on mathematics\nThree Weeks of Learning and Its \\\\&amp;quot;Ecco\\\\&amp;quot;\nIV Zhu Zaiyu and his &amp;ldquo;New Theory of Calculation&amp;rdquo; and &amp;ldquo;Ji-Suan Su Jing Jing&amp;rdquo;\nSection V Abacus Mathematicians and Mathematical Works\nA previous work on abacus\nTwo-way Big Place and Its \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot; and \\\\&amp;quot;Analysis of Algorithms\\\\&amp;quot;\nThree other abacus work\nChapter 24 Songs of Mathematics and Popularization of Abacus\nSection 1 Practicality and Songs of Mathematics\nA practical, popular and commercialized mathematics\nThe second song of mathematics\nMathematical Songs Since the End of the Three Yuan\nSection 2 Various \\\\&amp;quot;miscellaneous methods\\\\&amp;quot; in mathematics of the Ming Dynasty\nSection 3 Development and Popularization of Abacus\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties\nThe reflection of abacus in the second mathematic book\nThe disappearance of the popularity and calculation of the three abacus\nChapter 25 Some Mathematics Work in the Ming Dynasty\nSection 1 Numerical Solution of Squares and Equations\nOne-Mid-Year Growth and Opening Method\" addthis:url=\"https:\/\/www.amazon.com\/Mathematics-History-Science-Technology-CHUN\/dp\/7030290534?SubscriptionId=AKIAJCI3DJTKR6N4LR2A&amp;&amp;linkCode=xm2&amp;camp=2025&amp;creative=165953&amp;creativeASIN=7030290534\" class=\"addthis_button_gmail\"><\/a><\/div><\/div><div id=\"wpbl-similar-div\"><p style=\"font-weight:bold; font-size:18px; margin-bottom:5px;\" class=\"wpbl-posttd-share-text\">Similar Titles<\/p><span id=\"wpbooklist-post-span-hidden\" style=\"display:none;\"><\/span><\/div><div id=\"wpbl-posttd-post-quote\"><span id=\"wpbooklist-quote-italic\">\"What are men to rocks and mountains?\" <\/span> - <span id=\"wpbooklist-quote-bold\"> Jane Austen, Pride and Prejudice<\/span><\/div><\/div>\n\t<\/div>\n\t<div id=\"wpbl-posttd-right-row\"><h3 id=\"wpbl-posttd-book-title\">The Science and Technology in China: Mathematics Volume \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u53f2\u00b7\u6570\u5b66\u5377<\/h3><div id=\"wpbl-posttd-book-details-div\"><div id=\"wpbl-posttd-book-details-1\">\n\t\t\t<span>Author: <\/span> GUO SHU CHUN ?DENG\n\t\t<\/div><div id=\"wpbl-posttd-book-details-2\">\n\t\t<span>Pages: <\/span>892\n\t<\/div><div id=\"wpbl-posttd-book-details-3\">\n\t\t<span>Genre(s): <\/span><span class=\"SearchByTag-tag\" onmouseover=\"show_searchByTags_enter(this,'Science and Civilization in China \u4e2d\u570b\u79d1\u5b78\u6280\u8853\u53f2','https:\/\/www.yinyangbalance.asia\/blog\/tag\/science-and-civilization-in-china-%e4%b8%ad%e5%9c%8b%e7%a7%91%e5%ad%b8%e6%8a%80%e8%a1%93%e5%8f%b2\/');\" onmouseout=\"show_searchByTags_leave();\">Science and Civilization in China \u4e2d\u570b\u79d1\u5b78\u6280\u8853\u53f2<\/span>\n\t<\/div><div id=\"wpbl-posttd-book-details-4\">\n\t\t<span>Publisher: <\/span>\u79d1\u5b66\u51fa\u7248\u793e\n\t<\/div><div id=\"wpbl-posttd-book-details-4\">\n\t\t<span>Subject:  <\/span>\n\t<\/div><div id=\"wpbl-posttd-book-details-4\">\n\t\t<span>Country:  <\/span>\n\t<\/div><div 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href=\"http:\/\/www.barnesandnoble.com\/s\/9787030290533\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/www.yinyangbalance.asia\/blog\/wp-content\/plugins\/wpbooklist\/assets\/img\/bn.png\"><\/a><a class=\"wpbl-posttd-wpbooklist-purchase-img\" href=\"http:\/\/www.booksamillion.com\/p\/9787030290533\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/www.yinyangbalance.asia\/blog\/wp-content\/plugins\/wpbooklist\/assets\/img\/bam-icon.jpg\"><\/a><a class=\"wpbl-posttd-wpbooklist-purchase-img\" href=\"http:\/\/store.kobobooks.com\/en-ca\/Search?Query=9787030290533\" target=\"_blank\"><img decoding=\"async\" id=\"wpbl-posttd-itunes-img\" src=\"https:\/\/www.yinyangbalance.asia\/blog\/wp-content\/plugins\/wpbooklist\/assets\/img\/kobo-icon.png\"><\/a><\/div><div id=\"wpbl-posttd-book-description-div\">\n\t\t<h5 id=\"wpbl-posttd-book-description-h5\">Description<\/h5>\n\t\t<div id=\"wpbl-posttd-book-description-contents\">\u76ee\u5f55\n\u603b\u5e8f 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\u6e05\u672b\u6570\u5b66\u6559\u80b2\u6982\u8ff0\n\u4e00 \u6570\u5b66\u6559\u80b2\u7684\u53d8\u9769\n\u4e8c \u6e05\u672b\u7684\u6570\u5b66\u6559\u80b2\u89c2\u5ff5\n\u4e09 \u6e05\u672b\u7684\u7559\u5b66\u6d3b\u52a8\u4e0e\u6570\u5b66\u7559\u5b66\u751f\n\u7b2c\u4e8c\u8282 \u665a\u6e05\u6570\u5b66\u6559\u80b2\n\u4e00 \u6d0b\u52a1\u5b66\u5802\u7684\u6570\u5b66\u6559\u80b2\n\u4e8c \u4e66\u9662\u7684\u53d8\u9769\u4e0e\u6570\u5b66\u6559\u80b2\n\u4e09 \u6559\u4f1a\u5b66\u6821\u7684\u6570\u5b66\u6559\u79d1\u4e66\n\u56db \u7678\u536f\u5b66\u5236\u7684\u6570\u5b66\u8bfe\u7a0b\n\u7b2c\u4e09\u8282 \u6570\u5b66\u4e1b\u4e66\u3001\u6570\u5b66\u793e\u56e2\u4e0e\u520a\u7269\n\u4e00 \u6570\u5b66\u4e1b\u4e66\u7684\u7f16\u7e82\n\u4e8c \u6570\u5b66\u793e\u56e2\n\u4e09 \u6570\u5b66\u520a\u7269\n\n\u4e3b\u8981\u53c2\u8003\u6587\u732e\n\u540e\u8bb0\n\u603b\u8dcb\n\ntable of Contents\nGeneral Preface Lu Jiaxi\nForeword iii\n\nThe first series of Chinese mathematics forms a subject\n- Mathematics from the primitive society to the Western Zhou Dynasty\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society\nSection 1 The Formation of Graphic Concepts\nThe emergence of a graphic concept\nSecond, from the concept of orientation to see the concept of graphics\nThree original drawing tools - rules and regulations\nSection II The Formation of Number Concepts and Original Counting Methods\nThe emergence of a number concept\nTwo original counting methods\nSection 3 The legendary mathematical figure\nOne\nSecond Yellow Emperor and Lishou\nThree \u5c27, \u821c, \u79b9 and \u5015\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society\nChapter 2 Mathematics Forms a Discipline\u2014\u2014Mathematics of the Three Generations of Xia, Shang, and Xi Zhou\nSection 1 Formation of Decimal Value Notation\nA number in Oracle and Jinwen\nTwo decimal value notation\nSection 2 Mathematics Becomes a Discipline\nThe need for social management and work and the development of mathematics\nSecond Mathematics enters teaching subjects\nIII Shang Gao and its mastered mathematics knowledge\n\nPart Two Establishment of Traditional Chinese Mathematical Framework\n- Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background\nThe Second Qin and Han Mathematics and Social and Cultural Background\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period\nAn integer number of four operations in the Spring and Autumn Period\nSecond, the extensive use of scores, ratios and proportions\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era\u2014\u2014\u201cNine Numbers\u201d\nIV Other Mathematics Knowledge in Pre-Qin Period\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period\nA Mohist and Mathematics\nTwo homes of mathematics\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips\nA Qin Jian \"Numbers\"\nII. The style, expression and characteristics of the \"numeric book\"\nThree compilation of \"calculus book\"\nThe content of the \"numerical book\" and its position in the history of Chinese mathematics\nSection V. The Zhouyi Classics and Chen Zi\nOne Zhouyi Calculation\nTwo Chen Zi\nSection VI: \"Nine Chapters of Arithmetic\" and Zhang Cang, Yan Shouchang\nThe content of \"Chapter 9 Arithmetic\"\nII. The Style and Compilation of Nine Chapters of Arithmetic\nThree \"arithmetic book\" and \"Nine chapters of arithmetic\"\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World\nFive Versions of Nine Chapters of Arithmetic\nSix Zhang Canghe Yu Shouchang\nSection 7 Other Mathematicians and Mathematical Works\nA dealer and \"Business Arithmetic\" and \"Du Zhong Arithmetic\"\nSecond Yin Xianhe Liu Hao\nThree Zhang Heng and Ma continued\nChapter IV Insufficient scores, rates, and profits\nSection 1 Scores and Its Four Principles\nA score and its representation\nTwo fractional four algorithm\nSection II Surgery and Decline Surgery\nNow there is surgery\nSecond decline\nThree transmission techniques\nSection III Insufficiency\nInsufficiency\nThe Application of Insufficiency Technique in General Mathematical Problems\nChapter V Area, Volume, Pythagoreanism, and Observation\nSection 1 Area\nA linear area\nSecond curved area\nThree round and square\nFour curved surface area\nSection 2 Volume\na polyhedral volume\nTwo round body volume\nSection III Pythagorean Theorem and Unfolding Tacks\nAn Pythagorean Theorem\nThe second solution hook shape\nThree Pythagorean arrays\nThe fourth quarter\nA tick share\nTwo ticks\nSection V\nOne time\nThe bud of the second difference\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences\nThe first section of the prescription\nOpen square\nTwo open cubes\nSection II Equations and Positive and Negative Techniques\nOne equation and equation\nSecond profit and loss\nThree positive and negative surgery\nSection III Series\n\nPart III Completion of Chinese Traditional Mathematical Theory System\n- Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory\nII Society and Mathematics in the Southern and Northern Dynasties\nThe Society and Mathematics in the Middle of Tang Dynasty\nSection Two: Xu Yue's \"Surgical Relics\" and Zhao Shuang's \"Zhou Shuo's Recounts\"\nLiu Hong, Xu Yue, and The Record of the Numbers\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera\nAn Liu Hui\nTwo \"Nine chapters of arithmetic note\"\nThree \"The Island\"\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties\nA Study on \"Nine Chapters of Arithmetic\"\nSecond \"Sun Tzu Classic\"\nThree \"Xiahou Yang calculations\"\nFour \"Zhang Qiu Jian Su Jing\"\nV. Zu Chongzhi, Zu Yu's and \"Fuzheng\"\nSix books and their mathematical works\nSeven other mathematicians\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty\nLiu Yi\nII Wang Xiaotong and \"Ancient Gujing\"\nThe three Li Yufeng and other finishing ten calculations\nFour Lines and \"Da Yan Li\"\nFive Sides\nSection 6 Sui Tang School of Mathematics and Accounting\nA math school\nSecond Accounting Division\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools\nA large number of methods\nTwo Attempts to Improve Calculation Tools\nChapter VIII Principles of rate and principle\nSection 1 Definition and Nature of Rates\nThe definition of probability\nThe Method and Nature of Bivariate\nSection II Today's Promotion and Principles of Surgery\nThe current promotion of surgery\nTwo principles\nThe third section of the arithmetic and the least common multiple\nAn arithmetic problem\nII Solving Mathematical Problems Directly\nApplication of the three greatest common divisors and the least common multiple\nChapter Nine Pythagoreans, Observations, and Errors\nSection 1 Demonstration of Formulas for Explaining Pyramids\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui\nII Zhao Shuang and Liu Hui's Proof of the Formulas of the Solution\nThree Liu Hui's Proof of the Pythagorean Array Formula\nIV Wang Xiaotong's Expansion of the Hexagonal Shape Problem\nSection 2 Proof of Formulas and Formulas\nOne with the proof of the principle of entry and completion\nB. Proof of the Principle of Keeping Preference with Pythagoreanism\nSection III Correction\nOne difference in skill\nTwo Drawings Six Body and Mathematics\nSection IV Other Observation Problems\nAn Observation Problem in Zhang Qi Jian Jian Su Jing\nII. The Problem of Expectation in the \"Several Notes to the Book\"\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations\nSection 1 Geometric Explanation and Improvement of Alchemy\nA Liu Hui's Geometry Explanation of the Alchemy\nII Liu Hui and Wang Xiaotong's Creation of Opening Methods\nThe improvement of the three prescriptions\nIV Liu Hui's \"seeking micro-number\" and the approximate value of the root\nV. Zu Chongzhi's opening power and opening difference\nThe root formula of six lines\nSection II Progress of Equations\nLiu Hui's equation theory\nTwo mutual multiplication and denomination\nThree equations new surgery\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing\nSection III Indefinite issues\nA total of five wells\nTwo things do not know the problem\nThree hundred chicken\nSection 4 Arithmetic series and geometric series\nAn arithmetic progression\nTwo equal number arrays\nChapter 11 Infinitely small segmentation and limit thinking\nSection 1 Cutting\nSection II Principle of Liu Hui\nSection III Principles and volume of the ancestral hall\nAn ancestral principle\nTwo square cover and ball volume\nSection IV The Application of Limit Ideas in Approximate Calculation\na pi ratio\nSecond round rate and square rate\nArc field density\nSection V Liu Hui's area and volume derivation system\nLiu Hui's area derivation system\nTwo proofs of the polyhedral volume formula\nThree Liu Hui's volume derivation system\nSection 6 Liu Hui's Limitation Thought in the History of Mathematics\nThe Infinite Segmentation of Liu Hui's Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece\nChapter Twelve Liu Hui's Logic Thought and Mathematical Theory System\nThe first section Liu Hui's resignation and reason, class, and therefore\nOne reason\nCategory II\nThree\nSection 2 Definition\nSection III Analogy and Induction\nAn analogy\nInductive reasoning\nSection IV Deductive Reasoning of Liu Hui\nSyllogism and Relational Reasoning\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning\nThird, the prototype of mathematical induction\nSection 5 Mathematical Proof\nA comprehensive approach\nB. Analysis and synthesis\nIII Rebuttal and Liu Hui's mistakes\nSection VI Liu Hui's Mathematical Theory System\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nSection 1 The Creative Transformation of the Sui and Tang Calendars\nThe discovery of a letter and its significance\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties\nSection II Secondary interpolation algorithm\nOne \"The Imperial Calendar\"\nLiu Liu's Quadratic Interpolation Algorithm and Its Algorithmic Analysis\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar\nFour-phase subtractive multiplication\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties\nLiu Xi's \"Emperor\" calendar algorithm\nII Li Yingfeng's \"Lin Lun Li\" image algorithm\nThree-Line \"Dai Yan Li\" Nine Shadows Algorithm\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang's \"Chong Xuan Li\"\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties\nSection 1 Mathematical Communication between China and North Korea\nSection 2 Mathematics Exchange between China and Japan\nA Chinese calendar was introduced into Japan\nII Introduction of Early Learning Education System\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties\nSection 3 Mathematical Communication between China and India\nAn Indian mathematics introduced to China\nII The Influence of Chinese Mathematics on India\n\nPart IV The Climax of Chinese Traditional Mathematics\n\u2014\u2014Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty\nII Thoughtful easing is a necessary condition for the development of mathematics\nIII Social needs are a powerful force for the development of mathematics\nFourth Song and Yuan rulers attach importance to mathematics\nFive Characteristics of Mathematics in the Song and Yuan Dynasties\nThe second section of the book \"Xiahou Yang calculations\"\nA Biography of the Date and Content of the \"Xiahou Yang Scripture\"\nTwo versions of the \"Xiahou Yang Calculator\"\nThe third quarter Jia Xianhe's \"The Yellow Emperor's Nine Chapters, The Scriptures\"\nJia Xian and his teacher Chu Yan\nTwo Most Existential Examinations of \"The Yellow Emperor's Nine Chapters Calculating Caojing\"\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor's Nine Chapters.\nSection IV Liu Yihe's \"Proposal on Ancient Roots\"\nYi Liu Yi\nSecond, \"A discussion of Gu Gen Yuan\"\nSection Five Qin Jiulu and \"Numbers Chapter 9\"\nThe life of Qin Jiuhao\nSecond Qin Jiuyao character identification\nThree \"Numbers Chapter 9\"\nSection 6 Li Yehe's \"Measurement of Circular Oceanscope\" and \"Yigu Performance\"\nYi Ye\nThe two holes Jiurong and \"Test round sea mirror\"\nThree \"Yi Gu Ji\" and \"Yi Gu Performance\"\nSection 7 Yang Hui and \"Detailed Explanation of Chapter 9 Algorithm\" and \"Yang Hui Algorithm\"\nYihui Yang\nSecond, \"Detailed Nine Chapter Algorithms\"\nThree \"daily algorithm\" and \"Yang Hui algorithm\"\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book\nOne Zhu Shijie\nTwo \"Education Enlightenment\"\nThree \"Siyuan Yujian\"\nSection 9 Other Mathematicians and Mathematical Works\nA Li Jihe's \"Nine Chapters of Arithmetic and Meaning\" and \"Zhou Ji's Calculation of Sound and Meaning\"\nTwo \"Xiecha Microcalculus\"\nThree Shen Kuohe's Mathematical Achievements in \"Meng Xi Bi Tan\"\nFour Wang Xi, Guo Shoujing, and \"Time History\"\nFive Zhao Youqin and \"New Elephant\"\nSix Shakes and The River Defense Theory \u2022 Algorithm Gate\nSeven Other Mathematicians and Mathematical Works\nChapter 16 Improvements in Computing Technology and Invention of Abacus\nSection 1 \u25cb and Decimal Decimals\nOne and digital\nTwo decimal places\nSection II Improvements in Computing Technology\nOne for the law, one for the addition, subtraction, multiplication and division\nII Heading Multiplication and Nine Return and Elimination\nSection 3 The birth of abacus\nAbacus produces many\nThe second abacus was born in the Song Dynasty at the latest\nChapter 17 Going to Share Volume and Cutting Circles\nSection 1 Check Stock Volume\nOne\nTwo round city schema\nThree identification notes\nSection 2 Cutting\nA Shen Kuo\u2019s Tactics\nTwo Sagittal Cuts in the Time of Time\nThree Zhao Youqin's cutting\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple\nSection 1 Numerical Solution of High Order Equations\nAn upright release method\nSecond Jia Xian Triangle\nThree increase open method\nFour Benefits and Reductions\nFive positive and negative open\nSection II Tianyuan surgery\nOne-day history of metaphysics\nThe perfection and application of the two-day meta-technique\nThe third quarter of four\nThe historical development of a quadruple surgery\nTwo-quaternary elimination\nThree binary\nFour triples\nFive four yuan surgery\nChapter 19 Hoarding, tricks\nSection 1 Hoarding\nSlot technique\nII Hoarding\nSection II tricks surgery\nA trick of \u201cTime-giving Calendar\u201d\nTwo tricks of \"Syuanyuanjian\"\nChapter Twenty The total number of Da Yan and vertical and horizontal map\nThe first quarter total number of surgery\nThe origin of a major total\nTotal number of major\nSection II.\nA river map, Luo book and vertical and horizontal map\nSecond, Yang Hui, etc.\nThree Ding Yidong's map\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties\nSection 2 Chinese Mathematical Biography\nThe Impact of Chinese Mathematics on Islamic Countries\nII The Influence of Chinese Mathematics on North Korea and Japan\nSection III Introduction of Mathematics in Islamic Countries\nThe introduction of a mathematical work\nII Arabic Digital and Crosswords\nThree soil disc algorithm and lattice operator\n\nPart V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus\n- Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty\nSection 1 The Social Background of Mathematics in the Ming Dynasty\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty\nA \"Yongle Grand Ceremony \u2022 Calculation\" and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty\nThe loss of the second ancient book\nLoss of three mathematics results\nSection III The Mainstream of Mathematics in the Ming Dynasty\nA survey of mathematics books in the Ming Dynasty\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period\nOne\nTwo Ding Ju and his Ding Ju algorithm\nThree Jiaheng's \"Algorithm Set\"\nFour \"Detailed Algorithm\"\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty\nYan Gong and his \"Tongyuan algorithm\"\nLiu Shilong and his \"Nine Chapters Tuning Algorithm\"\nThree Xia Yuanze's \"specified algorithm\"\nFour other calculations\nSection 3 Mathematical and Mathematical Writings\nWu Jing and his \"Nine Chapter Algorithms\"\nII Wang Wensu and his \"Educational Poems\"\nThree other books\nSection IV: The Theory of Theoretical Mathematics\nTang Shunzhi and his \"Number Theory\" six\nII Gu Yingxiang and his four books on mathematics\nThree Weeks of Learning and Its \"Ecco\"\nIV Zhu Zaiyu and his \u201cNew Theory of Calculation\u201d and \u201cJi-Suan Su Jing Jing\u201d\nSection V Abacus Mathematicians and Mathematical Works\nA previous work on abacus\nTwo-way Big Place and Its \"Analysis of Algorithms\" and \"Analysis of Algorithms\"\nThree other abacus work\nChapter 24 Songs of Mathematics and Popularization of Abacus\nSection 1 Practicality and Songs of Mathematics\nA practical, popular and commercialized mathematics\nThe second song of mathematics\nMathematical Songs Since the End of the Three Yuan\nSection 2 Various \"miscellaneous methods\" in mathematics of the Ming Dynasty\nSection 3 Development and Popularization of Abacus\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties\nThe reflection of abacus in the second mathematic book\nThe disappearance of the popularity and calculation of the three abacus\nChapter 25 Some Mathematics Work in the Ming Dynasty\nSection 1 Numerical Solution of Squares and Equations\nOne-Mid-Year Growth and Opening Method<\/div>\n\t<\/div>\n\t<div id=\"wpbl-posttd-book-notes-div\">\n\t\t<h5 id=\"wpbl-posttd-book-notes-h5\">Notes<\/h5>\n\t\t<div id=\"wpbl-posttd-book-notes-contents\">HK$ Donated by:\n\nhttps:\/\/www.amazon.cn\/dp\/B0049FIV4O\/ref=sr_1_1?ie=UTF8&amp;qid=1522937223&amp;sr=8-1&amp;keywords=9787030290533 \n<\/div>\n\t<\/div><\/div>\n<\/div>\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u5f55<br \/>\n\u603b\u5e8f \u5362\u5609\u9521i<br \/>\n\u524d\u8a00iii<\/p>\n<p>\u7b2c\u4e00\u7f16 \u4e2d\u56fd\u6570\u5b66\u4ece\u5174\u8d77\u5230\u5f62\u6210\u4e00\u95e8\u5b66\u79d1<br \/>\n&mdash;&mdash;\u539f\u59cb\u793e\u4f1a\u5230\u897f\u5468\u65f6\u671f\u7684\u6570\u5b66<br \/>\n\u7b2c\u4e00\u7ae0 \u4e2d\u56fd\u6570\u5b66\u7684\u5174\u8d77&mdash;&mdash;\u539f\u59cb\u793e\u4f1a\u7684\u6570\u5b66<br \/>\n\u7b2c\u4e00\u8282 \u56fe\u5f62\u89c2\u5ff5\u7684\u5f62\u6210<br \/>\n\u4e00 \u56fe\u5f62\u89c2\u5ff5\u7684\u4ea7\u751f<br \/>\n\u4e8c \u4ece\u65b9\u4f4d\u89c2\u5ff5\u770b\u56fe\u5f62\u89c2\u5ff5<br \/>\n\u4e09 \u539f\u59cb\u7684\u4f5c\u56fe\u5de5\u5177&mdash;&mdash;\u89c4\u77e9\u51c6\u7ef3<br \/>\n\u7b2c\u4e8c\u8282 \u6570\u6982\u5ff5\u7684\u5f62\u6210\u4e0e\u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5<br \/>\n\u4e00 \u6570\u6982\u5ff5\u7684\u4ea7\u751f<br \/>\n\u4e8c \u539f\u59cb\u7684\u8bb0\u6570\u65b9\u6cd5<br \/>\n\u7b2c\u4e09\u8282 \u4f20\u8bf4\u4e2d\u7684\u6570\u5b66\u4eba\u7269<br \/>\n\u4e00 \u4f0f\u7fb2<br \/>\n\u4e8c \u9ec4\u5e1d\u548c\u96b6\u9996<br \/>\n\u4e09 \u5c27\u3001\u821c\u3001\u79b9\u548c\u5015<br \/>\n\u7b2c\u56db\u8282 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\/>\n\u4e00 \u8c08\u5929\u4e09\u53cb\u548c\u5176\u4ed6\u6570\u5b66\u5bb6<br \/>\n\u4e8c \u65b9\u7a0b\u8bba\u7814\u7a76<br \/>\n\u4e09 \u5176\u4ed6\u7814\u7a76\u5de5\u4f5c<br \/>\n\u7b2c\u4e09\u5341\u7ae0 \u5e42\u7ea7\u6570\u5c55\u5f00\u5f0f\u7684\u7814\u7a76<br \/>\n\u7b2c\u4e00\u8282 \u660e\u5b89\u56fe\u53ca\u5176\u300a\u5272\u571c\u5bc6\u7387\u6377\u6cd5\u300b<br \/>\n\u4e00 \u660e\u5b89\u56fe<br \/>\n\u4e8c \u300a\u5272\u571c\u5bc6\u7387\u6377\u6cd5\u300b<br \/>\n\u7b2c\u4e8c\u8282 \u8463\u7950\u8bda\u3001\u9879\u540d\u8fbe\u3001\u6234\u7166\u7b49\u7684\u5de5\u4f5c<br \/>\n\u4e00 \u8463\u7950\u8bda\u53ca\u5176\u300a\u5272\u571c\u8fde\u6bd4\u4f8b\u672f\u56fe\u89e3\u300b<br \/>\n\u4e8c \u9879\u540d\u8fbe\u53ca\u5176\u300a\u8c61\u6570\u4e00\u539f\u300b<br \/>\n\u4e09 \u6234\u7166\u53ca\u5176\u300a\u6c42\u8868\u6377\u672f\u300b<br \/>\n\u7b2c\u4e09\u8282 \u674e\u5584\u5170\u53ca\u5176\u5c16\u9525\u672f<br \/>\n\u4e00 \u674e\u5584\u5170<br \/>\n\u4e8c \u5c16\u9525\u672f<br \/>\n\u7b2c\u56db\u8282 \u5f90\u6709\u58ec\u3001\u987e\u89c2\u5149\u3001\u90b9\u4f2f\u5947\u7b49\u7684\u7814\u7a76\u5de5\u4f5c<br \/>\n\u4e00 \u5f90\u6709\u58ec\u53ca\u5176\u300a\u5272\u5706\u516b\u7ebf\u7f00\u672f\u300b<br \/>\n\u4e8c \u987e\u89c2\u5149\u3001\u90b9\u4f2f\u5947\u7684\u7814\u7a76\u5de5\u4f5c<br \/>\n\u7b2c\u4e09\u5341\u4e00\u7ae0 \u6e05\u672b\u897f\u65b9\u6570\u5b66\u7684\u4f20\u5165<br \/>\n\u7b2c\u4e00\u8282 \u6e05\u672b\u897f\u65b9\u6570\u5b66\u4f20\u5165\u6982\u51b5<br \/>\n\u4e00 \u674e\u5584\u5170\u7684\u6570\u5b66\u7ffb\u8bd1\u5de5\u4f5c<br \/>\n\u4e8c \u534e\u8605\u82b3\u53ca\u5176\u6570\u5b66\u7ffb\u8bd1\u7814\u7a76<br \/>\n\u7b2c\u4e8c\u8282 \u51e0\u4f55\u3001\u4ee3\u6570\u548c\u4e09\u89d2\u5b66\u8457\u4f5c\u7684\u7ffb\u8bd1<br \/>\n\u4e00 \u300a\u51e0\u4f55\u539f\u672c\u300b<br \/>\n\u4e8c \u300a\u4ee3\u6570\u5b66\u300b\u548c\u300a\u4ee3\u6570\u672f\u300b<br \/>\n\u4e09 \u300a\u4e09\u89d2\u6570\u7406\u300b\u53ca\u5176\u4ed6<br \/>\n\u7b2c\u4e09\u8282 \u5fae\u79ef\u5206\u548c\u6982\u7387\u8bba\u8457\u4f5c\u7684\u7ffb\u8bd1<br \/>\n\u4e00 \u300a\u4ee3\u5fae\u79ef\u62fe\u7ea7\u300b<br \/>\n\u4e8c \u300a\u5fae\u79ef\u6eaf\u6e90\u300b<br \/>\n\u4e09 \u5176\u4ed6\u6709\u5173\u5fae\u79ef\u5206\u7684\u8457\u4f5c<br \/>\n\u56db \u300a\u51b3\u7591\u6570\u5b66\u300b<br \/>\n\u7b2c\u4e09\u5341\u4e8c\u7ae0 \u6e05\u672b\u6570\u5b66\u7814\u7a76<br \/>\n\u7b2c\u4e00\u8282 \u590f\u9e3e\u7fd4\u3001\u767d\u8299\u5802\u8bf8\u5b50\u548c\u5176\u4ed6\u6570\u5b66\u5bb6<br \/>\n\u4e00 \u590f\u9e3e\u7fd4\u53ca\u5176\u6570\u5b66\u8457\u4f5c<br \/>\n\u4e8c \u767d\u8299\u5802\u8bf8\u5b50\u53ca\u5176\u6570\u5b66\u8457\u4f5c<br \/>\n\u4e09 \u5218\u5f5d\u7a0b\u53ca\u5176\u6570\u5b66\u8457\u4f5c<br \/>\n\u56db \u9648\u5fd7\u575a\u3001\u5468\u8fbe\u53ca\u5176\u6570\u5b66\u8457\u4f5c<br \/>\n\u7b2c\u4e8c\u8282 \u6570\u8bba\u7684\u7814\u7a76<br \/>\n\u4e00 \u7d20\u6570\u7684\u7814\u7a76<br \/>\n\u4e8c \u6574\u6570\u52fe\u80a1\u5f62\u7684\u7814\u7a76<br \/>\n\u4e09 \u767e\u9e21\u672f\u548c\u5927\u884d\u603b\u6570\u672f\u7684\u7814\u7a76<br \/>\n\u7b2c\u4e09\u8282 \u579b\u79ef\u672f\u4e0e\u62db\u5dee\u672f\u7684\u7814\u7a76<br \/>\n\u4e00 \u674e\u5584\u5170\u7684\u579b\u79ef\u672f<br \/>\n\u4e8c \u590f\u9e3e\u7fd4\u7684\u579b\u79ef\u62db\u5dee\u7814\u7a76<br \/>\n\u4e09 \u5218\u5f5d\u7a0b\u7684\u579b\u79ef\u672f\u7814\u7a76<br \/>\n\u7b2c\u56db\u8282 \u5f00\u65b9\u672f\u7684\u7814\u7a76<br \/>\n\u4e00 \u590f\u9e3e\u7fd4\u5bf9\u5f00\u65b9\u672f\u7684\u7814\u7a76<br \/>\n\u4e8c \u534e\u8605\u82b3\u7684\u6570\u6839\u5f00\u65b9\u672f\u4e0e\u79ef\u8f83\u5f00\u65b9\u672f<br \/>\n\u7b2c\u4e94\u8282 \u5bf9\u5706\u9525\u66f2\u7ebf\u548c\u5fae\u79ef\u5206\u7684\u7814\u7a76<br \/>\n\u4e00 \u5706\u9525\u66f2\u7ebf\u4f5c\u56fe<br \/>\n\u4e8c \u4e8c\u6b21\u66f2\u7ebf\u6c42\u79ef\u95ee\u9898<br \/>\n\u4e09 \u5e73\u5706\u5bb9\u5207\u4e0e\u7d2f\u5706<br \/>\n\u7b2c\u4e09\u5341\u4e09\u7ae0 \u6e05\u672b\u6570\u5b66\u6559\u80b2<br \/>\n\u7b2c\u4e00\u8282 \u6e05\u672b\u6570\u5b66\u6559\u80b2\u6982\u8ff0<br \/>\n\u4e00 \u6570\u5b66\u6559\u80b2\u7684\u53d8\u9769<br \/>\n\u4e8c \u6e05\u672b\u7684\u6570\u5b66\u6559\u80b2\u89c2\u5ff5<br \/>\n\u4e09 \u6e05\u672b\u7684\u7559\u5b66\u6d3b\u52a8\u4e0e\u6570\u5b66\u7559\u5b66\u751f<br \/>\n\u7b2c\u4e8c\u8282 \u665a\u6e05\u6570\u5b66\u6559\u80b2<br \/>\n\u4e00 \u6d0b\u52a1\u5b66\u5802\u7684\u6570\u5b66\u6559\u80b2<br \/>\n\u4e8c \u4e66\u9662\u7684\u53d8\u9769\u4e0e\u6570\u5b66\u6559\u80b2<br \/>\n\u4e09 \u6559\u4f1a\u5b66\u6821\u7684\u6570\u5b66\u6559\u79d1\u4e66<br \/>\n\u56db \u7678\u536f\u5b66\u5236\u7684\u6570\u5b66\u8bfe\u7a0b<br \/>\n\u7b2c\u4e09\u8282 \u6570\u5b66\u4e1b\u4e66\u3001\u6570\u5b66\u793e\u56e2\u4e0e\u520a\u7269<br \/>\n\u4e00 \u6570\u5b66\u4e1b\u4e66\u7684\u7f16\u7e82<br \/>\n\u4e8c \u6570\u5b66\u793e\u56e2<br \/>\n\u4e09 \u6570\u5b66\u520a\u7269<\/p>\n<p>\u4e3b\u8981\u53c2\u8003\u6587\u732e<br \/>\n\u540e\u8bb0<br \/>\n\u603b\u8dcb<\/p>\n<p>table of Contents<br \/>\nGeneral Preface Lu Jiaxi<br \/>\nForeword iii<\/p>\n<p>The first series of Chinese mathematics forms a subject<br \/>\n&#8211; Mathematics from the primitive society to the Western Zhou Dynasty<br \/>\nChapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society<br \/>\nSection 1 The Formation of Graphic Concepts<br \/>\nThe emergence of a graphic concept<br \/>\nSecond, from the concept of orientation to see the concept of graphics<br \/>\nThree original drawing tools &#8211; rules and regulations<br \/>\nSection II The Formation of Number Concepts and Original Counting Methods<br \/>\nThe emergence of a number concept<br \/>\nTwo original counting methods<br \/>\nSection 3 The legendary mathematical figure<br \/>\nOne<br \/>\nSecond Yellow Emperor and Lishou<br \/>\nThree \u5c27, \u821c, \u79b9 and \u5015<br \/>\nThe fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society<br \/>\nChapter 2 Mathematics Forms a Discipline&mdash;&mdash;Mathematics of the Three Generations of Xia, Shang, and Xi Zhou<br \/>\nSection 1 Formation of Decimal Value Notation<br \/>\nA number in Oracle and Jinwen<br \/>\nTwo decimal value notation<br \/>\nSection 2 Mathematics Becomes a Discipline<br \/>\nThe need for social management and work and the development of mathematics<br \/>\nSecond Mathematics enters teaching subjects<br \/>\nIII Shang Gao and its mastered mathematics knowledge<\/p>\n<p>Part Two Establishment of Traditional Chinese Mathematical Framework<br \/>\n&#8211; Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty<br \/>\nChapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty<br \/>\nSection 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period<br \/>\nA Spring and Autumn and Warring States Mathematics and Social and Cultural Background<br \/>\nThe Second Qin and Han Mathematics and Social and Cultural Background<br \/>\nSection 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period<br \/>\nAn integer number of four operations in the Spring and Autumn Period<br \/>\nSecond, the extensive use of scores, ratios and proportions<br \/>\nFrom the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era&mdash;&mdash;&ldquo;Nine Numbers&rdquo;<br \/>\nIV Other Mathematics Knowledge in Pre-Qin Period<br \/>\nSection 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period<br \/>\nA Mohist and Mathematics<br \/>\nTwo homes of mathematics<br \/>\nIII The Infinite Thought of Pre-Qin Taoists and Other Schools<br \/>\nIV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period<br \/>\nSection 4 The Qin Bamboo Slips and Han Bamboo Slips<br \/>\nA Qin Jian &quot;Numbers&quot;<br \/>\nII. The style, expression and characteristics of the &quot;numeric book&quot;<br \/>\nThree compilation of &quot;calculus book&quot;<br \/>\nThe content of the &quot;numerical book&quot; and its position in the history of Chinese mathematics<br \/>\nSection V. The Zhouyi Classics and Chen Zi<br \/>\nOne Zhouyi Calculation<br \/>\nTwo Chen Zi<br \/>\nSection VI: &quot;Nine Chapters of Arithmetic&quot; and Zhang Cang, Yan Shouchang<br \/>\nThe content of &quot;Chapter 9 Arithmetic&quot;<br \/>\nII. The Style and Compilation of Nine Chapters of Arithmetic<br \/>\nThree &quot;arithmetic book&quot; and &quot;Nine chapters of arithmetic&quot;<br \/>\n4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World<br \/>\nFive Versions of Nine Chapters of Arithmetic<br \/>\nSix Zhang Canghe Yu Shouchang<br \/>\nSection 7 Other Mathematicians and Mathematical Works<br \/>\nA dealer and &quot;Business Arithmetic&quot; and &quot;Du Zhong Arithmetic&quot;<br \/>\nSecond Yin Xianhe Liu Hao<br \/>\nThree Zhang Heng and Ma continued<br \/>\nChapter IV Insufficient scores, rates, and profits<br \/>\nSection 1 Scores and Its Four Principles<br \/>\nA score and its representation<br \/>\nTwo fractional four algorithm<br \/>\nSection II Surgery and Decline Surgery<br \/>\nNow there is surgery<br \/>\nSecond decline<br \/>\nThree transmission techniques<br \/>\nSection III Insufficiency<br \/>\nInsufficiency<br \/>\nThe Application of Insufficiency Technique in General Mathematical Problems<br \/>\nChapter V Area, Volume, Pythagoreanism, and Observation<br \/>\nSection 1 Area<br \/>\nA linear area<br \/>\nSecond curved area<br \/>\nThree round and square<br \/>\nFour curved surface area<br \/>\nSection 2 Volume<br \/>\na polyhedral volume<br \/>\nTwo round body volume<br \/>\nSection III Pythagorean Theorem and Unfolding Tacks<br \/>\nAn Pythagorean Theorem<br \/>\nThe second solution hook shape<br \/>\nThree Pythagorean arrays<br \/>\nThe fourth quarter<br \/>\nA tick share<br \/>\nTwo ticks<br \/>\nSection V<br \/>\nOne time<br \/>\nThe bud of the second difference<br \/>\nChapter 6 Alchemy, Positive and Negative, Equations and Sequences<br \/>\nThe first section of the prescription<br \/>\nOpen square<br \/>\nTwo open cubes<br \/>\nSection II Equations and Positive and Negative Techniques<br \/>\nOne equation and equation<br \/>\nSecond profit and loss<br \/>\nThree positive and negative surgery<br \/>\nSection III Series<\/p>\n<p>Part III Completion of Chinese Traditional Mathematical Theory System<br \/>\n&#8211; Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty<br \/>\nChapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty<br \/>\nSection 1 The Social Changes Beginning in the Late Han Dynasty, Wei and Jin Dynasties and the Mathematics from the End of the Han Dynasty to the Middle of the Tang Dynasty<br \/>\nThe Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory<br \/>\nII Society and Mathematics in the Southern and Northern Dynasties<br \/>\nThe Society and Mathematics in the Middle of Tang Dynasty<br \/>\nSection Two: Xu Yue&#39;s &quot;Surgical Relics&quot; and Zhao Shuang&#39;s &quot;Zhou Shuo&#39;s Recounts&quot;<br \/>\nLiu Hong, Xu Yue, and The Record of the Numbers<br \/>\nTwo Zhao Shuang and Zhou Shuo Jing Jing Zhu<br \/>\nSection III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera<br \/>\nAn Liu Hui<br \/>\nTwo &quot;Nine chapters of arithmetic note&quot;<br \/>\nThree &quot;The Island&quot;<br \/>\nSection IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties<br \/>\nA Study on &quot;Nine Chapters of Arithmetic&quot;<br \/>\nSecond &quot;Sun Tzu Classic&quot;<br \/>\nThree &quot;Xiahou Yang calculations&quot;<br \/>\nFour &quot;Zhang Qiu Jian Su Jing&quot;<br \/>\nV. Zu Chongzhi, Zu Yu&#39;s and &quot;Fuzheng&quot;<br \/>\nSix books and their mathematical works<br \/>\nSeven other mathematicians<br \/>\nSection 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty<br \/>\nLiu Yi<br \/>\nII Wang Xiaotong and &quot;Ancient Gujing&quot;<br \/>\nThe three Li Yufeng and other finishing ten calculations<br \/>\nFour Lines and &quot;Da Yan Li&quot;<br \/>\nFive Sides<br \/>\nSection 6 Sui Tang School of Mathematics and Accounting<br \/>\nA math school<br \/>\nSecond Accounting Division<br \/>\nSection 7 Attempt to Improve Numerical Methods and Improve Calculation Tools<br \/>\nA large number of methods<br \/>\nTwo Attempts to Improve Calculation Tools<br \/>\nChapter VIII Principles of rate and principle<br \/>\nSection 1 Definition and Nature of Rates<br \/>\nThe definition of probability<br \/>\nThe Method and Nature of Bivariate<br \/>\nSection II Today&#39;s Promotion and Principles of Surgery<br \/>\nThe current promotion of surgery<br \/>\nTwo principles<br \/>\nThe third section of the arithmetic and the least common multiple<br \/>\nAn arithmetic problem<br \/>\nII Solving Mathematical Problems Directly<br \/>\nApplication of the three greatest common divisors and the least common multiple<br \/>\nChapter Nine Pythagoreans, Observations, and Errors<br \/>\nSection 1 Demonstration of Formulas for Explaining Pyramids<br \/>\nA proof of Pythagorean Theorem by Zhao Shuang and Liu Hui<br \/>\nII Zhao Shuang and Liu Hui&#39;s Proof of the Formulas of the Solution<br \/>\nThree Liu Hui&#39;s Proof of the Pythagorean Array Formula<br \/>\nIV Wang Xiaotong&#39;s Expansion of the Hexagonal Shape Problem<br \/>\nSection 2 Proof of Formulas and Formulas<br \/>\nOne with the proof of the principle of entry and completion<br \/>\nB. Proof of the Principle of Keeping Preference with Pythagoreanism<br \/>\nSection III Correction<br \/>\nOne difference in skill<br \/>\nTwo Drawings Six Body and Mathematics<br \/>\nSection IV Other Observation Problems<br \/>\nAn Observation Problem in Zhang Qi Jian Jian Su Jing<br \/>\nII. The Problem of Expectation in the &quot;Several Notes to the Book&quot;<br \/>\nChapter 10 Improvements, uncertainties, and sequences of prescriptions, equations<br \/>\nSection 1 Geometric Explanation and Improvement of Alchemy<br \/>\nA Liu Hui&#39;s Geometry Explanation of the Alchemy<br \/>\nII Liu Hui and Wang Xiaotong&#39;s Creation of Opening Methods<br \/>\nThe improvement of the three prescriptions<br \/>\nIV Liu Hui&#39;s &quot;seeking micro-number&quot; and the approximate value of the root<br \/>\nV. Zu Chongzhi&#39;s opening power and opening difference<br \/>\nThe root formula of six lines<br \/>\nSection II Progress of Equations<br \/>\nLiu Hui&#39;s equation theory<br \/>\nTwo mutual multiplication and denomination<br \/>\nThree equations new surgery<br \/>\nIV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing<br \/>\nSection III Indefinite issues<br \/>\nA total of five wells<br \/>\nTwo things do not know the problem<br \/>\nThree hundred chicken<br \/>\nSection 4 Arithmetic series and geometric series<br \/>\nAn arithmetic progression<br \/>\nTwo equal number arrays<br \/>\nChapter 11 Infinitely small segmentation and limit thinking<br \/>\nSection 1 Cutting<br \/>\nSection II Principle of Liu Hui<br \/>\nSection III Principles and volume of the ancestral hall<br \/>\nAn ancestral principle<br \/>\nTwo square cover and ball volume<br \/>\nSection IV The Application of Limit Ideas in Approximate Calculation<br \/>\na pi ratio<br \/>\nSecond round rate and square rate<br \/>\nArc field density<br \/>\nSection V Liu Hui&#39;s area and volume derivation system<br \/>\nLiu Hui&#39;s area derivation system<br \/>\nTwo proofs of the polyhedral volume formula<br \/>\nThree Liu Hui&#39;s volume derivation system<br \/>\nSection 6 Liu Hui&#39;s Limitation Thought in the History of Mathematics<br \/>\nThe Infinite Segmentation of Liu Hui&#39;s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists<br \/>\nThe Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece<br \/>\nChapter Twelve Liu Hui&#39;s Logic Thought and Mathematical Theory System<br \/>\nThe first section Liu Hui&#39;s resignation and reason, class, and therefore<br \/>\nOne reason<br \/>\nCategory II<br \/>\nThree<br \/>\nSection 2 Definition<br \/>\nSection III Analogy and Induction<br \/>\nAn analogy<br \/>\nInductive reasoning<br \/>\nSection IV Deductive Reasoning of Liu Hui<br \/>\nSyllogism and Relational Reasoning<br \/>\nII. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning<br \/>\nThird, the prototype of mathematical induction<br \/>\nSection 5 Mathematical Proof<br \/>\nA comprehensive approach<br \/>\nB. Analysis and synthesis<br \/>\nIII Rebuttal and Liu Hui&#39;s mistakes<br \/>\nSection VI Liu Hui&#39;s Mathematical Theory System<br \/>\nChapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties<br \/>\nSection 1 The Creative Transformation of the Sui and Tang Calendars<br \/>\nThe discovery of a letter and its significance<br \/>\nThe mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties<br \/>\nSection II Secondary interpolation algorithm<br \/>\nOne &quot;The Imperial Calendar&quot;<br \/>\nLiu Liu&#39;s Quadratic Interpolation Algorithm and Its Algorithmic Analysis<br \/>\nThe Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar<br \/>\nFour-phase subtractive multiplication<br \/>\nSection III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties<br \/>\nLiu Xi&#39;s &quot;Emperor&quot; calendar algorithm<br \/>\nII Li Yingfeng&#39;s &quot;Lin Lun Li&quot; image algorithm<br \/>\nThree-Line &quot;Dai Yan Li&quot; Nine Shadows Algorithm<br \/>\nThe Computation of Yellow Equator and Moon Huang Wei by Sibian Gang&#39;s &quot;Chong Xuan Li&quot;<br \/>\nChapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties<br \/>\nSection 1 Mathematical Communication between China and North Korea<br \/>\nSection 2 Mathematics Exchange between China and Japan<br \/>\nA Chinese calendar was introduced into Japan<br \/>\nII Introduction of Early Learning Education System<br \/>\nIII The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties<br \/>\nSection 3 Mathematical Communication between China and India<br \/>\nAn Indian mathematics introduced to China<br \/>\nII The Influence of Chinese Mathematics on India<\/p>\n<p>Part IV The Climax of Chinese Traditional Mathematics<br \/>\n&mdash;&mdash;Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty<br \/>\nChapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty<br \/>\nThe first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty<br \/>\nThe social changes and the development of mathematics started in the middle of the Tang Dynasty<br \/>\nII Thoughtful easing is a necessary condition for the development of mathematics<br \/>\nIII Social needs are a powerful force for the development of mathematics<br \/>\nFourth Song and Yuan rulers attach importance to mathematics<br \/>\nFive Characteristics of Mathematics in the Song and Yuan Dynasties<br \/>\nThe second section of the book &quot;Xiahou Yang calculations&quot;<br \/>\nA Biography of the Date and Content of the &quot;Xiahou Yang Scripture&quot;<br \/>\nTwo versions of the &quot;Xiahou Yang Calculator&quot;<br \/>\nThe third quarter Jia Xianhe&#39;s &quot;The Yellow Emperor&#39;s Nine Chapters, The Scriptures&quot;<br \/>\nJia Xian and his teacher Chu Yan<br \/>\nTwo Most Existential Examinations of &quot;The Yellow Emperor&#39;s Nine Chapters Calculating Caojing&quot;<br \/>\nThree Mathematical Achievements and Mathematical Thought in The Yellow Emperor&#39;s Nine Chapters.<br \/>\nSection IV Liu Yihe&#39;s &quot;Proposal on Ancient Roots&quot;<br \/>\nYi Liu Yi<br \/>\nSecond, &quot;A discussion of Gu Gen Yuan&quot;<br \/>\nSection Five Qin Jiulu and &quot;Numbers Chapter 9&quot;<br \/>\nThe life of Qin Jiuhao<br \/>\nSecond Qin Jiuyao character identification<br \/>\nThree &quot;Numbers Chapter 9&quot;<br \/>\nSection 6 Li Yehe&#39;s &quot;Measurement of Circular Oceanscope&quot; and &quot;Yigu Performance&quot;<br \/>\nYi Ye<br \/>\nThe two holes Jiurong and &quot;Test round sea mirror&quot;<br \/>\nThree &quot;Yi Gu Ji&quot; and &quot;Yi Gu Performance&quot;<br \/>\nSection 7 Yang Hui and &quot;Detailed Explanation of Chapter 9 Algorithm&quot; and &quot;Yang Hui Algorithm&quot;<br \/>\nYihui Yang<br \/>\nSecond, &quot;Detailed Nine Chapter Algorithms&quot;<br \/>\nThree &quot;daily algorithm&quot; and &quot;Yang Hui algorithm&quot;<br \/>\nSection VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book<br \/>\nOne Zhu Shijie<br \/>\nTwo &quot;Education Enlightenment&quot;<br \/>\nThree &quot;Siyuan Yujian&quot;<br \/>\nSection 9 Other Mathematicians and Mathematical Works<br \/>\nA Li Jihe&#39;s &quot;Nine Chapters of Arithmetic and Meaning&quot; and &quot;Zhou Ji&#39;s Calculation of Sound and Meaning&quot;<br \/>\nTwo &quot;Xiecha Microcalculus&quot;<br \/>\nThree Shen Kuohe&#39;s Mathematical Achievements in &quot;Meng Xi Bi Tan&quot;<br \/>\nFour Wang Xi, Guo Shoujing, and &quot;Time History&quot;<br \/>\nFive Zhao Youqin and &quot;New Elephant&quot;<br \/>\nSix Shakes and The River Defense Theory &bull; Algorithm Gate<br \/>\nSeven Other Mathematicians and Mathematical Works<br \/>\nChapter 16 Improvements in Computing Technology and Invention of Abacus<br \/>\nSection 1 \u25cb and Decimal Decimals<br \/>\nOne and digital<br \/>\nTwo decimal places<br \/>\nSection II Improvements in Computing Technology<br \/>\nOne for the law, one for the addition, subtraction, multiplication and division<br \/>\nII Heading Multiplication and Nine Return and Elimination<br \/>\nSection 3 The birth of abacus<br \/>\nAbacus produces many<br \/>\nThe second abacus was born in the Song Dynasty at the latest<br \/>\nChapter 17 Going to Share Volume and Cutting Circles<br \/>\nSection 1 Check Stock Volume<br \/>\nOne<br \/>\nTwo round city schema<br \/>\nThree identification notes<br \/>\nSection 2 Cutting<br \/>\nA Shen Kuo&rsquo;s Tactics<br \/>\nTwo Sagittal Cuts in the Time of Time<br \/>\nThree Zhao Youqin&#39;s cutting<br \/>\nChapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple<br \/>\nSection 1 Numerical Solution of High Order Equations<br \/>\nAn upright release method<br \/>\nSecond Jia Xian Triangle<br \/>\nThree increase open method<br \/>\nFour Benefits and Reductions<br \/>\nFive positive and negative open<br \/>\nSection II Tianyuan surgery<br \/>\nOne-day history of metaphysics<br \/>\nThe perfection and application of the two-day meta-technique<br \/>\nThe third quarter of four<br \/>\nThe historical development of a quadruple surgery<br \/>\nTwo-quaternary elimination<br \/>\nThree binary<br \/>\nFour triples<br \/>\nFive four yuan surgery<br \/>\nChapter 19 Hoarding, tricks<br \/>\nSection 1 Hoarding<br \/>\nSlot technique<br \/>\nII Hoarding<br \/>\nSection II tricks surgery<br \/>\nA trick of &ldquo;Time-giving Calendar&rdquo;<br \/>\nTwo tricks of &quot;Syuanyuanjian&quot;<br \/>\nChapter Twenty The total number of Da Yan and vertical and horizontal map<br \/>\nThe first quarter total number of surgery<br \/>\nThe origin of a major total<br \/>\nTotal number of major<br \/>\nSection II.<br \/>\nA river map, Luo book and vertical and horizontal map<br \/>\nSecond, Yang Hui, etc.<br \/>\nThree Ding Yidong&#39;s map<br \/>\nChapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty<br \/>\nSection 1 Overview of Chinese and Foreign Mathematics Exchanges<br \/>\nAn Overview of the Development of Mathematics in Islamic Regions after the 9th Century<br \/>\nII Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties<br \/>\nSection 2 Chinese Mathematical Biography<br \/>\nThe Impact of Chinese Mathematics on Islamic Countries<br \/>\nII The Influence of Chinese Mathematics on North Korea and Japan<br \/>\nSection III Introduction of Mathematics in Islamic Countries<br \/>\nThe introduction of a mathematical work<br \/>\nII Arabic Digital and Crosswords<br \/>\nThree soil disc algorithm and lattice operator<\/p>\n<p>Part V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus<br \/>\n&#8211; Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty<br \/>\nChapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty<br \/>\nSection 1 The Social Background of Mathematics in the Ming Dynasty<br \/>\nSection II Loss of Ancient Works and Achievements in the Ming Dynasty<br \/>\nA &quot;Yongle Grand Ceremony &bull; Calculation&quot; and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty<br \/>\nThe loss of the second ancient book<br \/>\nLoss of three mathematics results<br \/>\nSection III The Mainstream of Mathematics in the Ming Dynasty<br \/>\nA survey of mathematics books in the Ming Dynasty<br \/>\nThe Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui<br \/>\nChapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty<br \/>\nSection I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period<br \/>\nOne<br \/>\nTwo Ding Ju and his Ding Ju algorithm<br \/>\nThree Jiaheng&#39;s &quot;Algorithm Set&quot;<br \/>\nFour &quot;Detailed Algorithm&quot;<br \/>\nSection II Mathematicians and Mathematical Works in Early Ming Dynasty<br \/>\nYan Gong and his &quot;Tongyuan algorithm&quot;<br \/>\nLiu Shilong and his &quot;Nine Chapters Tuning Algorithm&quot;<br \/>\nThree Xia Yuanze&#39;s &quot;specified algorithm&quot;<br \/>\nFour other calculations<br \/>\nSection 3 Mathematical and Mathematical Writings<br \/>\nWu Jing and his &quot;Nine Chapter Algorithms&quot;<br \/>\nII Wang Wensu and his &quot;Educational Poems&quot;<br \/>\nThree other books<br \/>\nSection IV: The Theory of Theoretical Mathematics<br \/>\nTang Shunzhi and his &quot;Number Theory&quot; six<br \/>\nII Gu Yingxiang and his four books on mathematics<br \/>\nThree Weeks of Learning and Its &quot;Ecco&quot;<br \/>\nIV Zhu Zaiyu and his &ldquo;New Theory of Calculation&rdquo; and &ldquo;Ji-Suan Su Jing Jing&rdquo;<br \/>\nSection V Abacus Mathematicians and Mathematical Works<br \/>\nA previous work on abacus<br \/>\nTwo-way Big Place and Its &quot;Analysis of Algorithms&quot; and &quot;Analysis of Algorithms&quot;<br \/>\nThree other abacus work<br \/>\nChapter 24 Songs of Mathematics and Popularization of Abacus<br \/>\nSection 1 Practicality and Songs of Mathematics<br \/>\nA practical, popular and commercialized mathematics<br \/>\nThe second song of mathematics<br \/>\nMathematical Songs Since the End of the Three Yuan<br \/>\nSection 2 Various &quot;miscellaneous methods&quot; in mathematics of the Ming Dynasty<br \/>\nSection 3 Development and Popularization of Abacus<br \/>\nThe situation reflected by several abacus historical materials during the Yuan and Ming dynasties<br \/>\nThe reflection of abacus in the second mathematic book<br \/>\nThe disappearance of the popularity and calculation of the three abacus<br \/>\nChapter 25 Some Mathematics Work in the Ming Dynasty<br \/>\nSection 1 Numerical Solution of Squares and Equations<br \/>\nOne-Mid-Year Growth and Opening Method<\/p>\n","protected":false},"author":5,"featured_media":2966,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[337,899,677,8],"tags":[695,572,250,586],"class_list":["post-2965","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-books-of-wisdom-","category-isbn-books-","category-wpbooklist-book-post-cat","category--taichi---differentiation-concept-cr","tag-ancient-balance-medicine-association-library-collection-","tag-mathematics---","tag-natural-science-","tag-science-and-civilization-in-china-"],"_links":{"self":[{"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/posts\/2965","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/comments?post=2965"}],"version-history":[{"count":3,"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/posts\/2965\/revisions"}],"predecessor-version":[{"id":2971,"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/posts\/2965\/revisions\/2971"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/media\/2966"}],"wp:attachment":[{"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/media?parent=2965"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/categories?post=2965"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.yinyangbalance.asia\/blog\/wp-json\/wp\/v2\/tags?post=2965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}