The Complete Collection of the History of Mathematics in China 中国数学史大系(第1卷/共8卷)ISBN: 9787303045556

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古中醫學會圖書館藏書 Ancient Balance Medicine Association Library Collection 

Draft English translation under editing:
全书编写要求与方法 Requirements and methods for writing and compilation of the whole book.
第一卷前言 Volume 1 Preface
第一编 总论 Part I: General Introduction to the Collection
第一章 中国数学史的研究对象、价值和任务
Chapter I: The research object, value and mission of Chinese History of Mathematics.
第二章 中国数学史的研究方法与要求
Chapter II: Research Methods and Requirements of Chinese History of Mathematics
第三章 中国数学史的分期
Chapter III: The periodic division of Chinese History of Mathematics
……
第二编 中国数学的萌芽
Part II The Budding of Chinese Mathematics
第一章 数学在中国的萌芽
Chapter 1 The Budding of Mathematics in China
第二章 甲骨文时代的数学
Chapter II Mathematics in the Oracle Times
第三章 金文中的数学知识
Chapter 3 Mathematical knowledge manifested in the bronze script culture
……
第三编 秦汉简牍中的数学与筹算
Part III Mathematics and calculations in the bamboo slip documentations in the Qin and Han dynasties
第一章 秦、西汉的时代背景
Chapter One The Time Background of Qin and Western Han Dynasty
第二章 竹简《算数术》与三阶纵横图
Chapter 2 Bamboo slip “Arithmetic” and the third-order magic square
第三章 简牍中的零星数学史料
Chapter 3 Sporadic historical Mathematics data in the Bamboo Slip documentations
第四章 算筹与筹算法
Chapter IV Calculations and Algorithms
第四编 秦汉天文历法与工程中的数学
Part IV Mathematics in the Astronomical Calendar and Engineering of Qin and Han Dynasty
第一章 “周髀”中的数学内容Chapter 1 Mathematical contents in “Zhou Bi”
第二章 《三统历》中的近似分数计算法
Chapter 2 Approximate Score Calculation Method in “Three Successive Calendar System”
第三章 汉历法中的不定分析――上元积年的推算
Chapter 3 Indefinite Analysis in the Han Dynasty Calendar—— Extrapolation of the Shang Yuan Accumulated Years
第四章 秦、汉时期工程技术和律学中的数学
Chapter 4: Mathematics in Engineering Technology and Musical Instrumentation during the Qin and Han Dynasties

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"The person, be it gentleman or lady, who has not pleasure in a good novel, must be intolerably stupid." - Jane Austen

The Complete Collection of the History of Mathematics in China 中国数学史大系(第1卷/共8卷)

Author: 白尚恕 编
Pages: 432
Category: Science and Civilization in China 中國科學技術史
Publisher: 北京师大
Publication Date: 1998
Finished? No
Signed? No
First Edition? No

Purchase this title at:

Notes
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Heaven * authentic humanity: the quasi-Chinese scientific thinking (The Tao of Heaven-Earth-Human Chinese-Trinity: The scientific thinking of Traditional Chinese Medicine) 天道·地道·人道:中医科学性的准思考 ISBN: 9787507734669

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中医科学性是必须进行论证的,否则,中医在中国,在世界的推广和普及就是一句空话。《天道·地道·人道:中医科学性的准思考》一书,运用赤道坐标系观测知识,展示了古代中国天文学那堪与现代天文学相媲美的科学时空观念。运用五大行星变化规律,阐明了阴阳五行相生相克原理。以无可辩驳的历史事实,介绍了中华文明“气”科学理论准确内涵。在证实历法科学性基础上,为证实中医学术理论科学性开了先河。不仅可以启发更多相关学科的学者,从更宽广的视角与更深远的空间,来聚焦中医科学性,而且非常有助于提升海内外学术界对中医科学性的理解与阐发。

中医科学性问题,历来颇有争议。中医所命名的脏腑,经络,不是与解剖出来的人体器官直接对应,而是与阴阳五行八卦、十干,十二支直接对应。阴阳五行八卦、干支这些气数,是远古中华民族先哲,根据北斗徊转,五大行星迁移与气候变化相互感应规律所制订的历法。

本书中涉及到的中华传统科学技术与思想文化知识,对很多非物质文化遗产之内在科技含量予以深刻揭示,应该说这些内容,是比非物质文化遗产还要珍贵的,值得广泛宣扬与推广。

目录
引言 中医是黑箱还是水晶球
第一编 中医学术理论源在何方
在揭示中医科学性问题上中医专业人士的缺席
一、有关死刑、死缓、起死回生的病例
二、不证实中医的科学性,中医的优势和特色就难以被认可
三、阴阳五行的科学性是探询中医学术理论科学性的切入点
四、阴阳五行与春、夏、长夏、秋、冬五个时节相通
五、与其他学科专业人士共同揭示中医学术理论科学性的必要
中医一西医,同医不同一
一、中医学不以解剖实物命名人体器官
1·所言“节”者,神气所游行出入也,非皮肉筋骨也
2.气血在人体经脉的运行与天地纲纪十二支直接对应
3.中医命名人体器官的依据是“天人相应”规律
二、中医不以生理、病理、生物化学作为基础理论
1.“感性直观经验”论抽掉了中医学活的灵魂
2.“不知年之所加,气之盛衰,虚实之所起,不可以为工矣”
三、中医不以西医的医理进行治疗
四、摆脱西学思维方式的桎梏
1.不揭示阴阳五行、八卦、干支的准确含义,中医自身就缺乏活力
2.母语流失,文化贬值,中医、中华传统科学思想文化丧失了合法话语权
3.“学术不分中西”的恶果
4.中医自我的悲哀在于没有找回能够正确指引航向的罗盘
阴阳五行、八卦、干支、二十四节气是中医理论的根
一、被掩盖的阴阳五行、八卦、干支
二、阴阳五行、八卦、干支只能还原到二十四节气
1.古人一定不会以为木生火即钻木可以取火,水生木即树木得水才能繁荣
2.阴阳五行、八卦、干支与彝族十月历
3.十二支纪十二月的历法
4.阴阳五行八卦起源于河图洛书,河图洛书与彝族十月历息息相通
5.依据二十四节气划分的十干、十二支与八卦
三、十干、十二支的物候依据
四、中医理论的根
五、通过实实在在的古代中国天文学知识来确定真理
阴阳五行——美丽优雅的普世真理
一、阴阳五行与四时五季的区别
二、阴阳五行——中医学及中华文明的科学物质生成观念
1.阴阳五行学说与基本粒子学说都是美丽优雅的普世真理
2.澄清特异功能与“气功”之间的区别,破解阴阳五行头顶上的伪科学紧箍咒
三、科学体系不会只有一种,客观真理也不会只有一个
1.共同的尺度从哪里来
……
第二编 阴阳五行、八卦、干支、二十四节气的时空背景
第三编 天地框架中的气科学理论
第四编 为本真中医精髓鸣冤辩屈

The scientific nature of Chinese medicine must be demonstrated. Otherwise, the promotion and popularization of Chinese medicine in China is an empty phrase. “Tiandao·Tao·Humanism: A quasi-thinking of the scientific nature of Chinese medicine”, using the observational knowledge of the equatorial coordinate system, shows the concept of scientific space-time that is comparable to modern astronomy in ancient Chinese astronomy. Using the laws of the five planets to change, the principles of the yin and yang eternal principles are illustrated. The irrefutable historical facts introduced the accurate connotation of the scientific theory of “chi” in the Chinese civilization. On the basis of confirming the scientific nature of the calendar, it is the first time to confirm the scientific nature of TCM academic theory. It can not only inspire more scholars of related disciplines, but also focus on the scientific nature of Chinese medicine from a broader perspective and far-reaching space, and it is very helpful in enhancing the understanding and interpretation of the scientific nature of Chinese medicine both at home and abroad.

The scientific issues of Chinese medicine have always been controversial. The organs and meridians named in traditional Chinese medicine do not directly correspond to the anatomized human organs. Instead, they directly correspond to the yin and yang elements of five lines, eight lines, ten dry lines, and twelve lines. The yin and yang of the Five Elements and Eight Guards, and the dry support of these numbers are ancient Chinese philosophers. According to the diversion of the Beidou, the calendar of the mutual induction of the five planets’ migration and climate change was established.

The traditional Chinese science, technology, and ideological and cultural knowledge involved in this book has profoundly revealed the intrinsic scientific and technological content of many intangible cultural heritages. It should be said that these contents are even more precious than intangible cultural heritages, and they deserve to be widely publicized and promoted. .

table of Contents
Introduction Chinese medicine is black box or crystal ball
Part I Where is the origin of TCM academic theory?
Absence of Chinese medicine professionals in revealing scientific issues in TCM
I. Cases Related to Death Penalty, Death Penalty, and Death-Returning
Second, without confirming the scientific nature of Chinese medicine, the advantages and characteristics of Chinese medicine are difficult to be recognized.
Third, the scientific nature of the five elements of yin and yang is the starting point for exploring the scientific nature of TCM academic theory
Fourth, the five elements of yin and yang communicate with the spring, summer, long summer, autumn and winter seasons.
V. Necessary to jointly reveal the scientific nature of TCM academic theory with professionals in other disciplines
A Western medicine doctor, different from the same medical
I. Chinese medicine does not name human organs by anatomical objects
1. Those who say “festival” in their speech, and that they march in and out of the air, are not skinny bones.
2. The direct relationship between the operation of human blood meridians and the twelve branches of the heaven and earth disciplines
3. The basis of traditional Chinese medicine for naming human organs is the “law of nature”
Second, Chinese medicine does not use physiology, pathology, and biochemistry as the basic theory
1. The Theory of “Perceptual Intuitive Experience” Pulled out the Living Soul of Chinese Medicine
2. “I don’t know what the year is, the ups and downs of the air, and the real and the real, it can’t be a job.”
Third, Chinese medicine is not treated with Western medicine
Fourth, get rid of the Western way of thinking
1. Do not reveal the exact meaning of yin and yang elements, gossip, and dry branches. Chinese medicine itself lacks vitality.
2. Loss of mother tongue, devaluation of culture, traditional Chinese medicine, traditional Chinese scientific ideology and culture lost its right to speak
3. The Causes of “Academic Division of China and the West”
4. The sadness of self-cultivation of Chinese medicine lies in not finding a compass that can correctly guide the course.
Yin and yang, five elements, gossip, stem and twenty-four solar terms are the roots of traditional Chinese medicine theory
First, the covered yin and yang elements, gossip, and dry branches
Second, the yin and yang elements, the gossip, and the dry support can only be restored to the 24th solar terms.
1. The ancients must not think that wood fires are drillable fires;
2. Yin and Yang Five Elements, Eight Diagrams, Ganzhi and the Yi People’s October Calendar
3. December Calendar of the Twelve Branches
4. The yin and yang gossip originated from He Tuluo. He Tuluo and the Yi’s October Calendar are connected.
5. According to the twenty-four solar terms divided ten dry, twelve and gossip
Three, ten dry and twelve branch phenology basis
Fourth, the root of traditional Chinese medicine theory
V. Determination of Truth Through Practical Knowledge of Ancient Chinese Astronomy
Yin Yang Five Elements – Beautiful and Elegant Worldly Truth
First, the difference between yin and yang and the five seasons
Second, yin and yang: the concept of scientific material generation in Chinese medicine and Chinese civilization
1. The yin and yang theory of five elements and basic particle theory are all beautiful and elegant universal truths
2. Clarify the distinction between specific functions and “Qigong” and break the pseudo-scientific spells on the top of the yin and yang elements
Third, there will not be only one scientific system, nor will there be only one objective truth.
1. Where do common dimensions come from?
……
Part II Space-time Background of Yinyang, Wuxing, Bagua, Ganzhi, 24 Solar Terms
The third part of the gas science theory in the framework of heaven and earth
The fourth series is based on the essence of true Chinese medicine

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"And now that you don’t have to be perfect, you can be good." - John Steinbeck, East of Eden

Heaven * authentic humanity: the quasi-Chinese scientific thinking (The Tao of Heaven-Earth-Human Chinese-Trinity: The scientific thinking of Traditional Chinese Medicine) 天道·地道·人道:中医科学性的准思考

Author: WU WEI 吴维
Pages: 293
Category: Mathematics 數學 道象理數 算術
Publisher: 学苑
Publication Date: 1991
Finished? No
Signed? No
First Edition? No

Purchase this title at:

Description
中医科学性是必须进行论证的,否则,中医在中国,在世界的推广和普及就是一句空话。《天道·地道·人道:中医科学性的准思考》一书,运用赤道坐标系观测知识,展示了古代中国天文学那堪与现代天文学相媲美的科学时空观念。运用五大行星变化规律,阐明了阴阳五行相生相克原理。以无可辩驳的历史事实,介绍了中华文明“气”科学理论准确内涵。在证实历法科学性基础上,为证实中医学术理论科学性开了先河。不仅可以启发更多相关学科的学者,从更宽广的视角与更深远的空间,来聚焦中医科学性,而且非常有助于提升海内外学术界对中医科学性的理解与阐发。 中医科学性问题,历来颇有争议。中医所命名的脏腑,经络,不是与解剖出来的人体器官直接对应,而是与阴阳五行八卦、十干,十二支直接对应。阴阳五行八卦、干支这些气数,是远古中华民族先哲,根据北斗徊转,五大行星迁移与气候变化相互感应规律所制订的历法。 本书中涉及到的中华传统科学技术与思想文化知识,对很多非物质文化遗产之内在科技含量予以深刻揭示,应该说这些内容,是比非物质文化遗产还要珍贵的,值得广泛宣扬与推广。 目录 引言 中医是黑箱还是水晶球 第一编 中医学术理论源在何方  在揭示中医科学性问题上中医专业人士的缺席  一、有关死刑、死缓、起死回生的病例  二、不证实中医的科学性,中医的优势和特色就难以被认可  三、阴阳五行的科学性是探询中医学术理论科学性的切入点  四、阴阳五行与春、夏、长夏、秋、冬五个时节相通  五、与其他学科专业人士共同揭示中医学术理论科学性的必要  中医一西医,同医不同一   一、中医学不以解剖实物命名人体器官  1·所言“节”者,神气所游行出入也,非皮肉筋骨也   2.气血在人体经脉的运行与天地纲纪十二支直接对应   3.中医命名人体器官的依据是“天人相应”规律   二、中医不以生理、病理、生物化学作为基础理论  1.“感性直观经验”论抽掉了中医学活的灵魂   2.“不知年之所加,气之盛衰,虚实之所起,不可以为工矣”   三、中医不以西医的医理进行治疗   四、摆脱西学思维方式的桎梏  1.不揭示阴阳五行、八卦、干支的准确含义,中医自身就缺乏活力   2.母语流失,文化贬值,中医、中华传统科学思想文化丧失了合法话语权   3.“学术不分中西”的恶果   4.中医自我的悲哀在于没有找回能够正确指引航向的罗盘  阴阳五行、八卦、干支、二十四节气是中医理论的根  一、被掩盖的阴阳五行、八卦、干支   二、阴阳五行、八卦、干支只能还原到二十四节气  1.古人一定不会以为木生火即钻木可以取火,水生木即树木得水才能繁荣   2.阴阳五行、八卦、干支与彝族十月历   3.十二支纪十二月的历法   4.阴阳五行八卦起源于河图洛书,河图洛书与彝族十月历息息相通   5.依据二十四节气划分的十干、十二支与八卦   三、十干、十二支的物候依据   四、中医理论的根  五、通过实实在在的古代中国天文学知识来确定真理  阴阳五行——美丽优雅的普世真理  一、阴阳五行与四时五季的区别   二、阴阳五行——中医学及中华文明的科学物质生成观念   1.阴阳五行学说与基本粒子学说都是美丽优雅的普世真理   2.澄清特异功能与“气功”之间的区别,破解阴阳五行头顶上的伪科学紧箍咒   三、科学体系不会只有一种,客观真理也不会只有一个   1.共同的尺度从哪里来 …… 第二编 阴阳五行、八卦、干支、二十四节气的时空背景 第三编 天地框架中的气科学理论 第四编 为本真中医精髓鸣冤辩屈
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The Science and Civilization in China: Mathematics Volume 中国科学技术史·数学卷 ISBN: 9787030290533

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目录
总序 卢嘉锡i
前言iii

第一编 中国数学从兴起到形成一门学科
——原始社会到西周时期的数学
第一章 中国数学的兴起——原始社会的数学
第一节 图形观念的形成
一 图形观念的产生
二 从方位观念看图形观念
三 原始的作图工具——规矩准绳
第二节 数概念的形成与原始的记数方法
一 数概念的产生
二 原始的记数方法
第三节 传说中的数学人物
一 伏羲
二 黄帝和隶首
三 尧、舜、禹和倕
第四节 从原始社会晚期的社会结构看当时数学的发展
第二章 数学形成一门学科——夏、商、西周三代的数学
第一节 十进位值制记数法的形成
一 甲骨文和金文中的数字
二 十进位值制记数法
第二节 数学成为一门学科
一 社会管理和工作的需要与数学的发展
二 数学进入教学科目
三 商高及其所掌握的数学知识

第二编 中国传统数学框架的确立
——春秋至东汉中期的数学
第三章 春秋至汉代数学概论
第一节 春秋战国秦汉数学与社会及文化背景
一 春秋战国数学与社会及文化背景
二 秦汉数学与社会及文化背景
第二节 算法式数学在春秋战国时期达到高峰
一 整数四则运算在春秋时期的普及
二 分数、比和比例的广泛使用
三 从先秦文献看春秋战国时代的算法化数学——“九数”
四 先秦时期的其他数学知识
第三节 理论思辨倾向——春秋战国数学的新动向
一 墨家与数学
二 名家的数学思想
三 先秦道家等学派的无限思想
四 春秋战国时期的理性思辨与数学
第四节 秦简《数》与汉简《算数书》
一 秦简《数》
二 《算数书》的体例、表达方式及特点
三 《算数书》的编纂
四 《算数书》的内容及其在中国数学史上的地位
第五节 《周髀算经》和陈子
一 《周髀算经》
二 陈子
第六节 《九章算术》和张苍、耿寿昌
一 《九章算术》的内容
二 《九章算术》的体例和编纂
三 《算数书》与《九章算术》
四 《九章算术》的特点与弱点及其在世界数学史上的地位
五 《九章算术》的版本
六 张苍和耿寿昌
第七节 其他数学家和数学著作
一 许商和《许商算术》、《杜忠算术》
二 尹咸和刘歆
三 张衡和马续
第四章 分数、率与盈不足
第一节 分数及其四则运算法则
一 分数及其表示
二 分数四则运算法则
第二节 今有术与衰分术、均输术
一 今有术
二 衰分术
三 均输术
第三节 盈不足术
一 盈不足诸术
二 盈不足术在一般数学问题中的应用
第五章 面积、体积、勾股与测望
第一节 面积
一 直线形面积
二 曲线形面积
三 圆方与方圆
四 曲面形面积
第二节 体积
一 多面体体积
二 圆体体积
第三节 勾股定理与解勾股形
一 勾股定理
二 解勾股形
三 勾股数组
第四节 勾股容方、容圆
一 勾股容方
二 勾股容圆
第五节 测望
一 一次测望
二 重差的萌芽
第六章 开方术、正负术、方程术与数列
第一节 开方术
一 开平方术
二 开立方术
第二节 方程术与正负术
一 方程和方程术
二 损益术
三 正负术
第三节 数列

第三编 中国传统数学理论体系的完成
——东汉末至唐中叶的数学
第七章 东汉末至唐中叶数学概论
第一节 汉末魏晋开始的社会变革与汉末至唐中叶的数学
一 汉末魏晋的社会变革与传统数学理论的奠基
二 南北朝的社会与数学
三 隋至唐中叶的社会与数学
第二节 徐岳《数术记遗》和赵爽《周髀算经注》
一 刘洪、徐岳与《数术记遗》
二 赵爽与《周髀算经注》
第三节 刘徽与《九章算术注》、《海岛算经》
一 刘徽
二 《九章算术注》
三 《海岛算经》
第四节 南北朝的数学著作和数学家
一 关于《九章算术》的研究
二 《孙子算经》
三 《夏侯阳算经》
四 《张丘建算经》
五 祖冲之、祖暅之与《缀术》
六 甄鸾及其数学著作
七 其他数学家
第五节 隋至唐中叶的数学著作和数学家
一 刘焯
二 王孝通与《缉古算经》
三 李淳风等整理十部算经
四 一行与《大衍历》
五 边冈
第六节 隋唐算学馆和明算科
一 算学馆
二 明算科
第七节 大数进法和改进计算工具的尝试
一 大数进法
二 改进计算工具的尝试
第八章 率与齐同原理
第一节 率的定义和性质
一 率的定义
二 率的求法和性质
第二节 今有术的推广与齐同原理
一 今有术的推广
二 齐同原理
第三节 算术趣题和最小公倍数
一 算术趣题
二 直接求解数学难题
三 最大公约数与最小公倍数的应用
第九章 勾股、测望和重差
第一节 解勾股形诸公式的证明
一 赵爽、刘徽对勾股定理的证明
二 赵爽、刘徽对解勾股形诸公式的证明
三 刘徽对勾股数组公式的证明
四 王孝通对解勾股形问题的拓展
第二节 勾股容方、容圆公式的证明
一 借助出入相补原理的证明
二 借助勾股相与之势不失本率原理的证明
第三节 重差术
一 重差诸术
二 制图六体与数学
第四节 其他测望问题
一 《张丘建算经》中的测望问题
二 《数术记遗注》中的测望问题
第十章 开方术、方程术的改进、不定问题和数列
第一节 开方术的几何解释和改进
一 刘徽关于开方术的几何解释
二 刘徽和王孝通关于开方式的造术
三 开方术的改进
四 刘徽“求微数”与根的近似值
五 祖冲之的开差幂和开差立
六 一行的求根公式
第二节 方程术的进展
一 刘徽的方程术理论
二 互乘相消法
三 方程新术
四 《孙子算经》和《张丘建算经》中的方程术
第三节 不定问题
一 五家共井
二 物不知数问题
三 百鸡术
第四节 等差数列和等比数列
一 等差数列
二 等比数列
第十一章 无穷小分割和极限思想
第一节 割圆术
第二节 刘徽原理
第三节 祖暅之原理与圆体体积
一 祖暅之原理
二 牟合方盖与球体积
第四节 极限思想在近似计算中的应用
一 圆周率
二 圆率和方率
三 弧田密率
第五节 刘徽的面积、体积的推导系统
一 刘徽的面积推导系统
二 对多面体体积公式的证明
三 刘徽的体积推导系统
第六节 刘徽的极限思想在数学史上的地位
一 刘徽的无穷小分割思想与先秦墨家、名家、道家
二 刘徽的极限和无穷小分割思想与古希腊的比较
第十二章 刘徽的逻辑思想和数学理论体系
第一节 刘徽的辞与理、类、故
一 理
二 类
三 故
第二节 定义
第三节 类比和归纳
一 类比
二 归纳推理
第四节 刘徽的演绎推理
一 三段论和关系推理
二 假言推理、选言推理、联言推理和二难推理
三 数学归纳法的雏形
第五节 数学证明
一 综合法
二 分析法与综合法相结合
三 反驳及刘徽的失误
第六节 刘徽的数学理论体系
第十三章 隋唐历法中的数学方法
第一节 隋唐历法的创造性转变
一 张子信的发现及其意义
二 隋唐历法计算结构的数学化
第二节 二次内插算法
一 《皇极历》
二 刘焯二次内插算法及其算理分析
三 唐代历法对二次内插算法的改进与发展
四 相减相乘法
第三节 隋唐历法中若干典型数学方法
一 刘焯《皇极历》定朔算法
二 李淳风《麟德历》晷影算法
三 一行《大衍历》的九服晷影算法
四 边冈《崇玄历》对黄赤道差与月亮黄纬的计算
第十四章 隋唐时期中国和朝鲜、日本、印度的数学交流
第一节 中国和朝鲜的数学交流
第二节 中国和日本的数学交流
一 中国历算传入日本
二 早期算学教育制度的引进
三 隋唐时期传入日本的中算书与日本古代算学内容的遗存
第三节 中国和印度的数学交流
一 印度数学传入中国
二 中国数学对印度的影响

第四编 中国传统数学的高潮
——唐中叶至元中叶的数学
第十五章 唐中叶至元中叶数学概论
第一节 传统数学的高潮与唐中叶开始的社会变革
一 唐中叶开始的社会变革和数学的发展
二 思想宽松是数学发展的必要条件
三 社会需要是数学发展的强大动力
四 宋元统治者重视数学
五 宋元数学的特点
第二节 传本《夏侯阳算经》
一 传本《夏侯阳算经》的年代与内容
二 《夏侯阳算经》的版本
第三节 贾宪和《黄帝九章算经细草》
一 贾宪和他的老师楚衍
二 《黄帝九章算经细草》大部存世考
三 《黄帝九章算经细草》的数学成就和数学思想
第四节 刘益和《议古根源》
一 刘益
二 《议古根源》
第五节 秦九韶和《数书九章》
一 秦九韶的生平
二 秦九韶人品辨
三 《数书九章》
第六节 李冶和《测圆海镜》、《益古演段》
一 李冶
二 洞渊九容和《测圆海镜》
三 《益古集》和《益古演段》
第七节 杨辉和《详解九章算法》、《杨辉算法》
一 杨辉
二 《详解九章算法》
三 《日用算法》和《杨辉算法》
第八节 朱世杰和《算学启蒙》、《四元玉鉴》
一 朱世杰
二 《算学启蒙》
三 《四元玉鉴》
第九节 其他数学家和数学著作
一 李籍和《九章算术音义》、《周髀算经音义》
二 《谢察微算经》
三 沈括和《梦溪笔谈》的数学成就
四 王恂、郭守敬和《授时历草》
五 赵友钦和《革象新书》
六 沙克什和《河防通议•算法门》
七 其他数学家和数学著作
第十六章 计算技术的改进和珠算的发明
第一节 ○和十进小数
一 〇和数码
二 十进小数
第二节 计算技术的改进
一 重因法、以加减代乘除与求一法
二 留头乘法与九归、归除
第三节 珠算的产生
一 珠算产生诸说
二 珠算最迟产生于宋代
第十七章 勾股容圆和割圆术
第一节 勾股容圆
一 洞渊九容
二 圆城图式
三 识别杂记
第二节 割圆术
一 沈括的会圆术
二 《授时历》的弧矢割圆术
三 赵友钦的割圆术
第十八章 高次方程数值解法与天元术、四元术
第一节 高次方程数值解法
一 立成释锁法
二 贾宪三角
三 增乘开方法
四 益积术和减纵术
五 正负开方术
第二节 天元术
一 天元术的历史
二 天元术的完善和应用
第三节 四元术
一 四元术的历史发展
二 四元消法
三 二元术
四 三元术
五 四元术
第十九章 垛积术、招差术
第一节 垛积术
一 隙积术
二 垛积术
第二节 招差术
一 《授时历》的招差术
二 《四元玉鉴》的招差术
第二十章 大衍总数术与纵横图
第一节 大衍总数术
一 大衍总数术的由来
二 大衍总数术
第二节 纵横图
一 河图、洛书与纵横图
二 杨辉等的纵横图
三 丁易东的纵横图
第二十一章 唐中叶至元的中外数学交流
第一节 中外数学交流概况
一 9世纪之后伊斯兰地区的数学发展概况
二 宋元时期中国与伊斯兰国家的数学交流
第二节 中国数学的外传
一 中国数学对伊斯兰国家的影响
二 中国数学对朝鲜和日本的影响
第三节 伊斯兰国家数学的传入
一 数学著作的传入
二 阿拉伯数码与纵横图
三 土盘算法及格子算

第五编 传统数学主流的转变与珠算的发展
——元中叶至明末数学
第二十二章 元中叶至明末数学概论
第一节 明代数学的社会背景
第二节 古算著作与成果在明代的失传
一 《永乐大典•算》与明初朝廷收藏的数学著作
二 古算书的失传
三 数学成果的失传
第三节 明代数学主流的转变
一 明代数学著作概况
二 明代数学的主流及杨辉的影响
第二十三章 元中叶至明末的主要数学家和数学著作
第一节 元中后期的数学家和数学著作
一 《透帘细草》
二 丁巨及其《丁巨算法》
三 贾亨的《算法全能集》
四 《详明算法》
第二节 明初的数学家和数学著作
一 严恭及其《通原算法》
二 刘仕隆及其《九章通明算法》
三 夏源泽的《指明算法》
四 其他算书
第三节 筹珠并用的数学家和数学著作
一 吴敬及其《九章算法比类大全》
二 王文素及其《算学宝鉴》
三 其他算书
第四节 理论数学研究的余绪
一 唐顺之及其《数论》六篇
二 顾应祥及其四部数学著作
三 周述学及其《历宗算会》
四 朱载堉及其《算学新说》和《嘉量算经》
第五节 珠算数学家和数学著作
一 《算法统宗》以前的珠算著作
二 程大位及其《算法统宗》和《算法纂要》
三 其他珠算著作
第二十四章 数学的歌诀化与珠算的普及
第一节 数学的实用化与歌诀化
一 数学的实用化、大众化与商业化
二 数学的歌诀化
三 元末以来的数学歌诀化算题
第二节 明代数学中的各种“杂法”
第三节 珠算的发展与普及
一 元明时代几项珠算史料所反映的情况
二 数学著作中对珠算的反映
三 珠算的普及与筹算的消失
第二十五章 明代的若干数学工作
第一节 开方及方程的数值解法
一 元中后期的增乘开方法

table of Contents
General Preface Lu Jiaxi
Foreword iii

The first series of Chinese mathematics forms a subject
– Mathematics from the primitive society to the Western Zhou Dynasty
Chapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society
Section 1 The Formation of Graphic Concepts
The emergence of a graphic concept
Second, from the concept of orientation to see the concept of graphics
Three original drawing tools – rules and regulations
Section II The Formation of Number Concepts and Original Counting Methods
The emergence of a number concept
Two original counting methods
Section 3 The legendary mathematical figure
One
Second Yellow Emperor and Lishou
Three 尧, 舜, 禹 and 倕
The fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society
Chapter 2 Mathematics Forms a Discipline——Mathematics of the Three Generations of Xia, Shang, and Xi Zhou
Section 1 Formation of Decimal Value Notation
A number in Oracle and Jinwen
Two decimal value notation
Section 2 Mathematics Becomes a Discipline
The need for social management and work and the development of mathematics
Second Mathematics enters teaching subjects
III Shang Gao and its mastered mathematics knowledge

Part Two Establishment of Traditional Chinese Mathematical Framework
– Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty
Chapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty
Section 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period
A Spring and Autumn and Warring States Mathematics and Social and Cultural Background
The Second Qin and Han Mathematics and Social and Cultural Background
Section 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period
An integer number of four operations in the Spring and Autumn Period
Second, the extensive use of scores, ratios and proportions
From the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era——“Nine Numbers”
IV Other Mathematics Knowledge in Pre-Qin Period
Section 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period
A Mohist and Mathematics
Two homes of mathematics
III The Infinite Thought of Pre-Qin Taoists and Other Schools
IV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period
Section 4 The Qin Bamboo Slips and Han Bamboo Slips
A Qin Jian “Numbers”
II. The style, expression and characteristics of the “numeric book”
Three compilation of “calculus book”
The content of the “numerical book” and its position in the history of Chinese mathematics
Section V. The Zhouyi Classics and Chen Zi
One Zhouyi Calculation
Two Chen Zi
Section VI: “Nine Chapters of Arithmetic” and Zhang Cang, Yan Shouchang
The content of “Chapter 9 Arithmetic”
II. The Style and Compilation of Nine Chapters of Arithmetic
Three “arithmetic book” and “Nine chapters of arithmetic”
4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World
Five Versions of Nine Chapters of Arithmetic
Six Zhang Canghe Yu Shouchang
Section 7 Other Mathematicians and Mathematical Works
A dealer and “Business Arithmetic” and “Du Zhong Arithmetic”
Second Yin Xianhe Liu Hao
Three Zhang Heng and Ma continued
Chapter IV Insufficient scores, rates, and profits
Section 1 Scores and Its Four Principles
A score and its representation
Two fractional four algorithm
Section II Surgery and Decline Surgery
Now there is surgery
Second decline
Three transmission techniques
Section III Insufficiency
Insufficiency
The Application of Insufficiency Technique in General Mathematical Problems
Chapter V Area, Volume, Pythagoreanism, and Observation
Section 1 Area
A linear area
Second curved area
Three round and square
Four curved surface area
Section 2 Volume
a polyhedral volume
Two round body volume
Section III Pythagorean Theorem and Unfolding Tacks
An Pythagorean Theorem
The second solution hook shape
Three Pythagorean arrays
The fourth quarter
A tick share
Two ticks
Section V
One time
The bud of the second difference
Chapter 6 Alchemy, Positive and Negative, Equations and Sequences
The first section of the prescription
Open square
Two open cubes
Section II Equations and Positive and Negative Techniques
One equation and equation
Second profit and loss
Three positive and negative surgery
Section III Series

Part III Completion of Chinese Traditional Mathematical Theory System
– Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty
Chapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty
Section 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
The Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory
II Society and Mathematics in the Southern and Northern Dynasties
The Society and Mathematics in the Middle of Tang Dynasty
Section Two: Xu Yue’s “Surgical Relics” and Zhao Shuang’s “Zhou Shuo’s Recounts”
Liu Hong, Xu Yue, and The Record of the Numbers
Two Zhao Shuang and Zhou Shuo Jing Jing Zhu
Section III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera
An Liu Hui
Two “Nine chapters of arithmetic note”
Three “The Island”
Section IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties
A Study on “Nine Chapters of Arithmetic”
Second “Sun Tzu Classic”
Three “Xiahou Yang calculations”
Four “Zhang Qiu Jian Su Jing”
V. Zu Chongzhi, Zu Yu’s and “Fuzheng”
Six books and their mathematical works
Seven other mathematicians
Section 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty
Liu Yi
II Wang Xiaotong and “Ancient Gujing”
The three Li Yufeng and other finishing ten calculations
Four Lines and “Da Yan Li”
Five Sides
Section 6 Sui Tang School of Mathematics and Accounting
A math school
Second Accounting Division
Section 7 Attempt to Improve Numerical Methods and Improve Calculation Tools
A large number of methods
Two Attempts to Improve Calculation Tools
Chapter VIII Principles of rate and principle
Section 1 Definition and Nature of Rates
The definition of probability
The Method and Nature of Bivariate
Section II Today’s Promotion and Principles of Surgery
The current promotion of surgery
Two principles
The third section of the arithmetic and the least common multiple
An arithmetic problem
II Solving Mathematical Problems Directly
Application of the three greatest common divisors and the least common multiple
Chapter Nine Pythagoreans, Observations, and Errors
Section 1 Demonstration of Formulas for Explaining Pyramids
A proof of Pythagorean Theorem by Zhao Shuang and Liu Hui
II Zhao Shuang and Liu Hui’s Proof of the Formulas of the Solution
Three Liu Hui’s Proof of the Pythagorean Array Formula
IV Wang Xiaotong’s Expansion of the Hexagonal Shape Problem
Section 2 Proof of Formulas and Formulas
One with the proof of the principle of entry and completion
B. Proof of the Principle of Keeping Preference with Pythagoreanism
Section III Correction
One difference in skill
Two Drawings Six Body and Mathematics
Section IV Other Observation Problems
An Observation Problem in Zhang Qi Jian Jian Su Jing
II. The Problem of Expectation in the “Several Notes to the Book”
Chapter 10 Improvements, uncertainties, and sequences of prescriptions, equations
Section 1 Geometric Explanation and Improvement of Alchemy
A Liu Hui’s Geometry Explanation of the Alchemy
II Liu Hui and Wang Xiaotong’s Creation of Opening Methods
The improvement of the three prescriptions
IV Liu Hui’s “seeking micro-number” and the approximate value of the root
V. Zu Chongzhi’s opening power and opening difference
The root formula of six lines
Section II Progress of Equations
Liu Hui’s equation theory
Two mutual multiplication and denomination
Three equations new surgery
IV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing
Section III Indefinite issues
A total of five wells
Two things do not know the problem
Three hundred chicken
Section 4 Arithmetic series and geometric series
An arithmetic progression
Two equal number arrays
Chapter 11 Infinitely small segmentation and limit thinking
Section 1 Cutting
Section II Principle of Liu Hui
Section III Principles and volume of the ancestral hall
An ancestral principle
Two square cover and ball volume
Section IV The Application of Limit Ideas in Approximate Calculation
a pi ratio
Second round rate and square rate
Arc field density
Section V Liu Hui’s area and volume derivation system
Liu Hui’s area derivation system
Two proofs of the polyhedral volume formula
Three Liu Hui’s volume derivation system
Section 6 Liu Hui’s Limitation Thought in the History of Mathematics
The Infinite Segmentation of Liu Hui’s Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists
The Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece
Chapter Twelve Liu Hui’s Logic Thought and Mathematical Theory System
The first section Liu Hui’s resignation and reason, class, and therefore
One reason
Category II
Three
Section 2 Definition
Section III Analogy and Induction
An analogy
Inductive reasoning
Section IV Deductive Reasoning of Liu Hui
Syllogism and Relational Reasoning
II. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning
Third, the prototype of mathematical induction
Section 5 Mathematical Proof
A comprehensive approach
B. Analysis and synthesis
III Rebuttal and Liu Hui’s mistakes
Section VI Liu Hui’s Mathematical Theory System
Chapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties
Section 1 The Creative Transformation of the Sui and Tang Calendars
The discovery of a letter and its significance
The mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties
Section II Secondary interpolation algorithm
One “The Imperial Calendar”
Liu Liu’s Quadratic Interpolation Algorithm and Its Algorithmic Analysis
The Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar
Four-phase subtractive multiplication
Section III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties
Liu Xi’s “Emperor” calendar algorithm
II Li Yingfeng’s “Lin Lun Li” image algorithm
Three-Line “Dai Yan Li” Nine Shadows Algorithm
The Computation of Yellow Equator and Moon Huang Wei by Sibian Gang’s “Chong Xuan Li”
Chapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties
Section 1 Mathematical Communication between China and North Korea
Section 2 Mathematics Exchange between China and Japan
A Chinese calendar was introduced into Japan
II Introduction of Early Learning Education System
III The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties
Section 3 Mathematical Communication between China and India
An Indian mathematics introduced to China
II The Influence of Chinese Mathematics on India

Part IV The Climax of Chinese Traditional Mathematics
——Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty
Chapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty
The first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty
The social changes and the development of mathematics started in the middle of the Tang Dynasty
II Thoughtful easing is a necessary condition for the development of mathematics
III Social needs are a powerful force for the development of mathematics
Fourth Song and Yuan rulers attach importance to mathematics
Five Characteristics of Mathematics in the Song and Yuan Dynasties
The second section of the book “Xiahou Yang calculations”
A Biography of the Date and Content of the “Xiahou Yang Scripture”
Two versions of the “Xiahou Yang Calculator”
The third quarter Jia Xianhe’s “The Yellow Emperor’s Nine Chapters, The Scriptures”
Jia Xian and his teacher Chu Yan
Two Most Existential Examinations of “The Yellow Emperor’s Nine Chapters Calculating Caojing”
Three Mathematical Achievements and Mathematical Thought in The Yellow Emperor’s Nine Chapters.
Section IV Liu Yihe’s “Proposal on Ancient Roots”
Yi Liu Yi
Second, “A discussion of Gu Gen Yuan”
Section Five Qin Jiulu and “Numbers Chapter 9”
The life of Qin Jiuhao
Second Qin Jiuyao character identification
Three “Numbers Chapter 9”
Section 6 Li Yehe’s “Measurement of Circular Oceanscope” and “Yigu Performance”
Yi Ye
The two holes Jiurong and “Test round sea mirror”
Three “Yi Gu Ji” and “Yi Gu Performance”
Section 7 Yang Hui and “Detailed Explanation of Chapter 9 Algorithm” and “Yang Hui Algorithm”
Yihui Yang
Second, “Detailed Nine Chapter Algorithms”
Three “daily algorithm” and “Yang Hui algorithm”
Section VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book
One Zhu Shijie
Two “Education Enlightenment”
Three “Siyuan Yujian”
Section 9 Other Mathematicians and Mathematical Works
A Li Jihe’s “Nine Chapters of Arithmetic and Meaning” and “Zhou Ji’s Calculation of Sound and Meaning”
Two “Xiecha Microcalculus”
Three Shen Kuohe’s Mathematical Achievements in “Meng Xi Bi Tan”
Four Wang Xi, Guo Shoujing, and “Time History”
Five Zhao Youqin and “New Elephant”
Six Shakes and The River Defense Theory • Algorithm Gate
Seven Other Mathematicians and Mathematical Works
Chapter 16 Improvements in Computing Technology and Invention of Abacus
Section 1 ○ and Decimal Decimals
One and digital
Two decimal places
Section II Improvements in Computing Technology
One for the law, one for the addition, subtraction, multiplication and division
II Heading Multiplication and Nine Return and Elimination
Section 3 The birth of abacus
Abacus produces many
The second abacus was born in the Song Dynasty at the latest
Chapter 17 Going to Share Volume and Cutting Circles
Section 1 Check Stock Volume
One
Two round city schema
Three identification notes
Section 2 Cutting
A Shen Kuo’s Tactics
Two Sagittal Cuts in the Time of Time
Three Zhao Youqin’s cutting
Chapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple
Section 1 Numerical Solution of High Order Equations
An upright release method
Second Jia Xian Triangle
Three increase open method
Four Benefits and Reductions
Five positive and negative open
Section II Tianyuan surgery
One-day history of metaphysics
The perfection and application of the two-day meta-technique
The third quarter of four
The historical development of a quadruple surgery
Two-quaternary elimination
Three binary
Four triples
Five four yuan surgery
Chapter 19 Hoarding, tricks
Section 1 Hoarding
Slot technique
II Hoarding
Section II tricks surgery
A trick of “Time-giving Calendar”
Two tricks of “Syuanyuanjian”
Chapter Twenty The total number of Da Yan and vertical and horizontal map
The first quarter total number of surgery
The origin of a major total
Total number of major
Section II.
A river map, Luo book and vertical and horizontal map
Second, Yang Hui, etc.
Three Ding Yidong’s map
Chapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty
Section 1 Overview of Chinese and Foreign Mathematics Exchanges
An Overview of the Development of Mathematics in Islamic Regions after the 9th Century
II Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties
Section 2 Chinese Mathematical Biography
The Impact of Chinese Mathematics on Islamic Countries
II The Influence of Chinese Mathematics on North Korea and Japan
Section III Introduction of Mathematics in Islamic Countries
The introduction of a mathematical work
II Arabic Digital and Crosswords
Three soil disc algorithm and lattice operator

Part V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus
– Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty
Chapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty
Section 1 The Social Background of Mathematics in the Ming Dynasty
Section II Loss of Ancient Works and Achievements in the Ming Dynasty
A “Yongle Grand Ceremony • Calculation” and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty
The loss of the second ancient book
Loss of three mathematics results
Section III The Mainstream of Mathematics in the Ming Dynasty
A survey of mathematics books in the Ming Dynasty
The Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui
Chapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty
Section I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period
One
Two Ding Ju and his Ding Ju algorithm
Three Jiaheng’s “Algorithm Set”
Four “Detailed Algorithm”
Section II Mathematicians and Mathematical Works in Early Ming Dynasty
Yan Gong and his “Tongyuan algorithm”
Liu Shilong and his “Nine Chapters Tuning Algorithm”
Three Xia Yuanze’s “specified algorithm”
Four other calculations
Section 3 Mathematical and Mathematical Writings
Wu Jing and his “Nine Chapter Algorithms”
II Wang Wensu and his “Educational Poems”
Three other books
Section IV: The Theory of Theoretical Mathematics
Tang Shunzhi and his “Number Theory” six
II Gu Yingxiang and his four books on mathematics
Three Weeks of Learning and Its “Ecco”
IV Zhu Zaiyu and his “New Theory of Calculation” and “Ji-Suan Su Jing Jing”
Section V Abacus Mathematicians and Mathematical Works
A previous work on abacus
Two-way Big Place and Its “Analysis of Algorithms” and “Analysis of Algorithms”
Three other abacus work
Chapter 24 Songs of Mathematics and Popularization of Abacus
Section 1 Practicality and Songs of Mathematics
A practical, popular and commercialized mathematics
The second song of mathematics
Mathematical Songs Since the End of the Three Yuan
Section 2 Various “miscellaneous methods” in mathematics of the Ming Dynasty
Section 3 Development and Popularization of Abacus
The situation reflected by several abacus historical materials during the Yuan and Ming dynasties
The reflection of abacus in the second mathematic book
The disappearance of the popularity and calculation of the three abacus
Chapter 25 Some Mathematics Work in the Ming Dynasty
Section 1 Numerical Solution of Squares and Equations
One-Mid-Year Growth and Opening Method

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"Differences of habit and language are nothing at all if our aims are identical and our hearts are open." - J.K. Rowling, Harry Potter and the Goblet of Fire

The Science and Technology in China: Mathematics Volume 中国科学技术史·数学卷

Author: GUO SHU CHUN ?DENG
Pages: 892
Category: Science and Civilization in China 中國科學技術史
Publisher: 科学出版社
Publication Date: 1991
Finished? No
Signed? No
First Edition? No

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目录 总序 卢嘉锡i 前言iii 第一编 中国数学从兴起到形成一门学科 ——原始社会到西周时期的数学 第一章 中国数学的兴起——原始社会的数学 第一节 图形观念的形成 一 图形观念的产生 二 从方位观念看图形观念 三 原始的作图工具——规矩准绳 第二节 数概念的形成与原始的记数方法 一 数概念的产生 二 原始的记数方法 第三节 传说中的数学人物 一 伏羲 二 黄帝和隶首 三 尧、舜、禹和倕 第四节 从原始社会晚期的社会结构看当时数学的发展 第二章 数学形成一门学科——夏、商、西周三代的数学 第一节 十进位值制记数法的形成 一 甲骨文和金文中的数字 二 十进位值制记数法 第二节 数学成为一门学科 一 社会管理和工作的需要与数学的发展 二 数学进入教学科目 三 商高及其所掌握的数学知识 第二编 中国传统数学框架的确立 ——春秋至东汉中期的数学 第三章 春秋至汉代数学概论 第一节 春秋战国秦汉数学与社会及文化背景 一 春秋战国数学与社会及文化背景 二 秦汉数学与社会及文化背景 第二节 算法式数学在春秋战国时期达到高峰 一 整数四则运算在春秋时期的普及 二 分数、比和比例的广泛使用 三 从先秦文献看春秋战国时代的算法化数学——“九数” 四 先秦时期的其他数学知识 第三节 理论思辨倾向——春秋战国数学的新动向 一 墨家与数学 二 名家的数学思想 三 先秦道家等学派的无限思想 四 春秋战国时期的理性思辨与数学 第四节 秦简《数》与汉简《算数书》 一 秦简《数》 二 《算数书》的体例、表达方式及特点 三 《算数书》的编纂 四 《算数书》的内容及其在中国数学史上的地位 第五节 《周髀算经》和陈子 一 《周髀算经》 二 陈子 第六节 《九章算术》和张苍、耿寿昌 一 《九章算术》的内容 二 《九章算术》的体例和编纂 三 《算数书》与《九章算术》 四 《九章算术》的特点与弱点及其在世界数学史上的地位 五 《九章算术》的版本 六 张苍和耿寿昌 第七节 其他数学家和数学著作 一 许商和《许商算术》、《杜忠算术》 二 尹咸和刘歆 三 张衡和马续 第四章 分数、率与盈不足 第一节 分数及其四则运算法则 一 分数及其表示 二 分数四则运算法则 第二节 今有术与衰分术、均输术 一 今有术 二 衰分术 三 均输术 第三节 盈不足术 一 盈不足诸术 二 盈不足术在一般数学问题中的应用 第五章 面积、体积、勾股与测望 第一节 面积 一 直线形面积 二 曲线形面积 三 圆方与方圆 四 曲面形面积 第二节 体积 一 多面体体积 二 圆体体积 第三节 勾股定理与解勾股形 一 勾股定理 二 解勾股形 三 勾股数组 第四节 勾股容方、容圆 一 勾股容方 二 勾股容圆 第五节 测望 一 一次测望 二 重差的萌芽 第六章 开方术、正负术、方程术与数列 第一节 开方术 一 开平方术 二 开立方术 第二节 方程术与正负术 一 方程和方程术 二 损益术 三 正负术 第三节 数列 第三编 中国传统数学理论体系的完成 ——东汉末至唐中叶的数学 第七章 东汉末至唐中叶数学概论 第一节 汉末魏晋开始的社会变革与汉末至唐中叶的数学 一 汉末魏晋的社会变革与传统数学理论的奠基 二 南北朝的社会与数学 三 隋至唐中叶的社会与数学 第二节 徐岳《数术记遗》和赵爽《周髀算经注》 一 刘洪、徐岳与《数术记遗》 二 赵爽与《周髀算经注》 第三节 刘徽与《九章算术注》、《海岛算经》 一 刘徽 二 《九章算术注》 三 《海岛算经》 第四节 南北朝的数学著作和数学家 一 关于《九章算术》的研究 二 《孙子算经》 三 《夏侯阳算经》 四 《张丘建算经》 五 祖冲之、祖暅之与《缀术》 六 甄鸾及其数学著作 七 其他数学家 第五节 隋至唐中叶的数学著作和数学家 一 刘焯 二 王孝通与《缉古算经》 三 李淳风等整理十部算经 四 一行与《大衍历》 五 边冈 第六节 隋唐算学馆和明算科 一 算学馆 二 明算科 第七节 大数进法和改进计算工具的尝试 一 大数进法 二 改进计算工具的尝试 第八章 率与齐同原理 第一节 率的定义和性质 一 率的定义 二 率的求法和性质 第二节 今有术的推广与齐同原理 一 今有术的推广 二 齐同原理 第三节 算术趣题和最小公倍数 一 算术趣题 二 直接求解数学难题 三 最大公约数与最小公倍数的应用 第九章 勾股、测望和重差 第一节 解勾股形诸公式的证明 一 赵爽、刘徽对勾股定理的证明 二 赵爽、刘徽对解勾股形诸公式的证明 三 刘徽对勾股数组公式的证明 四 王孝通对解勾股形问题的拓展 第二节 勾股容方、容圆公式的证明 一 借助出入相补原理的证明 二 借助勾股相与之势不失本率原理的证明 第三节 重差术 一 重差诸术 二 制图六体与数学 第四节 其他测望问题 一 《张丘建算经》中的测望问题 二 《数术记遗注》中的测望问题 第十章 开方术、方程术的改进、不定问题和数列 第一节 开方术的几何解释和改进 一 刘徽关于开方术的几何解释 二 刘徽和王孝通关于开方式的造术 三 开方术的改进 四 刘徽“求微数”与根的近似值 五 祖冲之的开差幂和开差立 六 一行的求根公式 第二节 方程术的进展 一 刘徽的方程术理论 二 互乘相消法 三 方程新术 四 《孙子算经》和《张丘建算经》中的方程术 第三节 不定问题 一 五家共井 二 物不知数问题 三 百鸡术 第四节 等差数列和等比数列 一 等差数列 二 等比数列 第十一章 无穷小分割和极限思想 第一节 割圆术 第二节 刘徽原理 第三节 祖暅之原理与圆体体积 一 祖暅之原理 二 牟合方盖与球体积 第四节 极限思想在近似计算中的应用 一 圆周率 二 圆率和方率 三 弧田密率 第五节 刘徽的面积、体积的推导系统 一 刘徽的面积推导系统 二 对多面体体积公式的证明 三 刘徽的体积推导系统 第六节 刘徽的极限思想在数学史上的地位 一 刘徽的无穷小分割思想与先秦墨家、名家、道家 二 刘徽的极限和无穷小分割思想与古希腊的比较 第十二章 刘徽的逻辑思想和数学理论体系 第一节 刘徽的辞与理、类、故 一 理 二 类 三 故 第二节 定义 第三节 类比和归纳 一 类比 二 归纳推理 第四节 刘徽的演绎推理 一 三段论和关系推理 二 假言推理、选言推理、联言推理和二难推理 三 数学归纳法的雏形 第五节 数学证明 一 综合法 二 分析法与综合法相结合 三 反驳及刘徽的失误 第六节 刘徽的数学理论体系 第十三章 隋唐历法中的数学方法 第一节 隋唐历法的创造性转变 一 张子信的发现及其意义 二 隋唐历法计算结构的数学化 第二节 二次内插算法 一 《皇极历》 二 刘焯二次内插算法及其算理分析 三 唐代历法对二次内插算法的改进与发展 四 相减相乘法 第三节 隋唐历法中若干典型数学方法 一 刘焯《皇极历》定朔算法 二 李淳风《麟德历》晷影算法 三 一行《大衍历》的九服晷影算法 四 边冈《崇玄历》对黄赤道差与月亮黄纬的计算 第十四章 隋唐时期中国和朝鲜、日本、印度的数学交流 第一节 中国和朝鲜的数学交流 第二节 中国和日本的数学交流 一 中国历算传入日本 二 早期算学教育制度的引进 三 隋唐时期传入日本的中算书与日本古代算学内容的遗存 第三节 中国和印度的数学交流 一 印度数学传入中国 二 中国数学对印度的影响 第四编 中国传统数学的高潮 ——唐中叶至元中叶的数学 第十五章 唐中叶至元中叶数学概论 第一节 传统数学的高潮与唐中叶开始的社会变革 一 唐中叶开始的社会变革和数学的发展 二 思想宽松是数学发展的必要条件 三 社会需要是数学发展的强大动力 四 宋元统治者重视数学 五 宋元数学的特点 第二节 传本《夏侯阳算经》 一 传本《夏侯阳算经》的年代与内容 二 《夏侯阳算经》的版本 第三节 贾宪和《黄帝九章算经细草》 一 贾宪和他的老师楚衍 二 《黄帝九章算经细草》大部存世考 三 《黄帝九章算经细草》的数学成就和数学思想 第四节 刘益和《议古根源》 一 刘益 二 《议古根源》 第五节 秦九韶和《数书九章》 一 秦九韶的生平 二 秦九韶人品辨 三 《数书九章》 第六节 李冶和《测圆海镜》、《益古演段》 一 李冶 二 洞渊九容和《测圆海镜》 三 《益古集》和《益古演段》 第七节 杨辉和《详解九章算法》、《杨辉算法》 一 杨辉 二 《详解九章算法》 三 《日用算法》和《杨辉算法》 第八节 朱世杰和《算学启蒙》、《四元玉鉴》 一 朱世杰 二 《算学启蒙》 三 《四元玉鉴》 第九节 其他数学家和数学著作 一 李籍和《九章算术音义》、《周髀算经音义》 二 《谢察微算经》 三 沈括和《梦溪笔谈》的数学成就 四 王恂、郭守敬和《授时历草》 五 赵友钦和《革象新书》 六 沙克什和《河防通议•算法门》 七 其他数学家和数学著作 第十六章 计算技术的改进和珠算的发明 第一节 ○和十进小数 一 〇和数码 二 十进小数 第二节 计算技术的改进 一 重因法、以加减代乘除与求一法 二 留头乘法与九归、归除 第三节 珠算的产生 一 珠算产生诸说 二 珠算最迟产生于宋代 第十七章 勾股容圆和割圆术 第一节 勾股容圆 一 洞渊九容 二 圆城图式 三 识别杂记 第二节 割圆术 一 沈括的会圆术 二 《授时历》的弧矢割圆术 三 赵友钦的割圆术 第十八章 高次方程数值解法与天元术、四元术 第一节 高次方程数值解法 一 立成释锁法 二 贾宪三角 三 增乘开方法 四 益积术和减纵术 五 正负开方术 第二节 天元术 一 天元术的历史 二 天元术的完善和应用 第三节 四元术 一 四元术的历史发展 二 四元消法 三 二元术 四 三元术 五 四元术 第十九章 垛积术、招差术 第一节 垛积术 一 隙积术 二 垛积术 第二节 招差术 一 《授时历》的招差术 二 《四元玉鉴》的招差术 第二十章 大衍总数术与纵横图 第一节 大衍总数术 一 大衍总数术的由来 二 大衍总数术 第二节 纵横图 一 河图、洛书与纵横图 二 杨辉等的纵横图 三 丁易东的纵横图 第二十一章 唐中叶至元的中外数学交流 第一节 中外数学交流概况 一 9世纪之后伊斯兰地区的数学发展概况 二 宋元时期中国与伊斯兰国家的数学交流 第二节 中国数学的外传 一 中国数学对伊斯兰国家的影响 二 中国数学对朝鲜和日本的影响 第三节 伊斯兰国家数学的传入 一 数学著作的传入 二 阿拉伯数码与纵横图 三 土盘算法及格子算 第五编 传统数学主流的转变与珠算的发展 ——元中叶至明末数学 第二十二章 元中叶至明末数学概论 第一节 明代数学的社会背景 第二节 古算著作与成果在明代的失传 一 《永乐大典•算》与明初朝廷收藏的数学著作 二 古算书的失传 三 数学成果的失传 第三节 明代数学主流的转变 一 明代数学著作概况 二 明代数学的主流及杨辉的影响 第二十三章 元中叶至明末的主要数学家和数学著作 第一节 元中后期的数学家和数学著作 一 《透帘细草》 二 丁巨及其《丁巨算法》 三 贾亨的《算法全能集》 四 《详明算法》 第二节 明初的数学家和数学著作 一 严恭及其《通原算法》 二 刘仕隆及其《九章通明算法》 三 夏源泽的《指明算法》 四 其他算书 第三节 筹珠并用的数学家和数学著作 一 吴敬及其《九章算法比类大全》 二 王文素及其《算学宝鉴》 三 其他算书 第四节 理论数学研究的余绪 一 唐顺之及其《数论》六篇 二 顾应祥及其四部数学著作 三 周述学及其《历宗算会》 四 朱载堉及其《算学新说》和《嘉量算经》 第五节 珠算数学家和数学著作 一 《算法统宗》以前的珠算著作 二 程大位及其《算法统宗》和《算法纂要》 三 其他珠算著作 第二十四章 数学的歌诀化与珠算的普及 第一节 数学的实用化与歌诀化 一 数学的实用化、大众化与商业化 二 数学的歌诀化 三 元末以来的数学歌诀化算题 第二节 明代数学中的各种“杂法” 第三节 珠算的发展与普及 一 元明时代几项珠算史料所反映的情况 二 数学著作中对珠算的反映 三 珠算的普及与筹算的消失 第二十五章 明代的若干数学工作 第一节 开方及方程的数值解法 一 元中后期的增乘开方法 二 《通原算法》的开方法 三 吴敬、王文素等的开方法 四 珠算开方法 五 开带从方法 第二节 一次同余方程组与不定方程 一 一次同余方程组的解法 二 不定方程问题 第三节 勾股术、测圆术与弧矢术 一 勾股术 二 测圆术 三 弧矢术 第四节 纵横图 第五节 九进位制与十进位制的小数换算 第二十六章 中国数学在朝鲜和日本的传播与影响 第一节 中国数学外传朝鲜半岛及其影响 一 中国数学在李氏朝鲜初期的流传与影响 二 17世纪朝鲜对中国历算著作的引进 三 宋元明数学著作的流传与影响 第二节 中国数学在日本的传播与影响 一 珠算与明代数学著作在日本的传播 二 宋元数学著作在日本的传播 三 宋元明著作对日本数学的影响 第三节 其他交流 第六编 西方数学的传入与中西数学的会通——明末至清末的数学 第二十七章 明末清初西方数学的传入与清初的研究 第一节 明末西方数学的传入 一 西方数学著作的编译 二 《崇祯历书》中的数学 第二节 王锡阐与薛凤祚的数学工作 一 王锡阐及其《圜解》 二 薛凤祚及其《比例对数表》等著作 第三节 梅文鼎及其数学研究 一 梅文鼎 二 数学著作的内容概述 三 立体几何与球面三角方面的创见 第四节 其他数学家的工作 一 方中通及其《数度衍》 二 李子金的数学工作 三 陈厚耀对排列组合的研究 四 陈世仁及其《少广补遗》 第二十八章 清初西方数学的传入 第一节 康熙帝与西方数学的再次传入 一 康熙的数学学习 二 安多和《算法纂要总纲》的编纂 第二节 《数理精蕴》 一 蒙养斋算学馆与《数理精蕴》的编纂 二 《数理精蕴》的内容及其西方数学来源 三 《数理精蕴》的影响 第三节 西学中源说与康熙的数学地位 一 借根方即天元术说 二 康熙与符号代数传入的失败 三 “西学中源”说及康熙的数学地位 第四节 康熙雍正时代传入的其他西方数学 一 对数表的传入 二 杜德美与杜氏三术 三 年希尧《视学》与Pozzo原著的关系 第二十九章 清中叶传统数学著作的整理和研究 第一节 清中叶数学概述 一 中国传统数学的复兴 二 西方数学的研究与中、西数学知识的互动 第二节 传统数学著作的整理和校勘 一 戴震与《四库全书》、《武英殿聚珍版丛书》中所收算书 二 清中叶对汉唐算经的校勘与研究 三 宋元数学书的传刻与研究 四 《畴人传》及其续编 第三节 传统数学的研究与发展 一 谈天三友和其他数学家 二 方程论研究 三 其他研究工作 第三十章 幂级数展开式的研究 第一节 明安图及其《割圜密率捷法》 一 明安图 二 《割圜密率捷法》 第二节 董祐诚、项名达、戴煦等的工作 一 董祐诚及其《割圜连比例术图解》 二 项名达及其《象数一原》 三 戴煦及其《求表捷术》 第三节 李善兰及其尖锥术 一 李善兰 二 尖锥术 第四节 徐有壬、顾观光、邹伯奇等的研究工作 一 徐有壬及其《割圆八线缀术》 二 顾观光、邹伯奇的研究工作 第三十一章 清末西方数学的传入 第一节 清末西方数学传入概况 一 李善兰的数学翻译工作 二 华蘅芳及其数学翻译研究 第二节 几何、代数和三角学著作的翻译 一 《几何原本》 二 《代数学》和《代数术》 三 《三角数理》及其他 第三节 微积分和概率论著作的翻译 一 《代微积拾级》 二 《微积溯源》 三 其他有关微积分的著作 四 《决疑数学》 第三十二章 清末数学研究 第一节 夏鸾翔、白芙堂诸子和其他数学家 一 夏鸾翔及其数学著作 二 白芙堂诸子及其数学著作 三 刘彝程及其数学著作 四 陈志坚、周达及其数学著作 第二节 数论的研究 一 素数的研究 二 整数勾股形的研究 三 百鸡术和大衍总数术的研究 第三节 垛积术与招差术的研究 一 李善兰的垛积术 二 夏鸾翔的垛积招差研究 三 刘彝程的垛积术研究 第四节 开方术的研究 一 夏鸾翔对开方术的研究 二 华蘅芳的数根开方术与积较开方术 第五节 对圆锥曲线和微积分的研究 一 圆锥曲线作图 二 二次曲线求积问题 三 平圆容切与累圆 第三十三章 清末数学教育 第一节 清末数学教育概述 一 数学教育的变革 二 清末的数学教育观念 三 清末的留学活动与数学留学生 第二节 晚清数学教育 一 洋务学堂的数学教育 二 书院的变革与数学教育 三 教会学校的数学教科书 四 癸卯学制的数学课程 第三节 数学丛书、数学社团与刊物 一 数学丛书的编纂 二 数学社团 三 数学刊物 主要参考文献 后记 总跋 table of Contents General Preface Lu Jiaxi Foreword iii The first series of Chinese mathematics forms a subject - Mathematics from the primitive society to the Western Zhou Dynasty Chapter 1 The Rise of Chinese Mathematics-Mathematics of Primitive Society Section 1 The Formation of Graphic Concepts The emergence of a graphic concept Second, from the concept of orientation to see the concept of graphics Three original drawing tools - rules and regulations Section II The Formation of Number Concepts and Original Counting Methods The emergence of a number concept Two original counting methods Section 3 The legendary mathematical figure One Second Yellow Emperor and Lishou Three 尧, 舜, 禹 and 倕 The fourth quarter sees the development of mathematics at that time from the social structure in the late primitive society Chapter 2 Mathematics Forms a Discipline——Mathematics of the Three Generations of Xia, Shang, and Xi Zhou Section 1 Formation of Decimal Value Notation A number in Oracle and Jinwen Two decimal value notation Section 2 Mathematics Becomes a Discipline The need for social management and work and the development of mathematics Second Mathematics enters teaching subjects III Shang Gao and its mastered mathematics knowledge Part Two Establishment of Traditional Chinese Mathematical Framework - Mathematics in the Spring and Autumn Period to the Middle Eastern Han Dynasty Chapter 3 Introduction to Mathematics in the Spring and Autumn Period to the Han Dynasty Section 1 Mathematics and Social and Cultural Background of the Qin and Han Dynasties in the Spring and Autumn and Warring States Period A Spring and Autumn and Warring States Mathematics and Social and Cultural Background The Second Qin and Han Mathematics and Social and Cultural Background Section 2 Algorithmic Mathematics Achieves Peak in Spring and Autumn and Warring States Period An integer number of four operations in the Spring and Autumn Period Second, the extensive use of scores, ratios and proportions From the Documents of the Pre-Qin Period to See the Algorithmic Mathematics of the Spring and Autumn and Warring States Era——“Nine Numbers” IV Other Mathematics Knowledge in Pre-Qin Period Section 3 Theoretical Thinking Tendency: New Trends in Mathematics in Spring and Autumn and Warring States Period A Mohist and Mathematics Two homes of mathematics III The Infinite Thought of Pre-Qin Taoists and Other Schools IV Rational speculation and mathematics during the Spring and Autumn Period and the Warring States period Section 4 The Qin Bamboo Slips and Han Bamboo Slips A Qin Jian "Numbers" II. The style, expression and characteristics of the "numeric book" Three compilation of "calculus book" The content of the "numerical book" and its position in the history of Chinese mathematics Section V. The Zhouyi Classics and Chen Zi One Zhouyi Calculation Two Chen Zi Section VI: "Nine Chapters of Arithmetic" and Zhang Cang, Yan Shouchang The content of "Chapter 9 Arithmetic" II. The Style and Compilation of Nine Chapters of Arithmetic Three "arithmetic book" and "Nine chapters of arithmetic" 4. The Characteristics and Weakness of Nine Chapters of Arithmetic and Their Position in the History of Mathematics in the World Five Versions of Nine Chapters of Arithmetic Six Zhang Canghe Yu Shouchang Section 7 Other Mathematicians and Mathematical Works A dealer and "Business Arithmetic" and "Du Zhong Arithmetic" Second Yin Xianhe Liu Hao Three Zhang Heng and Ma continued Chapter IV Insufficient scores, rates, and profits Section 1 Scores and Its Four Principles A score and its representation Two fractional four algorithm Section II Surgery and Decline Surgery Now there is surgery Second decline Three transmission techniques Section III Insufficiency Insufficiency The Application of Insufficiency Technique in General Mathematical Problems Chapter V Area, Volume, Pythagoreanism, and Observation Section 1 Area A linear area Second curved area Three round and square Four curved surface area Section 2 Volume a polyhedral volume Two round body volume Section III Pythagorean Theorem and Unfolding Tacks An Pythagorean Theorem The second solution hook shape Three Pythagorean arrays The fourth quarter A tick share Two ticks Section V One time The bud of the second difference Chapter 6 Alchemy, Positive and Negative, Equations and Sequences The first section of the prescription Open square Two open cubes Section II Equations and Positive and Negative Techniques One equation and equation Second profit and loss Three positive and negative surgery Section III Series Part III Completion of Chinese Traditional Mathematical Theory System - Mathematics in the late Eastern Han Dynasty to the middle of the Tang Dynasty Chapter VII Introduction to Mathematics in the Late Eastern Han Dynasty and Mid Tang Dynasty Section 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 The Social Transformation of the Late Han Dynasty and the Wei Dynasty and the Foundation of the Traditional Mathematical Theory II Society and Mathematics in the Southern and Northern Dynasties The Society and Mathematics in the Middle of Tang Dynasty Section Two: Xu Yue's "Surgical Relics" and Zhao Shuang's "Zhou Shuo's Recounts" Liu Hong, Xu Yue, and The Record of the Numbers Two Zhao Shuang and Zhou Shuo Jing Jing Zhu Section III Liu Hui and The Nine Chapters of Arithmetic Note, The Island Opera An Liu Hui Two "Nine chapters of arithmetic note" Three "The Island" Section IV Mathematical Works and Mathematicians of the Southern and Northern Dynasties A Study on "Nine Chapters of Arithmetic" Second "Sun Tzu Classic" Three "Xiahou Yang calculations" Four "Zhang Qiu Jian Su Jing" V. Zu Chongzhi, Zu Yu's and "Fuzheng" Six books and their mathematical works Seven other mathematicians Section 5 Mathematical Works and Mathematicians in the Middle Tang Dynasty Liu Yi II Wang Xiaotong and "Ancient Gujing" The three Li Yufeng and other finishing ten calculations Four Lines and "Da Yan Li" Five Sides Section 6 Sui Tang School of Mathematics and Accounting A math school Second Accounting Division Section 7 Attempt to Improve Numerical Methods and Improve Calculation Tools A large number of methods Two Attempts to Improve Calculation Tools Chapter VIII Principles of rate and principle Section 1 Definition and Nature of Rates The definition of probability The Method and Nature of Bivariate Section II Today's Promotion and Principles of Surgery The current promotion of surgery Two principles The third section of the arithmetic and the least common multiple An arithmetic problem II Solving Mathematical Problems Directly Application of the three greatest common divisors and the least common multiple Chapter Nine Pythagoreans, Observations, and Errors Section 1 Demonstration of Formulas for Explaining Pyramids A proof of Pythagorean Theorem by Zhao Shuang and Liu Hui II Zhao Shuang and Liu Hui's Proof of the Formulas of the Solution Three Liu Hui's Proof of the Pythagorean Array Formula IV Wang Xiaotong's Expansion of the Hexagonal Shape Problem Section 2 Proof of Formulas and Formulas One with the proof of the principle of entry and completion B. Proof of the Principle of Keeping Preference with Pythagoreanism Section III Correction One difference in skill Two Drawings Six Body and Mathematics Section IV Other Observation Problems An Observation Problem in Zhang Qi Jian Jian Su Jing II. The Problem of Expectation in the "Several Notes to the Book" Chapter 10 Improvements, uncertainties, and sequences of prescriptions, equations Section 1 Geometric Explanation and Improvement of Alchemy A Liu Hui's Geometry Explanation of the Alchemy II Liu Hui and Wang Xiaotong's Creation of Opening Methods The improvement of the three prescriptions IV Liu Hui's "seeking micro-number" and the approximate value of the root V. Zu Chongzhi's opening power and opening difference The root formula of six lines Section II Progress of Equations Liu Hui's equation theory Two mutual multiplication and denomination Three equations new surgery IV. The equations in The Sun Zi Bi Jing and Zhang Qi Jian Jian Su Jing Section III Indefinite issues A total of five wells Two things do not know the problem Three hundred chicken Section 4 Arithmetic series and geometric series An arithmetic progression Two equal number arrays Chapter 11 Infinitely small segmentation and limit thinking Section 1 Cutting Section II Principle of Liu Hui Section III Principles and volume of the ancestral hall An ancestral principle Two square cover and ball volume Section IV The Application of Limit Ideas in Approximate Calculation a pi ratio Second round rate and square rate Arc field density Section V Liu Hui's area and volume derivation system Liu Hui's area derivation system Two proofs of the polyhedral volume formula Three Liu Hui's volume derivation system Section 6 Liu Hui's Limitation Thought in the History of Mathematics The Infinite Segmentation of Liu Hui's Thoughts and the Pre-Qin Mohists, Famous Artists and Taoists The Comparison of the Limit and the Infinite Segmentation Thoughts of Liu Hui and Ancient Greece Chapter Twelve Liu Hui's Logic Thought and Mathematical Theory System The first section Liu Hui's resignation and reason, class, and therefore One reason Category II Three Section 2 Definition Section III Analogy and Induction An analogy Inductive reasoning Section IV Deductive Reasoning of Liu Hui Syllogism and Relational Reasoning II. Hypothetical Reasoning, Selective Reasoning, Coherent Reasoning and Second-reasoning Reasoning Third, the prototype of mathematical induction Section 5 Mathematical Proof A comprehensive approach B. Analysis and synthesis III Rebuttal and Liu Hui's mistakes Section VI Liu Hui's Mathematical Theory System Chapter Thirteen Mathematical Methods in the Calendar of the Sui and Tang Dynasties Section 1 The Creative Transformation of the Sui and Tang Calendars The discovery of a letter and its significance The mathematicalization of the computational structure of the calendar of the Sui and Tang Dynasties Section II Secondary interpolation algorithm One "The Imperial Calendar" Liu Liu's Quadratic Interpolation Algorithm and Its Algorithmic Analysis The Improvement and Development of the Secondary Interpolation Algorithm in the Tang Dynasty Calendar Four-phase subtractive multiplication Section III Some Typical Mathematical Methods in the Calendar of the Sui and Tang Dynasties Liu Xi's "Emperor" calendar algorithm II Li Yingfeng's "Lin Lun Li" image algorithm Three-Line "Dai Yan Li" Nine Shadows Algorithm The Computation of Yellow Equator and Moon Huang Wei by Sibian Gang's "Chong Xuan Li" Chapter 14 Mathematical Communication between China and North Korea, Japan and India during the Sui and Tang Dynasties Section 1 Mathematical Communication between China and North Korea Section 2 Mathematics Exchange between China and Japan A Chinese calendar was introduced into Japan II Introduction of Early Learning Education System III The Remains of the Medium-sized Books Into Japan and the Remains of Japanese Ancient Arithmetic Contents during the Sui and Tang Dynasties Section 3 Mathematical Communication between China and India An Indian mathematics introduced to China II The Influence of Chinese Mathematics on India Part IV The Climax of Chinese Traditional Mathematics ——Mathematics in Middle Tang Dynasty to Middle Yuan Dynasty Chapter 15 Introduction to Mathematics in the Middle Tang Dynasty to the Mid-Yan Dynasty The first quarter The climax of traditional mathematics and the social transformation that began in the middle of Tang Dynasty The social changes and the development of mathematics started in the middle of the Tang Dynasty II Thoughtful easing is a necessary condition for the development of mathematics III Social needs are a powerful force for the development of mathematics Fourth Song and Yuan rulers attach importance to mathematics Five Characteristics of Mathematics in the Song and Yuan Dynasties The second section of the book "Xiahou Yang calculations" A Biography of the Date and Content of the "Xiahou Yang Scripture" Two versions of the "Xiahou Yang Calculator" The third quarter Jia Xianhe's "The Yellow Emperor's Nine Chapters, The Scriptures" Jia Xian and his teacher Chu Yan Two Most Existential Examinations of "The Yellow Emperor's Nine Chapters Calculating Caojing" Three Mathematical Achievements and Mathematical Thought in The Yellow Emperor's Nine Chapters. Section IV Liu Yihe's "Proposal on Ancient Roots" Yi Liu Yi Second, "A discussion of Gu Gen Yuan" Section Five Qin Jiulu and "Numbers Chapter 9" The life of Qin Jiuhao Second Qin Jiuyao character identification Three "Numbers Chapter 9" Section 6 Li Yehe's "Measurement of Circular Oceanscope" and "Yigu Performance" Yi Ye The two holes Jiurong and "Test round sea mirror" Three "Yi Gu Ji" and "Yi Gu Performance" Section 7 Yang Hui and "Detailed Explanation of Chapter 9 Algorithm" and "Yang Hui Algorithm" Yihui Yang Second, "Detailed Nine Chapter Algorithms" Three "daily algorithm" and "Yang Hui algorithm" Section VIII Zhu Shijie, Encyclopedia of Enlightenment, and Four Elements Jade Book One Zhu Shijie Two "Education Enlightenment" Three "Siyuan Yujian" Section 9 Other Mathematicians and Mathematical Works A Li Jihe's "Nine Chapters of Arithmetic and Meaning" and "Zhou Ji's Calculation of Sound and Meaning" Two "Xiecha Microcalculus" Three Shen Kuohe's Mathematical Achievements in "Meng Xi Bi Tan" Four Wang Xi, Guo Shoujing, and "Time History" Five Zhao Youqin and "New Elephant" Six Shakes and The River Defense Theory • Algorithm Gate Seven Other Mathematicians and Mathematical Works Chapter 16 Improvements in Computing Technology and Invention of Abacus Section 1 ○ and Decimal Decimals One and digital Two decimal places Section II Improvements in Computing Technology One for the law, one for the addition, subtraction, multiplication and division II Heading Multiplication and Nine Return and Elimination Section 3 The birth of abacus Abacus produces many The second abacus was born in the Song Dynasty at the latest Chapter 17 Going to Share Volume and Cutting Circles Section 1 Check Stock Volume One Two round city schema Three identification notes Section 2 Cutting A Shen Kuo’s Tactics Two Sagittal Cuts in the Time of Time Three Zhao Youqin's cutting Chapter 18 Numerical Solutions of High Order Equations and Tian Yuan, Quadruple Section 1 Numerical Solution of High Order Equations An upright release method Second Jia Xian Triangle Three increase open method Four Benefits and Reductions Five positive and negative open Section II Tianyuan surgery One-day history of metaphysics The perfection and application of the two-day meta-technique The third quarter of four The historical development of a quadruple surgery Two-quaternary elimination Three binary Four triples Five four yuan surgery Chapter 19 Hoarding, tricks Section 1 Hoarding Slot technique II Hoarding Section II tricks surgery A trick of “Time-giving Calendar” Two tricks of "Syuanyuanjian" Chapter Twenty The total number of Da Yan and vertical and horizontal map The first quarter total number of surgery The origin of a major total Total number of major Section II. A river map, Luo book and vertical and horizontal map Second, Yang Hui, etc. Three Ding Yidong's map Chapter 21 Chinese and Foreign Mathematics Communication in the Middle of Tang Dynasty Section 1 Overview of Chinese and Foreign Mathematics Exchanges An Overview of the Development of Mathematics in Islamic Regions after the 9th Century II Mathematical exchanges between China and Islamic countries during Song and Yuan Dynasties Section 2 Chinese Mathematical Biography The Impact of Chinese Mathematics on Islamic Countries II The Influence of Chinese Mathematics on North Korea and Japan Section III Introduction of Mathematics in Islamic Countries The introduction of a mathematical work II Arabic Digital and Crosswords Three soil disc algorithm and lattice operator Part V The Transformation of the Mainstream of Traditional Mathematics and the Development of Abacus - Mathematics from the middle of Yuan Dynasty to the end of Ming Dynasty Chapter 22 Introduction to Mathematics from the Mid-Yuan Dynasty to the Late Ming Dynasty Section 1 The Social Background of Mathematics in the Ming Dynasty Section II Loss of Ancient Works and Achievements in the Ming Dynasty A "Yongle Grand Ceremony • Calculation" and the Mathematical Works of the Imperial Court Collection in the Early Ming Dynasty The loss of the second ancient book Loss of three mathematics results Section III The Mainstream of Mathematics in the Ming Dynasty A survey of mathematics books in the Ming Dynasty The Mainstream of Ming Dynasty Mathematics and the Influence of Yang Hui Chapter 23 Major mathematicians and mathematical writings from the middle of Yuan Dynasty to the end of Ming Dynasty Section I Mathematicians and Mathematical Works in the Later Mid-Mid-Year Period One Two Ding Ju and his Ding Ju algorithm Three Jiaheng's "Algorithm Set" Four "Detailed Algorithm" Section II Mathematicians and Mathematical Works in Early Ming Dynasty Yan Gong and his "Tongyuan algorithm" Liu Shilong and his "Nine Chapters Tuning Algorithm" Three Xia Yuanze's "specified algorithm" Four other calculations Section 3 Mathematical and Mathematical Writings Wu Jing and his "Nine Chapter Algorithms" II Wang Wensu and his "Educational Poems" Three other books Section IV: The Theory of Theoretical Mathematics Tang Shunzhi and his "Number Theory" six II Gu Yingxiang and his four books on mathematics Three Weeks of Learning and Its "Ecco" IV Zhu Zaiyu and his “New Theory of Calculation” and “Ji-Suan Su Jing Jing” Section V Abacus Mathematicians and Mathematical Works A previous work on abacus Two-way Big Place and Its "Analysis of Algorithms" and "Analysis of Algorithms" Three other abacus work Chapter 24 Songs of Mathematics and Popularization of Abacus Section 1 Practicality and Songs of Mathematics A practical, popular and commercialized mathematics The second song of mathematics Mathematical Songs Since the End of the Three Yuan Section 2 Various "miscellaneous methods" in mathematics of the Ming Dynasty Section 3 Development and Popularization of Abacus The situation reflected by several abacus historical materials during the Yuan and Ming dynasties The reflection of abacus in the second mathematic book The disappearance of the popularity and calculation of the three abacus Chapter 25 Some Mathematics Work in the Ming Dynasty Section 1 Numerical Solution of Squares and Equations One-Mid-Year Growth and Opening Method
Notes
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数理视野下的易学(精)/跨学科视野下的易学丛书 (I Ching under the perspective of Mathematics and Science – The Series of I Ching Study under Transdisciplinary perspectives) ISBN: 9787562352761

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目录
第一章象数新探
第一节易卦是什么
一、易卦是数
二、易卦集是群
三、易卦集是几何模型
四、易卦集是二项式
五、易卦与集合
六、易卦与矩阵
七、易卦与代数域
第二节大衍之数的数学内涵
一、大衍之数的含义
二、大衍之数是互乘之数
三、大衍之数勾股解
四、大衍之数与占筮的性质和数学有关
第三节筮法程序、卦序和演卦中的数学
一、筮法程序中的数学
二、卦序中的数学
三、演卦中的数学
四、简短的评论
第二章演易新法
第一节爻群(爻式)演卦法
一、京房的八宫卦变
二、《周易》的太极原理
三、爻群(爻式)的特殊结构
第二节易矩阵研究
一、经典易矩阵理论述评
二、易矩阵理论的建构
三、邵雍演卦法的矩阵表示
第三节爻群的矩阵结构
一、易矩阵的本质
二、伏羲爻群的另一种表示方法
三、奇偶演卦法的矩阵表示
四、爻群的矩阵结构
五、满卦矩阵的爻群构造法
第三章易卦新证
第一节爻群的数学本质
一、加一倍法:经典演易理论新解
二、爻群演卦法:现代演易理论简介
第二节关于一个演易定理的数学证明
一、Gray码及其性质
二、演易爻群的数学本质:Walsh函数及其生成
三、演易定理及其证明
第三节完备的易卦演绎定理及其证明
一、Walsh函数的定义及性质
二、Walsh函数新应用:区组设计
三、Walsh函数、区组设计与演易
四、Walsh函数与加强演易定理
第四章易数新知
第一节爻群变序研究
一、爻群变序与易数
二、变序数列与变序卦群
三、变序与置换
四、变序规则的交比不变性
第二节八宫数论与爻群的构造
一、八宫矩阵与爻群的构造
二、八宫矩阵与沃尔什奇函数
三、完美的十六元变序爻群
第三节典型八卦次序的数学统一性
一、文献记载的经典八卦卦序举要
二、可表为数学函数式的八卦卦序
第五章变卦新解
第一节先天八卦方位图与周期对称函数
一、周期对称函数的性质
二、实例分析
第二节易卦的向量表示及其变换
一、易卦的数学内涵
二、易卦的向量表示
三、易向量的变换
四、对角矩阵:变卦的变换算子
第三节6阶算子:六十四卦的变换
一、不倒覆、只变号变换(主对角矩阵)
二、先倒覆、后变号变换(副对角矩阵)
三、对卦变换(Ⅰ型):上卦倒覆、下卦正置变换
四、对卦变换(Ⅱ型):下卦倒覆、上卦正置变换
第六章序卦新论
第一节今本《周易》卦序结构及其演绎
一、今本《周易》卦序的结构分析
二、今本《周易》卦序的演绎生成
三、讨论:关于特区A和B在今本《周易》卦序中的地位
第二节今本《周易》卦序排列数学规律初探
一、序卦及其卦序编码
二、序卦分布的基本规律
第三节今本《周易》卦序排列数学规律再探
一、再论一阴五阳卦分布律
二、再论三阴三阳卦分布律
三、试论十二辟卦分布律
四、序卦分布容斥律
第四节今本《周易》卦序排列数学规律i探
一、一类特殊的简单数列及其通项的数学表示
二、序卦布排的数列规律及其通项表示
三、序卦布排的统合原理
四、卦序数理的进一步探究
第五节今本《周易》序卦、杂卦分布规律坐标几何通解
一、杂卦及其卦序编码
二、三十六格棋盘与河洛七七方阵图的构建
三、直线的艺术:《序卦》卦序平面几何图解
四、平面的创造:《杂卦》卦序立体几何图解
五、讨论
参考文献
索引

table of Contents
The first chapter explores the number of elephants
The first quarter is what is easy
One, easy to count
Second, easy to set is a group
Third, easy to set is a geometric model
Fourth, easy to set is binomial
V. Easy to collect and collect
Sixth, easy and matrix
Seven, easy-to-use and algebraic domains
The second part of the mathematical connotation of the number of students
First, the meaning of the number of major
Second, the number of major differences is the number of mutual multiplication
Third, the number of major gouache solution
4. The number of major differences is related to the nature and mathematics of divination.
Section III. Mathematics in Defamation Process, Order and Deduction
One, mathematics in the law of defamation
Second, the sequence of mathematics
Third, the interpretation of mathematics
Four, brief comments
The second chapter of the new law
The first section of the 爻 group (爻式) deduction method
I. The Eighth Palace Transmutation in Beijing
Second, the “Book of Changes” Tai Chi principle
Third, the special structure of the group
The second section of the matrix study
First, review of the classic matrix theory
Second, the construction of the matrix theory
Third, matrix representation of Shao Shao deduction method
Section III The Matrix Structure of the Quail Group
First, the nature of the matrix
Second, another way of expressing Fuxi Group
Third, the matrix representation of the parity deduction method
Fourth, the matrix structure of the group
Fifth, the ensemble group structure method
The third chapter is easy new certificate
Section 1 The Mathematical Essence of Qun Group
One, plus twice: a new solution to the theory of classical music
Second, the group deduction method: Introduction to modern theory
Section II Mathematical Proof of a Relevant Theorem
I. Gray code and its properties
Second, the mathematical nature of Yan Yiqun: Walsh function and its generation
Third, the recurrence theory and its proof
The Complete and Easy Interpretation of the Third Section Theorem and Its Proof
First, the definition and nature of the Walsh function
Second, the new application of Walsh function: block design
Third, Walsh function, block design and performance
Fourth, Walsh function and strengthen the relativity theory
The fourth chapter is the number of new knowledge
Section 1 Study on the Order of Groups
First, group order and number
Second, the order of the sequence and order group
Third, the order and replacement
Fourth, the invariance of cross ratio rules
The Second Section of Eighth Palace Number Theory and the Structure of Dai Group
The Structure of One and Eight Palaces and the Group
The two-octagon matrix and the Walsh function
Three, perfect sixteen yuan order group
The mathematical unity of the typical gossip sequence in the third quarter
First, the documentary records of the classic gossip sequence
Second, the table can be expressed as a mathematical function
The fifth chapter changes the new solution
Section 1 Intrinsic figure and periodic symmetry function
First, the nature of the periodic symmetry function
Second, the case analysis
The second section of the easy vector representation and its transformation
First, the easy mathematical connotation
Second, easy vector representation
Third, the transformation of the easy vector
IV. Diagonal matrix: transform operator
Section 6 6-order Operators: Sixty-four Shifts
One, no overturning, only change sign (main diagonal matrix)
Second, first inverted, post-transformation (subdiagonal matrix)
Third, pair transformation (I type): upside down, upside down transformation
Fourth, confrontation transformation (type II): squat down, upside down
Chapter 6: New Theory of Order
The first section of the current “Book of Changes” sequence structure and its interpretation
First, the structural analysis of this “Book of Changes” order
Second, today’s “Book of Changes” sequence deduction generation
III. Discussion: The status of SAR A and B in the current “Book of Changes” preface
A Preliminary Study on the Arrangement of Mathematical Rules in the Second Section of Today’s Book of Changes
First, sequence and sequence code
Second, the basic rules of order distribution
The Third Quarter: Revisiting the Mathematical Rules of the Book of Changes
First, discuss the distribution law of Yin and Wuyang
Second, discuss the distribution law of Sanyin Sanyang
Third, on the distribution law of the twelve rumor
IV. Ordinal Disposition Distribution
The fourth quarter of this book “Book of Changes” arranges the mathematics law
A mathematical representation of a special simple sequence and its general terms
Second, the order of the layout of the law and its general terms
Third, the principle of integration of sequence layout
Fourth, the further study of order and order
Section 5: The Coordinate Geometric Solution to the Distribution Rules of Preface and Miscellaneous in Zhouyi
First, hybrid and its code sequence
The construction of two, thirty-six grid checkerboard and Helu seventy-six square chart
Third, the art of straight lines: “Preface and Postscript”
Fourth, the creation of the plane: “mixed mantis” order three-dimensional geometric illustration
V. Discussion
references
index

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"It doesn't matter who you are or what you look like, so long as somebody loves you." - Roald Dahl, The Witches

(I Ching under the perspective of Mathematics and Science - The Series of I Ching Study under Transdisciplinary perspectives) 数理视野下的易学(精)/跨学科视野下的易学丛书

Author: 王俊龙
Pages: 192
Category: Mathematics 數學 道象理數 算術
Publisher: South China University of Technology Press
Publication Date: 2017
Finished? No
Signed? No
First Edition? No

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王俊龙著的《数理视野下的易学(精)》从数理的视野解读演易新法、易卦新证、易数新知、变卦新解和《序卦》新论,使易学成为当代知识体系中一个组成部分,使得易卦数理在现代科学中的主导地位而显得尤为突出。具体包括第一章象数新探,第二章演易新法,第三章易卦新证,第四章易数新知,第五章变卦新解,第六章序卦新论。 目录 第一章象数新探 第一节易卦是什么 一、易卦是数 二、易卦集是群 三、易卦集是几何模型 四、易卦集是二项式 五、易卦与集合 六、易卦与矩阵 七、易卦与代数域 第二节大衍之数的数学内涵 一、大衍之数的含义 二、大衍之数是互乘之数 三、大衍之数勾股解 四、大衍之数与占筮的性质和数学有关 第三节筮法程序、卦序和演卦中的数学 一、筮法程序中的数学 二、卦序中的数学 三、演卦中的数学 四、简短的评论 第二章演易新法 第一节爻群(爻式)演卦法 一、京房的八宫卦变 二、《周易》的太极原理 三、爻群(爻式)的特殊结构 第二节易矩阵研究 一、经典易矩阵理论述评 二、易矩阵理论的建构 三、邵雍演卦法的矩阵表示 第三节爻群的矩阵结构 一、易矩阵的本质 二、伏羲爻群的另一种表示方法 三、奇偶演卦法的矩阵表示 四、爻群的矩阵结构 五、满卦矩阵的爻群构造法 第三章易卦新证 第一节爻群的数学本质 一、加一倍法:经典演易理论新解 二、爻群演卦法:现代演易理论简介 第二节关于一个演易定理的数学证明 一、Gray码及其性质 二、演易爻群的数学本质:Walsh函数及其生成 三、演易定理及其证明 第三节完备的易卦演绎定理及其证明 一、Walsh函数的定义及性质 二、Walsh函数新应用:区组设计 三、Walsh函数、区组设计与演易 四、Walsh函数与加强演易定理 第四章易数新知 第一节爻群变序研究 一、爻群变序与易数 二、变序数列与变序卦群 三、变序与置换 四、变序规则的交比不变性 第二节八宫数论与爻群的构造 一、八宫矩阵与爻群的构造 二、八宫矩阵与沃尔什奇函数 三、完美的十六元变序爻群 第三节典型八卦次序的数学统一性 一、文献记载的经典八卦卦序举要 二、可表为数学函数式的八卦卦序 第五章变卦新解 第一节先天八卦方位图与周期对称函数 一、周期对称函数的性质 二、实例分析 第二节易卦的向量表示及其变换 一、易卦的数学内涵 二、易卦的向量表示 三、易向量的变换 四、对角矩阵:变卦的变换算子 第三节6阶算子:六十四卦的变换 一、不倒覆、只变号变换(主对角矩阵) 二、先倒覆、后变号变换(副对角矩阵) 三、对卦变换(Ⅰ型):上卦倒覆、下卦正置变换 四、对卦变换(Ⅱ型):下卦倒覆、上卦正置变换 第六章序卦新论 第一节今本《周易》卦序结构及其演绎 一、今本《周易》卦序的结构分析 二、今本《周易》卦序的演绎生成 三、讨论:关于特区A和B在今本《周易》卦序中的地位 第二节今本《周易》卦序排列数学规律初探 一、序卦及其卦序编码 二、序卦分布的基本规律 第三节今本《周易》卦序排列数学规律再探 一、再论一阴五阳卦分布律 二、再论三阴三阳卦分布律 三、试论十二辟卦分布律 四、序卦分布容斥律 第四节今本《周易》卦序排列数学规律i探 一、一类特殊的简单数列及其通项的数学表示 二、序卦布排的数列规律及其通项表示 三、序卦布排的统合原理 四、卦序数理的进一步探究 第五节今本《周易》序卦、杂卦分布规律坐标几何通解 一、杂卦及其卦序编码 二、三十六格棋盘与河洛七七方阵图的构建 三、直线的艺术:《序卦》卦序平面几何图解 四、平面的创造:《杂卦》卦序立体几何图解 五、讨论 参考文献 索引 table of Contents The first chapter explores the number of elephants The first quarter is what is easy One, easy to count Second, easy to set is a group Third, easy to set is a geometric model Fourth, easy to set is binomial V. Easy to collect and collect Sixth, easy and matrix Seven, easy-to-use and algebraic domains The second part of the mathematical connotation of the number of students First, the meaning of the number of major Second, the number of major differences is the number of mutual multiplication Third, the number of major gouache solution 4. The number of major differences is related to the nature and mathematics of divination. Section III. Mathematics in Defamation Process, Order and Deduction One, mathematics in the law of defamation Second, the sequence of mathematics Third, the interpretation of mathematics Four, brief comments The second chapter of the new law The first section of the 爻 group (爻式) deduction method I. The Eighth Palace Transmutation in Beijing Second, the "Book of Changes" Tai Chi principle Third, the special structure of the group The second section of the matrix study First, review of the classic matrix theory Second, the construction of the matrix theory Third, matrix representation of Shao Shao deduction method Section III The Matrix Structure of the Quail Group First, the nature of the matrix Second, another way of expressing Fuxi Group Third, the matrix representation of the parity deduction method Fourth, the matrix structure of the group Fifth, the ensemble group structure method The third chapter is easy new certificate Section 1 The Mathematical Essence of Qun Group One, plus twice: a new solution to the theory of classical music Second, the group deduction method: Introduction to modern theory Section II Mathematical Proof of a Relevant Theorem I. Gray code and its properties Second, the mathematical nature of Yan Yiqun: Walsh function and its generation Third, the recurrence theory and its proof The Complete and Easy Interpretation of the Third Section Theorem and Its Proof First, the definition and nature of the Walsh function Second, the new application of Walsh function: block design Third, Walsh function, block design and performance Fourth, Walsh function and strengthen the relativity theory The fourth chapter is the number of new knowledge Section 1 Study on the Order of Groups First, group order and number Second, the order of the sequence and order group Third, the order and replacement Fourth, the invariance of cross ratio rules The Second Section of Eighth Palace Number Theory and the Structure of Dai Group The Structure of One and Eight Palaces and the Group The two-octagon matrix and the Walsh function Three, perfect sixteen yuan order group The mathematical unity of the typical gossip sequence in the third quarter First, the documentary records of the classic gossip sequence Second, the table can be expressed as a mathematical function The fifth chapter changes the new solution Section 1 Intrinsic figure and periodic symmetry function First, the nature of the periodic symmetry function Second, the case analysis The second section of the easy vector representation and its transformation First, the easy mathematical connotation Second, easy vector representation Third, the transformation of the easy vector IV. Diagonal matrix: transform operator Section 6 6-order Operators: Sixty-four Shifts One, no overturning, only change sign (main diagonal matrix) Second, first inverted, post-transformation (subdiagonal matrix) Third, pair transformation (I type): upside down, upside down transformation Fourth, confrontation transformation (type II): squat down, upside down Chapter 6: New Theory of Order The first section of the current "Book of Changes" sequence structure and its interpretation First, the structural analysis of this "Book of Changes" order Second, today's "Book of Changes" sequence deduction generation III. Discussion: The status of SAR A and B in the current "Book of Changes" preface A Preliminary Study on the Arrangement of Mathematical Rules in the Second Section of Today's Book of Changes First, sequence and sequence code Second, the basic rules of order distribution The Third Quarter: Revisiting the Mathematical Rules of the Book of Changes First, discuss the distribution law of Yin and Wuyang Second, discuss the distribution law of Sanyin Sanyang Third, on the distribution law of the twelve rumor IV. Ordinal Disposition Distribution The fourth quarter of this book "Book of Changes" arranges the mathematics law A mathematical representation of a special simple sequence and its general terms Second, the order of the layout of the law and its general terms Third, the principle of integration of sequence layout Fourth, the further study of order and order Section 5: The Coordinate Geometric Solution to the Distribution Rules of Preface and Miscellaneous in Zhouyi First, hybrid and its code sequence The construction of two, thirty-six grid checkerboard and Helu seventy-six square chart Third, the art of straight lines: "Preface and Postscript" Fourth, the creation of the plane: "mixed mantis" order three-dimensional geometric illustration V. Discussion references index
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The Informal History of the Science and Civilization in China (The History of Science and Technology in China: A collection of topical papers) 中国科学技术史稿(修订版) (Chinese Edition) ISBN:9787301200018

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第四章古代科学技术体系的形成
Chapter 4 Formation of Ancient Science and Technology System

  • 五、数学体系的形成
  • 六、地图测绘技术与疆域地理志
  • 七、医药学体系的充实与提高
  • 5. Formation of Mathematical System
  • 6. Map Surveying and Mapping Technology and Territory Geography

第六章 Chapter 6

  • 六、算经的注释和数学的发展
    6. The development of nine arithmetical notes and the development of mathematics.
  • 十、中医药学的进步
    10.The progress of Traditional Chinese medicine

第七章古代科学技术发展的高峰

  • 4、七数学的辉煌成就
    4. the peak of the development of ancient science and technology.

第八章传统科学技术的缓慢发展
Chapter 8 Slow Development of Traditional Science and Technology

  • 七、商业数学与珠算
    7 Business Mathematics and Abacus

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"All happy families are alike: each unhappy family is unhappy in its own way." - Anna Karenina

The Informal History of the Science and Civilization in China 中国科学技术史稿(修订版) (Chinese Edition)

Author: 杜石然
Pages: 464
Category: Science and Civilization in China 中國科學技術史
Publisher: 北京大学出版社
Publication Date: 2012
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《中国科学技术史稿(修订版)》是中国科学院自然科学史研究所组织骨干力量,由杜石然先生领衔用三年时间编写的一部中国科学技术通史的经典著作。数十位中国科学史界的顶级人物参与了本书的编写或为本书编写提供了资料和修改意见。本书是集体智慧结晶,由名家执笔、精心雕琢,书中内容详而不繁,约而不漏,论述严谨。本书1982年由科学出版社出版。出版以来一直是大学“中国科学技术史”的指定教材和优秀普及读物。本书多次重印,并被译成日文由东京大学出版部出版发行。现在重新出版这部著作,对于普及科学知识、弘扬中国传统科技文化都将起到积极的作用。本书可以作为本科生选修课“中国科技史”的教材,也可作为科技史专业的研究生教材和中国传统科技文化普及读物。
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Celestial Creations (Graphic Classics 16) – The Illustrated Encyclopaedia of Ancient Chinese Technology (Chinese Edition) 图解天工开物 ISBN: 9787544238755

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"It might be that to surrender to happiness was to accept defeat, but it was a defeat better than many victories." - W. Somerset Maugham, Of Human Bondage

Graphic Havenly Creations (Graphic Classics 16) - Ancient Chinese Technology Daquan(Chinese Edition) 图解天工开物

Author: (MING )SONG YING XING 宋应星
Pages: 511
Category: Science and Civilization in China 中國科學技術史
Publisher: Nanhai Publishing Company 南海
Publication Date: 2007
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本书成书于400年前,是系统介绍古代中国农业、工业、手工业的一部集大成之作。以系统的、统计的方式记录了迄于明代为止的古中国重要的农业和手工业生产,并配有大量精美的图片。
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Yin and Yang of Mathematics and its applications in medicine (Traditional Chinese Medicine) (paperback) 阴阳五行数学及其在中医学上的应用 ISBN: 9787030195227

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"History, Stephen said, is a nightmare from which I am trying to awake." - James Joyce, Ulysses

yin and yang of Mathematics and its applications in medicine (Traditional Chinese Medicine) (paperback) 阴阳五行数学及其在中医学上的应用

Author: MENG KAI TAO 孟凯韬
Pages: 331
Category: Mathematics 數學 道象理數 算術
Publisher: 科学
Publication Date: 1991
Finished? No
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First Edition? No

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国家攀登计划特别支持项目国家重大基础研究前期研究专项支持项目国家重点基础研究发展计划(“973”计划)支持项目; 《阴阳五行数学及其在中医学上的应用》适合中医、哲学和数学专业的在校大学生和教师阅读,也适合中医爱好者阅读。阴阳五行数学是哲理数学的分支学科。《阴阳五行数学及其在中医学上的应用》论及阴阳五行数学的基本理论及其在中医学,特别是辨证论治中的应用。其中的数十个定理是根据从阴阳五行的特征抽象出的3个公理严格推导出来的。这些定理破解了中医界几千年悬而未解的理论之谜。由其中一些定理所推出的阴阳五行生理和病理公式揭示出入体生理和病理活动的普遍规律。由之不仅可以对中医的治疗方法进行严格的数学论证,从而从逻辑检验的角度证明中医治疗方法的科学性或对不完善者揭示出完善的途径;而且可以反推出中医经典处方并判断其是否完善和对不完善者揭示出完善的途径,从而为中医的创新开辟一条道路。这种用公式推导处方的方法将东方的整体思维与西方的分析思维相结合,将中医的理、法、方、药熔于一炉,不仅使中医变得容易理解,而且可以和计算机结合,使辨证论治规范化和现代化成为可能,使中医学有可能成为具有现代科学特征的科学。书中列举反推经典处方的实例100个,涉及经典处方109则。 The "Yin and Yang Five Elements Mathematics and Its Application in Traditional Chinese Medicine" is suitable for college students and teachers of Chinese medicine, philosophy, and mathematics. It is also suitable for Chinese medicine enthusiasts to read. The yin and yang five-element mathematics is a branch of philosophy mathematics. "Yin and Yang Five Elements Mathematics and Its Application in Traditional Chinese Medicine" discusses the basic theories of yin and yang and the five elements of mathematics and their application in traditional Chinese medicine, especially syndrome differentiation. Dozens of theorems are strictly derived from the three axioms abstracted from the features of Yin-Yang and Five Elements. These theorems break the mystery of the unresolved theory for thousands of years in the Chinese medicine community. The physiology and pathology of yin and yang, which were introduced by some of these theorems, reveals the general laws of physiology and pathology of the body. Therefore, it is not only possible to conduct strict mathematical argumentation on the treatment of traditional Chinese medicine, thus demonstrating the scientificity of the treatment of traditional Chinese medicine from the point of view of logic testing, or revealing perfect ways for the imperfect; it is also possible to reverse the introduction of traditional Chinese medicine prescriptions and determine whether it is Perfecting and revealing perfect ways for imperfect people to open up a path for innovation in Chinese medicine. This method of deducing prescriptions using formulas combines eastern thinking with western analytical thinking, and melts the principles, methods, prescriptions, and medicines of traditional Chinese medicine in a furnace. This not only makes Chinese medicine easier to understand, but also integrates with computers. It is possible to standardize and modernize syndrome differentiation and treatment, so that Chinese medicine may become a science with modern scientific characteristics. The book lists 100 examples of reflexive classic prescriptions, involving classic prescriptions 109.
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Fuzziness: the accuracy of the other half (Department of academicians Popular Science. primary and secondary school science quality education library )(Chinese Edition) 模糊性–精确性的另一半 ISBN: 7302042063

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"No one forgets the truth, they just get better at lying." - Richard Yates, Revolutionary Road

Department of academicians Popular Science. primary and secondary school science quality education library fuzziness: the accuracy of the other half (as amended)(Chinese Edition) 模糊性--精确性的另一半

Author: LIU YING MING REN PING. LU YONG XIANG
Pages: 149
Category: Mathematics 數學 道象理數 算術
Publisher: Tsinghua University Press. Jinan University Press
Publication Date: 2000
Finished? No
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Paperback. Pub Date: 2011 Jun Pages: 149 Language: Chinese in Publisher: Tsinghua University Press. Jinan University Press precise and fuzzy is a contradiction. under different circumstances. sometimes requires accurate. sometimes requires fuzzy. Added fuzzy mathematics in traditional mathematical content. will be more conducive to the cultivation of people thinking ability and scientific quality. Academicians Popular Science Department. primary and secondary school science quality education library vagueness: the accuracy of the other half (Amendment). describes the basic concepts of fuzzy sets and fuzzy logic. Principles and Applications of Fuzzy Control and development prospects. Contents: a few basic concepts 1.1 collection of propositions and logical relations 1.3 1.4 collection features 1.2 mapping function from accurate to 2.1 fuzzy fuzzy subset the 2.2 image recognit...
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Introduction to the Fuzzy methodology for Traditional Chinese Medicine 中医模糊方法导论 ISBN: 9787313051660

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Introduction to the Fuzzy methodology for Traditional Chinese Medicine 中医模糊方法导论

Author: 朱训生
Pages: 212
Category: Mathematics 數學 道象理數 算術
Publisher: 上海交通大學出版社
Publication Date: 2008
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上海科技专著出版资金资助上海交通大学学术出版基金资助 目录 第1章 绪论 1.1 实际引例 1.2 传统中医中的模糊现象俯拾皆是 1.3 模糊性的哲学基础 1.4 中医中模糊性事物的数学描述 1.5 中医与模糊的天然联系 1.6 模糊技术的应用及中医模糊方法的发展 第2章 中医中的经典集与模糊集 2.1 中医中的经典集合、映射和模糊集合 2.2 两类集合的运算及中医中的实例 2.3 中医中的直积和关系 2.4 模糊集合与经典集合的联系 第3章 中医模糊方法的基础——隶属(度)函数的确定 3.1 隶属函数可以成为中医量化的一个手段一实际引例 3.2 用统计方法求中医模糊集的隶属函数 3.3 中医处方优选的二元对比排序法 3.4 二元对比倒数法求健康隶属度 3.5 中医症状量化一模糊数的概念及其应用 3.6 本章小结 第4章 中医模糊模式识别 4.1 中医模糊模式识别概述 4.2 从邮政编码识别到舌象仪的模板匹配原理 4.3 中医模糊模式识别中“个体识别——最大隶属度原则”的应用 4.4 中医模糊模式识别中“群体识别——最大贴近度原则”的应用 4.5 肝炎后肝硬化中医模糊模式识别实例 第5章 中医模糊聚类分析 5.1 中医中模糊关系合成的常用性质 5.2 分解定理和扩张原理及其在中医中的一个应用 5.3 关系及中医模糊关系的自反、对称、传递等性质 5.4 中医模糊等价关系和相似关系 5.5 模糊聚类分析中模糊相似矩阵的建立 5.6 模糊聚类分析中的传递偏差及模糊聚类分析的步骤 第6章 中医模糊综合评判 6.1 综合评判、模糊综合评判与中医模糊综合评判 6.2 中医一级模糊综合评判及其逆问题 6.3 中医中算子模型、权重、评判指标及评判矩阵的讨论 6.4 中医多级模糊综合评判 第7章 中医模糊预测与决策 7.1 预测、模糊预测与中医模糊预测 7.2 模糊预测原理、方法及生理和医学上的应用实例 7.3 模糊决策原理、方法及中医中的一个应用 7.4 其他模糊预测与决策方法介绍 附录 参考文献 后记 序言 我与朱训生教授都是20世纪60年代的大学生和我国机械工程的首批工学博士。他原毕业于复旦大学数学系,在那史无前例的特殊历史时期,分配到某机械厂生产现场锻炼十几年并自学机械;恢复研究生招生后报考上海交通大学机械系。我则在西安交通大学机械系。我们不但神交已久,且在国家自然科学基金课题汇报会、学术交流会、成果展示会等科技活动中,经常谋面;以他为第1完成人的课题组,将现代数学与精密加工、精密测量结合,1992年和1997年先后获国家教育委员会科技进步奖(甲类)2等奖和发明2等奖,1998年获国家技术发明奖4等奖;此后在学术会议上却多年不见其身影,原来他大病一场。然而他从小喜欢的中医,特别是1989年起应上海针灸经络研究所之邀合作针灸课题学习的医学知识给他帮助不小,这次他索性针对自己的病钻研起医学来,博采各医院、众医生及多种医学文献之长,几年后竟痊愈了,很多人包括很多医生都啧啧称奇。近年我正从事交叉学科研究,呼吁重视理工交叉,工管交叉,机、电、热、声、光、计一体化,医工结合,2005年我与他重逢,得知他病中与病后竟还完成了多个中医与工程结合的课题,我大喜过望,我呼吁的交叉范围更扩大了。 利用现代科技手段来实现中医药现代化是大家所盼望的。但在实践中一些人简单地将它变成了西医化,引起老中医反感。朱训生教授扎扎实实地深入到中医药领域,老老实实地学习中医药理论,切切实实地与中医医师合作,尝试将工程方法与古老的中医文化接轨,他和合作者及双方学生一起从大量实际数据出发,严严实实地进行数据分析、处理、归纳、挖掘,借用在很多工程领域使用得很成熟的一些方法来解决传统中医药学术中的一些问题,取得了初步成功。 table of Contents Chapter 1 Introduction 1.1 Actual cited examples 1.2 Ambiguities in Traditional Chinese Medicine 1.3 The Philosophical Foundation of Ambiguity 1.4 Mathematical Description of Ambiguous Things in Traditional Chinese Medicine 1.5 The natural connection between traditional Chinese medicine and vagueness 1.6 Application of Fuzzy Technology and Development of Fuzzy Methods in Traditional Chinese Medicine Chapter 2 Classical and Fuzzy Sets in Traditional Chinese Medicine 2.1 Classical Collection, Mapping and Fuzzy Collection in Traditional Chinese Medicine 2.2 Two sets of operations and examples in Chinese medicine 2.3 Direct Product and Relationship in Traditional Chinese Medicine 2.4 The relationship between fuzzy sets and classic collections Chapter 3 Basics of Fuzzy Method of Traditional Chinese Medicine: Determination of Subordinate (Degree) Functions 3.1 Membership functions can be a means of quantification in Chinese medicine - a practical example 3.2 Finding membership functions of TCM fuzzy sets by statistical methods 3.3 Binary Contrast Sorting Method for Traditional Chinese Medicine Prescription 3.4 Binary comparison reciprocal method for healthy membership 3.5 The concept of quantifying a fuzzy number in TCM symptoms and its application 3.6 Summary of this chapter Chapter 4 Fuzzy Pattern Recognition of Traditional Chinese Medicine 4.1 Overview of Fuzzy Pattern Recognition in Traditional Chinese Medicine 4.2 Template Matching from Postal Code Recognition to Tongue Imager 4.3 Application of "Individual Identification - Principle of Maximum Degree of Membership" in TCM Pattern Recognition 4.4 Application of "Group Identification - Principle of Maximum Closeness Degree" in TCM Pattern Recognition 4.5 Examples of Fuzzy Pattern Recognition of Traditional Chinese Medicine for Posthepatitic Cirrhosis Chapter 5 TCM Fuzzy Cluster Analysis 5.1 Common Properties of Fuzzy Relation Synthesis in Traditional Chinese Medicine 5.2 Decomposition Theorem and Expansion Principle and Its Application in Traditional Chinese Medicine 5.3 Relationships and reflexivity, symmetry, transmission, etc. 5.4 TCM Fuzzy Equivalent Relationship and Similarity Relationship 5.5 Establishment of Fuzzy Similarity Matrix in Fuzzy Clustering Analysis 5.6 Transfer Bias in Fuzzy Cluster Analysis and the Steps of Fuzzy Cluster Analysis Chapter 6 Fuzzy Comprehensive Evaluation of Traditional Chinese Medicine 6.1 Comprehensive Evaluation, Fuzzy Comprehensive Evaluation and Fuzzy Comprehensive Evaluation of Traditional Chinese Medicine 6.2 TCM First Level Fuzzy Comprehensive Evaluation and Its Inverse Problem 6.3 Discussion on Operator Model, Weights, Judgement Criteria and Judgment Matrix in Traditional Chinese Medicine 6.4 Multilevel Fuzzy Comprehensive Evaluation of Traditional Chinese Medicine Chapter 7 TCM Fuzzy Prediction and Decision 7.1 Prediction, Fuzzy Prediction and TCM Fuzzy Prediction 7.2 Principles and Methods of Fuzzy Prediction and Examples of Physiological and Medical Applications 7.3 Fuzzy Decision Principles, Methods and an Application in Traditional Chinese Medicine 7.4 Introduction to Other Fuzzy Prediction and Decision Methods appendix references postscript Preface Professor Zhu Xunsheng and I were both university students in the 1960s and the first batch of engineering doctorates in China's mechanical engineering. He graduated from the Department of Mathematics of Fudan University. In an unprecedented historical period, he was assigned to a mechanical factory to produce on-site exercise for more than ten years and self-learning machinery. After resuming postgraduate enrollment, he applied to the Department of Mechanical Engineering of Shanghai Jiaotong University. I am in the Mechanical Department of Xi'an Jiaotong University. We have not only divine exchanges for a long time, but we have often met in scientific and technological activities such as the National Natural Science Foundation project briefing, academic exchanges, and product exhibitions. We have used the task of the first person to set up modern mathematics and precision machining and precision. Measure combination, 1992 and 1997 won the National Education Commission Science and Technology Progress Award (A) 2nd Prize and Invention 2nd Prize, and won the 4th National Technology Invention Award in 1998; it has not been seen in the academic conference for many years. It turned out that he was seriously ill. However, the Chinese medicine that he liked since he was a child, especially since 1989, has been assisted by the Shanghai Acupuncture and Meridian Research Institute in the cooperation of acupuncture and moxibustion. This time, he has been assisting his ailments in the development of medicine. The length of the doctors and many medical literatures was cured several years later. Many people, including many doctors, were amazed. In recent years, I am engaged in cross-discipline research, calling for attention to the intersection of science and engineering, cross-sectoral management, integration of mechanics, electricity, heat, sound, light, and instrumentation, and integration of medical work. In 2005, I reunited with him and learned that he was ill and sick. I have also completed a number of topics in the combination of traditional Chinese medicine and engineering. I am overjoyed and the scope of my appeal is even wider. It is everyone's hope to use modern scientific and technological means to realize the modernization of Chinese medicine. However, in practice, some people simply turned it into western medicine, which caused an aversion to old Chinese medicine. Professor Zhu Xunsheng took a solid and in-depth understanding of the field of traditional Chinese medicine, honestly studied the theories of traditional Chinese medicine, and practically collaborated with TCM physicians to try to integrate engineering methods with ancient Chinese medicine culture. He and his partners and students from both sides learned a lot from actual data. Starting from this, data analysis, processing, induction, and excavation were conducted rigorously, and some methods used in many fields of engineering were used to solve some problems in traditional Chinese medicine academics, and initial successes were achieved.
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(Square and Circle into all the Worlds) 因方就圆幻万象 ISBN: 9787811104912

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"I wished to know the meaning of things. I am the meaning. I wished to find a warrant for being. I need no warrant for being, and no word of sanction upon my being. I am the warrant and the sanction." - Ayn Rand, Anthem

(Square and Circle into all the Worlds) 因方就圆幻万象

Author: 其亮·张
Pages: 174
Category: Mathematics 數學 道象理數 算術
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Publication Date: 2009
Finished? No
Signed? No
First Edition? No

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本书共六章,分别为绪论、数学的萌芽时期、初等数学时期、近代数学时期、现代数学时期和数学常识,其中包括解析几何的诞生、微积分的兴起与繁荣、概率论的起源与发展、代数学的前进等. There are six chapters in this book, which are introduction, mathematics sprouting, elementary mathematics, modern mathematics, modern mathematics, and mathematics. These include the birth of analytical geometry, the rise and prosperity of calculus, and the origin and development of probability theory. , advancement of algebra and so on.
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