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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"It’s only after we’ve lost everything that we’re free to do anything." - Chuck Palahniuk, Fight Club

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

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会通与嬗变(明末清初东传数学与中国数学及儒学理的观念的演化)(精) (Integration and Transmutation – The meeting of Western mathematical ideas with traditional Chinese mathematical and Confucius philosophies in the late Ming and early Qing Dynasties) ISBN: 9787532578337

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

目录

序:“科學與儒學關係研究”的若干方法論問題 馬來平
導言
一、古數復原———明末清初數學史研究的一種思路
二、明末清初東傳數學與中國文化互動研究綜述
第一章 會通與嬗變的文化環境
一、中國數學學科名稱及其文化含義的演變
二、拘儒•達儒•真儒
三、達儒對東西方數學、科學的認識
四、西學中源説與儒學的理器劃分
第二章 外算會通的成就
一、傳統外算概況
二、中西數學會通觀念的形成與發展
三、社會與文化互動中的數學會通
四、數學會通與東傳數學的先進性
第三章 外算會通案例研究
一、爲什麽翻譯《幾何原本》
二、徐、利譯《幾何原本》若干史實新證
三、“幾何”曾經不是幾何學
四、明末清初中算家與公理化
第四章 内算會通案例研究
一、明末清初内算概覽
二、薛鳳祚中西占驗會通與曆法改革
三、用科學方法達成占驗目的的嘗試
四、數學會通與内算外算的易位
第五章 數學會通與“理”觀念的演化
一、數學會通與“物理”凸顯
二、數學會通與“至理”變换
三、數學會通與“宰理”威脅
四、明末清初的科學話語空間
結語
一、中西數學會通
二、傳統數學和理學的“嬗變”
參考文獻
後記

table of Contents
Preface: Some Methodological Issues on “Research on the Relationship between Science and Confucianism”
preface
I. Restoration of Ancient Numbers——An Idea for Studying the History of Mathematics in the Late Ming and Early Qing Dynasty
II.Summary of the Research on the Interaction between Eastward Mathematics and Chinese Culture in Late Ming and Early Qing Dynasty
Chapter 1 The Cultural Environment of Communication and Change
I. The evolution of the names of Chinese mathematics disciplines and their cultural meanings
Second, Confucianism, Confucianism, Confucianism, Confucianism
Daru’s Understanding of Mathematics and Science in the East and the West
IV. The Division of Sources in Western Learning and Confucianism
Chapter II Achievements of External Communication
I. Traditional Foreign Overview
Second, the formation and development of the concept of communication between Chinese and Western mathematics
Third, mathematics in social and cultural interaction
IV. The Advancement of Mathematics Communication and Eastward Mathematics
Chapter III Case Study of External Computer Communication
First, why the translation of “geometry original”
Second, Xu and Li translated “Geometry Original” some historical facts
Third, “geometry” was not geometry
IV. Chinese abacus and axiomatization in the late Ming and early Qing Dynasty
Chapter IV Case study of internal calculation
I. Overview of the internal calculation in the late Ming and early Qing Dynasty
Second, Xue Fengzhen’s Chinese and Western Affairs Inspection Association and Calendar Reform
Third, using scientific methods to achieve the purpose of inspection purposes
Fourth, mathematics and internal and external calculations of translocation
Chapter 5 The Evolution of Mathematical Communication and the Concept of “Li”
First, mathematics and “physical” highlight
Second, mathematics will pass and “to the” transformation
Third, the mathematics will pass the threat of “Zioni”
Fourth, the scientific discourse space in the late Ming and early Qing
Conclusion
First, the Chinese and Western Mathematics Association
Second, the “transmutation” of traditional mathematics and science
references
postscript

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"Good friends, good books, and a sleepy conscience: this is the ideal life." - Mark Twain

(Integration and Transmutation - The meeting of Western mathematical ideas with traditional Chinese mathematical and Confucius philosophies in the late Ming and early Qing Dynasties) 会通与嬗变(明末清初东传数学与中国数学及儒学理的观念的演化)(精)

Author: 宋芝业
Pages: 460
Category: Mathematics 數學 道象理數 算術
Publisher: Shanghai ancient books publishing house
Publication Date: 2016
Finished? No
Signed? No
First Edition? No

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Description
由宋芝业所著的《会通与嬗变(明末清初东传数学与中国数学及儒学理的观念的演化)(精)》一书主要主要涵盖两方面研究成果。一是推进中国数学史研究的新思想方法--古数复原。二是在这一思想方法指导下对明末清初西方数学东传背景下的中国传统数学的嬗变轨迹进行了研究,得出如下结论:这一时期中国数学发展的特点是中西数学会通,中国传统数学和儒学理的观念在会通过程中发生了嬗变。 目录 序:“科學與儒學關係研究”的若干方法論問題 馬來平 導言 一、古數復原———明末清初數學史研究的一種思路 二、明末清初東傳數學與中國文化互動研究綜述 第一章 會通與嬗變的文化環境 一、中國數學學科名稱及其文化含義的演變 二、拘儒•達儒•真儒 三、達儒對東西方數學、科學的認識 四、西學中源説與儒學的理器劃分 第二章 外算會通的成就 一、傳統外算概況 二、中西數學會通觀念的形成與發展 三、社會與文化互動中的數學會通 四、數學會通與東傳數學的先進性 第三章 外算會通案例研究 一、爲什麽翻譯《幾何原本》 二、徐、利譯《幾何原本》若干史實新證 三、“幾何”曾經不是幾何學 四、明末清初中算家與公理化 第四章 内算會通案例研究 一、明末清初内算概覽 二、薛鳳祚中西占驗會通與曆法改革 三、用科學方法達成占驗目的的嘗試 四、數學會通與内算外算的易位 第五章 數學會通與“理”觀念的演化 一、數學會通與“物理”凸顯 二、數學會通與“至理”變换 三、數學會通與“宰理”威脅 四、明末清初的科學話語空間 結語 一、中西數學會通 二、傳統數學和理學的“嬗變” 參考文獻 後記 table of Contents Preface: Some Methodological Issues on "Research on the Relationship between Science and Confucianism" preface I. Restoration of Ancient Numbers——An Idea for Studying the History of Mathematics in the Late Ming and Early Qing Dynasty II.Summary of the Research on the Interaction between Eastward Mathematics and Chinese Culture in Late Ming and Early Qing Dynasty Chapter 1 The Cultural Environment of Communication and Change I. The evolution of the names of Chinese mathematics disciplines and their cultural meanings Second, Confucianism, Confucianism, Confucianism, Confucianism Daru’s Understanding of Mathematics and Science in the East and the West IV. The Division of Sources in Western Learning and Confucianism Chapter II Achievements of External Communication I. Traditional Foreign Overview Second, the formation and development of the concept of communication between Chinese and Western mathematics Third, mathematics in social and cultural interaction IV. The Advancement of Mathematics Communication and Eastward Mathematics Chapter III Case Study of External Computer Communication First, why the translation of "geometry original" Second, Xu and Li translated "Geometry Original" some historical facts Third, "geometry" was not geometry IV. Chinese abacus and axiomatization in the late Ming and early Qing Dynasty Chapter IV Case study of internal calculation I. Overview of the internal calculation in the late Ming and early Qing Dynasty Second, Xue Fengzhen’s Chinese and Western Affairs Inspection Association and Calendar Reform Third, using scientific methods to achieve the purpose of inspection purposes Fourth, mathematics and internal and external calculations of translocation Chapter 5 The Evolution of Mathematical Communication and the Concept of "Li" First, mathematics and "physical" highlight Second, mathematics will pass and "to the" transformation Third, the mathematics will pass the threat of "Zioni" Fourth, the scientific discourse space in the late Ming and early Qing Conclusion First, the Chinese and Western Mathematics Association Second, the "transmutation" of traditional mathematics and science references postscript
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Tai ji tai xuan ti xi: Pu shi gui lü di yi xue tan ao (Mandarin Chinese Edition) (Taichi Taiyin System) 太极太玄体系 ISBN: 9787500411048

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

序 引言

第一章 从周期运动和三维角度对太极太玄体系作一简单介绍

一、太极体系的四种表示形式

二、太极大玄体系和二、三进制

三、大玄体系的扼要介绍

第二章 化学元素的周期变化及其太极大玄时空结构

一、关于化学元素周期的完整性--周期的结构和始点终点问题

二、化学元素周期太极太玄结构表现出来的几种性质

三、易学空间与现实空间

第三章 月地日系统的周期运动及其时空的太极太玄结构

一、以易学原理研究月地日运动的新进展

二、月地运行周期与太极太玄模型的对比

三、月亮远(近)地点的回归运动和60 特征点的卦象结构四、干支纪年方法的来源及其科学内容

五、五行的含义及其应用中医“五运六气” 起源的破译

第四章 极移钱德勒周期与中医五运六气周期关系的对应

一、关于月地日周期

二、关于极移钱德勒周期

三、中医五运六气周期及其与极移钱德勒周期的对应

四、关于月地日周期的小结,一历元可推算吗?

第五章 也谈《老子》的是与非

一、《老子》集古代方法论研究之大成,从而成为全面阐述朴素辩证法的专著

二、《易》、《老》、《太玄》对辩证法运动的认识与现代认识的比较

三、也谈《老子》的评价第六章 太极太玄模型的内容、普适性和应用前景

一、太极大玄体系是物质周期运动的普适数学模型——关于时空的讨论

二、太极太玄模型的内容及其演算规则

三、研究太极太玄模型的实用意义

Preface

Chapter 1 A Brief Introduction to Taiji Tai Xuan System from Periodic Movement and Three-dimensional Perspective

I. Four representations of Tai Chi system

Second, Taiyuan Xuan system and second and third systems

Third, the brief introduction of Daxuan system

Chapter II The Periodic Changes of Chemical Elements and Their Hyperspace and Space-time Structure

I. The completeness of the cycle of chemical elements–The structure of the cycle and the end of the cycle

Second, the chemical element cycle Taiji Tai Xuan structure shows several properties

Third, easy to learn space and reality space

Chapter III The Periodic Movement of the Moon-Sun System and Its Temporal and Taiji Structure

I. Studying the New Development of the Moon-Day Movement with the Principle of Yi-ology

Second, the monthly operation cycle and Taiji Tai Xuan model comparison

III. The regressive movement of the moon’s distant (near) locations and the structure of the 60-feature elephants. IV. Sources and scientific content of the method of dry branches

The Meanings of the Five and Five Elements and the Application of the Breakthrough of the Origin of the Chinese Medicine “Five Movements and Six Gases”

Chapter 4 The Correspondence between the Polar Shift Chandler Cycle and the TCM Cycle of Five Transports and Six Gases

I. About the Moon Day Cycle

Second, on the polar movement Chandler cycle

III. Correspondence between TCM’s five-transport and six-gas cycle and its polar movement to Chandler’s cycle

Fourth, on the summary of the monthly cycle of the moon, can an epoch be calculated?

The fifth chapter also talk about “Laozi” is right and wrong

First, Lao Tzu’s collection of ancient methodological studies has become a monograph to comprehensively expound the simple dialectic method.

II. Comparison of Understanding and Modern Understanding of Dialectics between Yi, Lao, and Tai Xuan

Third, also talk about the evaluation of “Laozi” The sixth chapter Taiji Tai Xuan model content, universality and application prospects

1. The tai-hyeon system is a universal mathematical model of the material cycle movement – discussion on space-time

Second, Tai Chi Tai Xuan model content and its calculation rules

Third, study the practical significance of the Taiji Tai Xuan model

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"Nothing is so painful to the human mind as a great and sudden change." - Mary Shelley, Frankenstein

Tai ji tai xuan ti xi: Pu shi gui lü di yi xue tan ao (Mandarin Chinese Edition) (Taichi Taiyin System) 太极太玄体系

Author: Jun Zheng 郑军
Pages: 155
Category: Science and Civilization in China 中國科學技術史
Publisher: jing xiao Xin hua shu dian
Publication Date: 1992
Finished? No
Signed? No
First Edition? No

Purchase this title at:

Description
Discussing "Chou i" and "T°ai hsèuan ching" and their relations to natural sciences. 序 引言 第一章 从周期运动和三维角度对太极太玄体系作一简单介绍 一、太极体系的四种表示形式 二、太极大玄体系和二、三进制 三、大玄体系的扼要介绍 第二章 化学元素的周期变化及其太极大玄时空结构 一、关于化学元素周期的完整性--周期的结构和始点终点问题 二、化学元素周期太极太玄结构表现出来的几种性质 三、易学空间与现实空间 第三章 月地日系统的周期运动及其时空的太极太玄结构 一、以易学原理研究月地日运动的新进展 二、月地运行周期与太极太玄模型的对比 三、月亮远(近)地点的回归运动和60 特征点的卦象结构四、干支纪年方法的来源及其科学内容 五、五行的含义及其应用中医“五运六气” 起源的破译 第四章 极移钱德勒周期与中医五运六气周期关系的对应 一、关于月地日周期 二、关于极移钱德勒周期 三、中医五运六气周期及其与极移钱德勒周期的对应 四、关于月地日周期的小结,一历元可推算吗? 第五章 也谈《老子》的是与非 一、《老子》集古代方法论研究之大成,从而成为全面阐述朴素辩证法的专著 二、《易》、《老》、《太玄》对辩证法运动的认识与现代认识的比较 三、也谈《老子》的评价第六章 太极太玄模型的内容、普适性和应用前景 一、太极大玄体系是物质周期运动的普适数学模型——关于时空的讨论 二、太极太玄模型的内容及其演算规则 三、研究太极太玄模型的实用意义 Preface Chapter 1 A Brief Introduction to Taiji Tai Xuan System from Periodic Movement and Three-dimensional Perspective I. Four representations of Tai Chi system Second, Taiyuan Xuan system and second and third systems Third, the brief introduction of Daxuan system Chapter II The Periodic Changes of Chemical Elements and Their Hyperspace and Space-time Structure I. The completeness of the cycle of chemical elements--The structure of the cycle and the end of the cycle Second, the chemical element cycle Taiji Tai Xuan structure shows several properties Third, easy to learn space and reality space Chapter III The Periodic Movement of the Moon-Sun System and Its Temporal and Taiji Structure I. Studying the New Development of the Moon-Day Movement with the Principle of Yi-ology Second, the monthly operation cycle and Taiji Tai Xuan model comparison III. The regressive movement of the moon's distant (near) locations and the structure of the 60-feature elephants. IV. Sources and scientific content of the method of dry branches The Meanings of the Five and Five Elements and the Application of the Breakthrough of the Origin of the Chinese Medicine "Five Movements and Six Gases" Chapter 4 The Correspondence between the Polar Shift Chandler Cycle and the TCM Cycle of Five Transports and Six Gases I. About the Moon Day Cycle Second, on the polar movement Chandler cycle III. Correspondence between TCM's five-transport and six-gas cycle and its polar movement to Chandler's cycle Fourth, on the summary of the monthly cycle of the moon, can an epoch be calculated? The fifth chapter also talk about "Laozi" is right and wrong First, Lao Tzu's collection of ancient methodological studies has become a monograph to comprehensively expound the simple dialectic method. II. Comparison of Understanding and Modern Understanding of Dialectics between Yi, Lao, and Tai Xuan Third, also talk about the evaluation of "Laozi" The sixth chapter Taiji Tai Xuan model content, universality and application prospects 1. The tai-hyeon system is a universal mathematical model of the material cycle movement - discussion on space-time Second, Tai Chi Tai Xuan model content and its calculation rules Third, study the practical significance of the Taiji Tai Xuan model
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(The Science and Civilization in China: Medicine Volume) Zhongguo ke xue ji shu shi (Mandarin Chinese Edition) 中国科学技术史:医学卷 (精装) ISBN: 9787030061607

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目录
总序
第一篇先秦时期
第一章医学的起源
第一节本能的作用
第二节巫医与巫术
一“医源于巫”的观点
二原始宗教与医学
三巫术的结构
四巫术的作用力与转移方式
五巫术在医学中的地位
第三节理论起源的多种途径
一经验的积累与总结
二经络理论的特殊性
三与古代哲学的关系
第四节卫生保健的起源
一火的使用
二居住条件的改善
三饮水卫生
四服装
第二章早期的医药知识积累
第一节以汉文化为核心的医药知识体系
第二节对疾病的认识
一疾病的概念
二疾病的名称与种类
三疾病的原因
第三节药物知识
一药的概念
二《山海经》中的药物知识
三酒与医、药
第四节外治法
一按摩术
二灸熨
三针砭
第三章医学体系的形成
一医事制度
二医学分科
三医学知识的传承
四医学的构成
第二节医学理论
一经脉学说
二脏腑学说
三阴阳学说的运用
四五行学说的运用
第三节养生学
一养生的概念
二养形之术
三养性之论
第四节著名医家
一俞跗
二医缓与医和
三扁鹊与秦越人
四文挚
第二篇秦汉两晋时期
第四章秦与西汉的医学
第一节医学著作与重要人物
一马王堆出土医籍
二张家山汉简《脉书》与《引书》
三阜阳汉简《万物》
四淳于意及其“诊籍”
五今本《黄帝内经》——《素问》与《灵枢》
第二节医学基础理论的确立
一经脉学说体系的形成
二解剖知识与医学理论
三对疾病的认识
第三节诊断技术
一望色
二切脉
第四节治疗技术
一针灸疗法
二药物疗法
第五节本草之学的成立
一“本草”的概念
二本草之名的出现
第六节养生之道与房中术
一神仙方术与养生
二养生方法
三“房中”之术
第七节医事制度
第五章东汉、三国的医学
第一节医学著作与著名医家
一《黄帝明堂经》
二《黄帝八十一难经》
三《神农本草经》
四张仲景与《伤寒杂病论》
五华佗
六吴普与《吴普本草》
七郭玉、吕广、董奉
第二节药物学与方剂学
一本草学的发展
二药物剂型的转变
三炼丹术与矿物药
四方荆学
第三节医学发展的时代特征
一“伤寒”之学的成立
二运气学说
三阴阳、五行与医学的进一步结合
四性、命双修的养生学
第四节医事制度
第六章两晋医学
第一节重要的医学人物与著作
一王叔和与《脉经》
二皇甫谧与《针灸甲乙经》
三葛洪与《肘后备急方》
第二节医学发展的时代特征
一方书盛世的开始
二佛道两教与医学
三服石之风
四灸法的独立发展
第三节医事制度
第三篇南北朝隋唐时期
第七章南北朝的医学
第一节医学发展及其特征
第二节道教佛教对医学发展的影响
一炼丹术和炼丹家
二道教及其著作对医学理论的影响
三僧医及佛教医学对传统医学的影响
第三节著名医家与医籍
一陈延之和《小品方》
二刘涓子和《刘涓子鬼遗方》
三褚澄和《褚澄遗书》
四姚僧垣和《集验方》
五东海徐氏世家
六馆陶李氏世家
七高阳许氏世家
八清河崔氏世家
九释深师等僧医
十全元起
十一王显
十二褚该
十三周澹
十四羊欣
十五秦承祖
十六王微
第四节药物学的发展
一《本草经集注》
二专科类本草
三图谱类本草
四采药和种植类本草
五炮制类本草
六本草音义及其他
第五节病因学和诊断学的发展
一病因学的发展
二诊断技术的发展
第六节针灸学的发展
第七节临床医学的发展
一内科
二外科
三妇产科
四儿科
五五官科
第八节医事制度
第八章隋唐医学
第一节隋唐医学发展的基本特征
一佛教医学的渗入
二大型医书的编撰
三医学经典的注释
四注意专病的研究
五兴办医学教育
第二节著名医家与著作
一巢元方与《诸病源候论》
二孙思邈与《千金方》
三王焘与《外台秘要》
四咎殷与《产宝》
五甄权与《明堂人形图》
六杨上善与《黄帝内经太素》
七王冰与《黄帝内经素问》
八蔺道人与《仙授理伤续断秘方》
九张文仲
第三节本草学的发展
一官修本草
二图谱的编撰
三食疗类本草
四海外药物专著
五《本草拾遗》
第四节医学理论和诊断技术的发展
一医学理论
二诊断技术
第五节针灸学的发展
一针灸图谱
二针灸专著
三针灸临床
第六节临床医学的发展
一内科
二外伤科
三妇产科
四儿科
五五官科及口腔科
六按摩科
第七节医事制度
一尚药局
二药藏局
三太医署
四地方医事机构
第九章藏医学的形成和发展
第一节藏医学的理论
一生理学说
二解剖和胚胎学说
三人体类型学说
四病因学说
五藏医学的诊断治疗方法
第二节月王药诊
第三节宇陀·宁玛元丹贡布与《四部医典》
一生平简述
二《四部医典》
……
第四篇宋金元时期
第五篇明清时期
第六篇中外医学交流
索引
后记
总跋
table of Contents
General order
The first pre-Qin period
Chapter 1 The Origin of Medicine
The first section of the role of instinct
The Second Witch Doctor and Witchcraft
A point of view of “medical origins from witches”
Two original religions and medicine
Three Witchcraft Structures
Four Witchcraft Forces and Methods of Transfer
Five Sorcery’s Position in Medicine
The third section of the theory of the origin of a variety of ways
Accumulation and summary of an experience
The speciality of the theory of two meridians
The relationship between the three and ancient philosophy
Section IV The Origin of Health Care
The use of a fire
II Improvement of living conditions
Three drinking water hygiene
Four clothing
Chapter 2 Accumulation of Early Medical Knowledge
Section 1 Medical Knowledge System with Chinese Culture as the Core
Section II Understanding of Disease
The concept of a disease
The name and type of disease
The cause of the three diseases
The third section of drug knowledge
The concept of a drug
The Drug Knowledge in Shan Hai Jing
Three wines and medicine, medicine
Section IV External Treatment
a massage
Two moxibustion
Three needles
Chapter III Formation of Medical System
A medical system
Second Medical Branch
Third, the inheritance of medical knowledge
The composition of four medicines
Section II Medical Theory
The theory of pulse
Two internal organs
The Use of Sanyinyang Theory
The use of four or five lines of theory
Section III Health Education
A concept of health
Two Forms of Shaping
Sanitarianism
The fourth quarter famous doctors
Yu Yue
Two medical doctors and doctors
Three flat and Qin Yue people
Four texts
The second part of Qin and Han Dynasties
Chapter IV Medicine of Qin and Western Han Dynasty
Section 1 Medical Works and Important Persons
A Mawangdui Unearthed Medical Register
The Zhangjiashan Han Jian Ji Ke and Cishu
Three Suiyang Han Jian “All Things”
Four tips and their “diagnosis”
Five present editions of The Yellow Emperor’s Internal Classic – Su Wen and Lingshu
Section II Establishment of Basic Medical Theory
The formation of a pulse theory system
Second Anatomy Knowledge and Medical Theory
Three understanding of the disease
Section III Diagnostic Techniques
A look
Second cut
Section IV Treatment Technology
Acupuncture therapy
Two drug therapy
The establishment of the fifth section of Herbalism
The concept of a “Materia Medica”
The emergence of the name of the two herbs
Section VI Health Road and Room Surgery
One Immortal Xian Fang and health
Two health methods
Three “room” technique
Section 7 Medical System
Chapter V Medicine of Eastern Han and Three Kingdoms
Section 1 Medical Works and Famous Medical Doctors
A “The Yellow Emperor Ming Tang Jing”
Two “The Yellow Emperor Eighty-one Difficulties”
Three “Shen Nong Ben Cao Jing”
Four Zhang Zhongjing and The Treatise on Febrile and Miscellaneous Diseases
Wuhuan
Six Wu Pu and Wu Pu Materia Medica
Qi Guoyu, Lu Guang, Dong Feng
Section II Pharmacology and Formulae
A scholastic development
Two drug dosage forms
Three alchemy and mineral medicine
Quartet learning
Section 3 Characteristics of the Times of Medical Development
The establishment of a school of “typhoid fever”
Second Luck Theory
The Combination of Sanyinyang, Five Elements and Medicine
Four sex, life double cultivation of health
Section IV Medical System
The sixth chapter two Jin medicine
Section 1 Important Medical Characters and Works
One Uncle Wang Shuhe and The Pulses
The Second Emperor and “Acupuncture and Moxibustion”
Sange Hong and Elbow Emergency Preparedness
Section 2 Characteristics of the Times of Medical Development
The beginning of the prosperity of the party
Two Buddhas and Taoism
Three Stones
The independent development of four moxibustion
Section III Medical System
The third part of the Southern and Northern Dynasties and the Tang Dynasty
Chapter VII Medicine of the Southern and Northern Dynasties
Section 1 Medical Development and Its Features
Section 2 Influence of Daoist Buddhism on Medical Development
An Alchemy and Alchemist
The Influence of Erdaoism and Its Works on Medical Theory
The Influence of Sanzhao Medical and Buddhist Medicine on Traditional Medicine
Section III Famous Doctors and Medical Registers
Yi Yanzhi and Xiao Ping Fang
The Second of Liu Yizi and Liu Yizi’s Left Behind
Sanzhao Chenghe and “Zhi Cheng’s Last Book”
Four Yao Yao and “Set prescription”
The East China Sea Xu Family
Liu Guan Tao Li Family
Seven Goyang Family Hsu
Eight Rivers Cui Family
Nine Interpretations of Shen Shi et al
From ten yuan
Eleven Wang Xian
Twelve times
Thirteen weeks
Fourteen sheep
15th Qin Chengzu
Sixteen Wang Wei
Section IV Development of Pharmacology
A “Ben Cao Jing Ji”
Two specialist herbal medicine
Three maps
Four Herbs and Planting Herbs
Five herbs
Roppongi and other
Section 5 Development of Etiology and Diagnostics
The development of an etiology
Second, the development of diagnostic technology
Section 6 Development of Acupuncture and Moxibustion
Section 7 Development of Clinical Medicine
An internal medicine
Second surgery
Three Obstetricians
Four pediatrics
Five Five Officials
Section VIII Medical System
Chapter Eight Sui and Tang Medicine
Section I Basic Features of Medical Development in Sui Tang
Infiltration of a Buddhist medicine
Compilation of two large medical books
Three medical classic notes
Four attention to special disease research
Wuxing Medical Education
Section II Famous Doctors and Books
A Nested Yuanfang and “Theory of Diseases and Diseases”
Sun Shuangyi and Qianjin Fang
Three Kings and “Taiwan Secrets”
Four Yin Yin and “Production Po”
Five Right and “Mingtang Human Figure”
Liu Yangshan and “Huang Di Neijing Tai Su”
Seven Kings Ice and The Yellow Emperor Neijing
Gossip Man and “Lessons Divorce”
Nine Zhang Wenzhong
The third section of the development of herbal medicine
An official repair grass
Compilation of two maps
Three diet herbs
Four overseas drug monographs
Five “Herbal Supplements”
Section IV Development of Medical Theory and Diagnostic Techniques
a medical theory
Diagnose technology
Section 5 Development of Acupuncture and Moxibustion
Acupuncture map
Second Acupuncture Monograph
Three acupuncture clinical
Section 6 Development of Clinical Medicine
An internal medicine
Second trauma department
Three Obstetricians
Four pediatrics
Fifty-five disciplines and dentistry
Six massages
Section 7 Medical System
Yishang Pharmacy
Two drug reservoirs
Santai Medical Department
Four local medical institutions
Chapter 9 Formation and Development of Tibetan Medicine
The first section of Tibetan medicine theory
a physiological theory
Second Anatomy and Embryology
Three types of human body theory
Four etiology
Diagnosis and treatment of five Tibetan medicine
The second quarter of the month Wang pharmacy
The third section Yu Tuo Ning Ma Yuangong Gong Bu and “Four Medical Books”
A brief biography
Two “Four Medical Codes”
……
The fourth Song Jinyuan Period
The fifth article of the Ming and Qing Dynasties
The sixth chapter of Chinese and foreign medical exchanges
Index
Postscript
Total

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"′Classic′... a book which people praise and don't read." - Mark Twain

(The Science and Civilization in China: Medicine Volume) Zhongguo ke xue ji shu shi (Mandarin Chinese Edition) 中国科学技术史:医学卷 (精装)

Author: Yuqun Liao 廖育群
Pages: 512
Category: Science and Civilization in China 中國科學技術史
Publisher: Ke xue chu ban she 科学出版社
Publication Date: 1998
Finished? No
Signed? No
First Edition? No

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Description
目录 总序 第一篇先秦时期 第一章医学的起源 第一节本能的作用 第二节巫医与巫术 一“医源于巫”的观点 二原始宗教与医学 三巫术的结构 四巫术的作用力与转移方式 五巫术在医学中的地位 第三节理论起源的多种途径 一经验的积累与总结 二经络理论的特殊性 三与古代哲学的关系 第四节卫生保健的起源 一火的使用 二居住条件的改善 三饮水卫生 四服装 第二章早期的医药知识积累 第一节以汉文化为核心的医药知识体系 第二节对疾病的认识 一疾病的概念 二疾病的名称与种类 三疾病的原因 第三节药物知识 一药的概念 二《山海经》中的药物知识 三酒与医、药 第四节外治法 一按摩术 二灸熨 三针砭 第三章医学体系的形成 一医事制度 二医学分科 三医学知识的传承 四医学的构成 第二节医学理论 一经脉学说 二脏腑学说 三阴阳学说的运用 四五行学说的运用 第三节养生学 一养生的概念 二养形之术 三养性之论 第四节著名医家 一俞跗 二医缓与医和 三扁鹊与秦越人 四文挚 第二篇秦汉两晋时期 第四章秦与西汉的医学 第一节医学著作与重要人物 一马王堆出土医籍 二张家山汉简《脉书》与《引书》 三阜阳汉简《万物》 四淳于意及其“诊籍” 五今本《黄帝内经》——《素问》与《灵枢》 第二节医学基础理论的确立 一经脉学说体系的形成 二解剖知识与医学理论 三对疾病的认识 第三节诊断技术 一望色 二切脉 第四节治疗技术 一针灸疗法 二药物疗法 第五节本草之学的成立 一“本草”的概念 二本草之名的出现 第六节养生之道与房中术 一神仙方术与养生 二养生方法 三“房中”之术 第七节医事制度 第五章东汉、三国的医学 第一节医学著作与著名医家 一《黄帝明堂经》 二《黄帝八十一难经》 三《神农本草经》 四张仲景与《伤寒杂病论》 五华佗 六吴普与《吴普本草》 七郭玉、吕广、董奉 第二节药物学与方剂学 一本草学的发展 二药物剂型的转变 三炼丹术与矿物药 四方荆学 第三节医学发展的时代特征 一“伤寒”之学的成立 二运气学说 三阴阳、五行与医学的进一步结合 四性、命双修的养生学 第四节医事制度 第六章两晋医学 第一节重要的医学人物与著作 一王叔和与《脉经》 二皇甫谧与《针灸甲乙经》 三葛洪与《肘后备急方》 第二节医学发展的时代特征 一方书盛世的开始 二佛道两教与医学 三服石之风 四灸法的独立发展 第三节医事制度 第三篇南北朝隋唐时期 第七章南北朝的医学 第一节医学发展及其特征 第二节道教佛教对医学发展的影响 一炼丹术和炼丹家 二道教及其著作对医学理论的影响 三僧医及佛教医学对传统医学的影响 第三节著名医家与医籍 一陈延之和《小品方》 二刘涓子和《刘涓子鬼遗方》 三褚澄和《褚澄遗书》 四姚僧垣和《集验方》 五东海徐氏世家 六馆陶李氏世家 七高阳许氏世家 八清河崔氏世家 九释深师等僧医 十全元起 十一王显 十二褚该 十三周澹 十四羊欣 十五秦承祖 十六王微 第四节药物学的发展 一《本草经集注》 二专科类本草 三图谱类本草 四采药和种植类本草 五炮制类本草 六本草音义及其他 第五节病因学和诊断学的发展 一病因学的发展 二诊断技术的发展 第六节针灸学的发展 第七节临床医学的发展 一内科 二外科 三妇产科 四儿科 五五官科 第八节医事制度 第八章隋唐医学 第一节隋唐医学发展的基本特征 一佛教医学的渗入 二大型医书的编撰 三医学经典的注释 四注意专病的研究 五兴办医学教育 第二节著名医家与著作 一巢元方与《诸病源候论》 二孙思邈与《千金方》 三王焘与《外台秘要》 四咎殷与《产宝》 五甄权与《明堂人形图》 六杨上善与《黄帝内经太素》 七王冰与《黄帝内经素问》 八蔺道人与《仙授理伤续断秘方》 九张文仲 第三节本草学的发展 一官修本草 二图谱的编撰 三食疗类本草 四海外药物专著 五《本草拾遗》 第四节医学理论和诊断技术的发展 一医学理论 二诊断技术 第五节针灸学的发展 一针灸图谱 二针灸专著 三针灸临床 第六节临床医学的发展 一内科 二外伤科 三妇产科 四儿科 五五官科及口腔科 六按摩科 第七节医事制度 一尚药局 二药藏局 三太医署 四地方医事机构 第九章藏医学的形成和发展 第一节藏医学的理论 一生理学说 二解剖和胚胎学说 三人体类型学说 四病因学说 五藏医学的诊断治疗方法 第二节月王药诊 第三节宇陀·宁玛元丹贡布与《四部医典》 一生平简述 二《四部医典》 …… 第四篇宋金元时期 第五篇明清时期 第六篇中外医学交流 索引 后记 总跋 table of Contents General order The first pre-Qin period Chapter 1 The Origin of Medicine The first section of the role of instinct The Second Witch Doctor and Witchcraft A point of view of "medical origins from witches" Two original religions and medicine Three Witchcraft Structures Four Witchcraft Forces and Methods of Transfer Five Sorcery's Position in Medicine The third section of the theory of the origin of a variety of ways Accumulation and summary of an experience The speciality of the theory of two meridians The relationship between the three and ancient philosophy Section IV The Origin of Health Care The use of a fire II Improvement of living conditions Three drinking water hygiene Four clothing Chapter 2 Accumulation of Early Medical Knowledge Section 1 Medical Knowledge System with Chinese Culture as the Core Section II Understanding of Disease The concept of a disease The name and type of disease The cause of the three diseases The third section of drug knowledge The concept of a drug The Drug Knowledge in Shan Hai Jing Three wines and medicine, medicine Section IV External Treatment a massage Two moxibustion Three needles Chapter III Formation of Medical System A medical system Second Medical Branch Third, the inheritance of medical knowledge The composition of four medicines Section II Medical Theory The theory of pulse Two internal organs The Use of Sanyinyang Theory The use of four or five lines of theory Section III Health Education A concept of health Two Forms of Shaping Sanitarianism The fourth quarter famous doctors Yu Yue Two medical doctors and doctors Three flat and Qin Yue people Four texts The second part of Qin and Han Dynasties Chapter IV Medicine of Qin and Western Han Dynasty Section 1 Medical Works and Important Persons A Mawangdui Unearthed Medical Register The Zhangjiashan Han Jian Ji Ke and Cishu Three Suiyang Han Jian "All Things" Four tips and their "diagnosis" Five present editions of The Yellow Emperor's Internal Classic - Su Wen and Lingshu Section II Establishment of Basic Medical Theory The formation of a pulse theory system Second Anatomy Knowledge and Medical Theory Three understanding of the disease Section III Diagnostic Techniques A look Second cut Section IV Treatment Technology Acupuncture therapy Two drug therapy The establishment of the fifth section of Herbalism The concept of a "Materia Medica" The emergence of the name of the two herbs Section VI Health Road and Room Surgery One Immortal Xian Fang and health Two health methods Three "room" technique Section 7 Medical System Chapter V Medicine of Eastern Han and Three Kingdoms Section 1 Medical Works and Famous Medical Doctors A "The Yellow Emperor Ming Tang Jing" Two "The Yellow Emperor Eighty-one Difficulties" Three "Shen Nong Ben Cao Jing" Four Zhang Zhongjing and The Treatise on Febrile and Miscellaneous Diseases Wuhuan Six Wu Pu and Wu Pu Materia Medica Qi Guoyu, Lu Guang, Dong Feng Section II Pharmacology and Formulae A scholastic development Two drug dosage forms Three alchemy and mineral medicine Quartet learning Section 3 Characteristics of the Times of Medical Development The establishment of a school of "typhoid fever" Second Luck Theory The Combination of Sanyinyang, Five Elements and Medicine Four sex, life double cultivation of health Section IV Medical System The sixth chapter two Jin medicine Section 1 Important Medical Characters and Works One Uncle Wang Shuhe and The Pulses The Second Emperor and "Acupuncture and Moxibustion" Sange Hong and Elbow Emergency Preparedness Section 2 Characteristics of the Times of Medical Development The beginning of the prosperity of the party Two Buddhas and Taoism Three Stones The independent development of four moxibustion Section III Medical System The third part of the Southern and Northern Dynasties and the Tang Dynasty Chapter VII Medicine of the Southern and Northern Dynasties Section 1 Medical Development and Its Features Section 2 Influence of Daoist Buddhism on Medical Development An Alchemy and Alchemist The Influence of Erdaoism and Its Works on Medical Theory The Influence of Sanzhao Medical and Buddhist Medicine on Traditional Medicine Section III Famous Doctors and Medical Registers Yi Yanzhi and Xiao Ping Fang The Second of Liu Yizi and Liu Yizi's Left Behind Sanzhao Chenghe and "Zhi Cheng's Last Book" Four Yao Yao and "Set prescription" The East China Sea Xu Family Liu Guan Tao Li Family Seven Goyang Family Hsu Eight Rivers Cui Family Nine Interpretations of Shen Shi et al From ten yuan Eleven Wang Xian Twelve times Thirteen weeks Fourteen sheep 15th Qin Chengzu Sixteen Wang Wei Section IV Development of Pharmacology A "Ben Cao Jing Ji" Two specialist herbal medicine Three maps Four Herbs and Planting Herbs Five herbs Roppongi and other Section 5 Development of Etiology and Diagnostics The development of an etiology Second, the development of diagnostic technology Section 6 Development of Acupuncture and Moxibustion Section 7 Development of Clinical Medicine An internal medicine Second surgery Three Obstetricians Four pediatrics Five Five Officials Section VIII Medical System Chapter Eight Sui and Tang Medicine Section I Basic Features of Medical Development in Sui Tang Infiltration of a Buddhist medicine Compilation of two large medical books Three medical classic notes Four attention to special disease research Wuxing Medical Education Section II Famous Doctors and Books A Nested Yuanfang and "Theory of Diseases and Diseases" Sun Shuangyi and Qianjin Fang Three Kings and "Taiwan Secrets" Four Yin Yin and "Production Po" Five Right and "Mingtang Human Figure" Liu Yangshan and "Huang Di Neijing Tai Su" Seven Kings Ice and The Yellow Emperor Neijing Gossip Man and "Lessons Divorce" Nine Zhang Wenzhong The third section of the development of herbal medicine An official repair grass Compilation of two maps Three diet herbs Four overseas drug monographs Five "Herbal Supplements" Section IV Development of Medical Theory and Diagnostic Techniques a medical theory Diagnose technology Section 5 Development of Acupuncture and Moxibustion Acupuncture map Second Acupuncture Monograph Three acupuncture clinical Section 6 Development of Clinical Medicine An internal medicine Second trauma department Three Obstetricians Four pediatrics Fifty-five disciplines and dentistry Six massages Section 7 Medical System Yishang Pharmacy Two drug reservoirs Santai Medical Department Four local medical institutions Chapter 9 Formation and Development of Tibetan Medicine The first section of Tibetan medicine theory a physiological theory Second Anatomy and Embryology Three types of human body theory Four etiology Diagnosis and treatment of five Tibetan medicine The second quarter of the month Wang pharmacy The third section Yu Tuo Ning Ma Yuangong Gong Bu and "Four Medical Books" A brief biography Two "Four Medical Codes" ...... The fourth Song Jinyuan Period The fifth article of the Ming and Qing Dynasties The sixth chapter of Chinese and foreign medical exchanges Index Postscript Total
Notes
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Chinese remainder theorem: the sum of the Construction of Chinese History Timeline(Chinese Edition) 中国剩余定理:总数法构建中国历史年表 ISBN: 9787560350899

DO NOT DELETE
目录
第0章 从“韩信点兵”到“孙子定理”
§1 韩信点兵
§2 物不知总
§3 孙子定理
§4 “百鸡问题”
§5 求五星会合周期的公倍数
第1章 用孙子定理证明若干竞赛题
第2章 话说祖冲之大衍法
§1 秦九韶传承了《缀术》
§2 “大衍求一术”是衍化方阵的方法
§3 连分数与商数列
第3章 从“秦一左表”到“秦一左定理”
§1 更相减损求等数
§2 乘加迭代找乘率
§3 最 佳渐近分数与秦一左定理
第4章 祖冲之用最 佳逼近法开方——开差幂开差立
§1 刘徽的开方术
§2 祖冲之更开密法
§3 用古法解一元二次方程
第5章 祖冲之用内外逼近法求圆周率
第6章 用总数法、消元法解一次不定方程组
§1 从“程行相及”谈起
§2 注释“古历会积”介绍总数法
§3 用消元法(演纪法)求总数
§4 祖冲之的上元积年数
第7章 岁差“治历推闰”交食周期
§1 岁差
§2 “治历推闰”
§3 日月交食周期
第8章 用总数法敲定“五星聚”的真伪
§1 岁星纪年法与岁星超辰
§2 历元定于公元1962年2月5日
§3 249个五星聚为构建《五千年中国历史年表》打基础
§4 “五星聚于房”与武王伐纣
§5 公元前2289年“辰弗集于房”
§6 炎帝“七曜起于天关”在公元前2863年
第9章 万物周期旋转之道
§1 周期运动的轨道方程
§2 万物周期运动的中心力场与势函数
§3 量子数竹与原子结构
§4 万有引力斥力公式的发现过程
第10章 推广到多项式理论
§1 多项式理论中与它相似的定理
§2 交换环理论中的直和分解定理
§3 赋值论中的逼近定理
附录1 五星会合周期Ti的公倍数Ni与Ti的比值表
附录2 位于黄道附近的星宿、星座图
附录3 十二星次及二十八宿与黄道经度对照表
附录4 岁星纪年、干支纪年与公历纪年的对照表五星聚与《五千年中国历史年表》(压缩版)
参考文献
table of Contents
Chapter 0 From “Hanshin Soldier” to “Grandson Theorem”
§1 Han Xin Bingbing
§ 2 things do not know
§3 Grandson Theorem
§4 “The problem of chickens”
§5 Seeking the common multiple of the five-star convergence period
Chapter 1 Proving Some Competition Questions with Sun Theorem
Chapter 2 Saying the Great Descent of Zu Chong
§1 Qin Jiuyi inherited the “Decoration Technique”
§2 “Big Exhortation” is a method of deriving a phalanx
§ 3 consecutive scores and quotient columns
Chapter 3 From “Qin Yi Zuo Table” to “Qin Yi Zuo Theorem”
§1 More derogation loss equal number
§ 2 multiplication plus iteration rate
§3 Best Asymptotic Fraction and Qin Yi Zuo Theorem
Chapter 4 Zuchong’s Use of the Best Approach to Formulation – Opening Power
§1 Liu Hui’s prescription
§2 Zu Chongzhi’s more secret method
§3 Using the ancient method to solve a quadratic equation
Chapter 5 Zu Chong uses the inside and outside approximation method to find the pi
Chapter 6 Solving Indefinite Equations with the Total Method and Elimination Method
§1 From the perspective of “process and phase”
§2 Commentary “Ancient Calendar Convergence” Introduction to Total Number Method
§3 Use total elimination method
§4 Zuo Chongzhi’s Upper Element Accumulated Years
Chapter 7 Precession of the “administrative calendar” delivery cycle
§ 1 precession
§ 2 “Placing the government”
§ 3 day and month food delivery cycle
Chapter 8 Finalizing the “Five Stars” with the Total Method
§ 1 year old star age method and age super star
§2 The epoch is scheduled for February 5, 1962 AD
§ 3 249 five-star gatherings laid the foundation for the construction of a “five-thousand-year Chinese chronology”
§ 4 “Five Stars in the House” and King Wu
§ 5 2289 BC “Chen Fu Set in the House”
§ 6 Yandi “Seven Pillars Began at Tianguan” in 2863 BC
Chapter 9 The Road to the Revolution of Everything
§ 1 orbital equation of periodic motion
§2 The center force field and potential function of the periodic motion
§3 Quantum number bamboo and atomic structure
§4 The discovery process of gravitational repulsion formula
Chapter 10 Generalization to Polynomial Theory
§1 Similar theorems in polynomial theory
§2 The direct sum decomposition theorem in the theory of exchange rings
§3 Approximation Theorem in Assignment Theory
Appendix 1 Ratio of Common Multiples Ni to Ti for the Five-Star Convergence Period Ti
Appendix 2 Astrology and constellation diagrams located near the ecliptic
Appendix 3 Comparison between the 12-star and the 28-sugar and the longitude of the ecliptic
Appendices 4 Years of Age, Years of Ganzhi, and Years of the Lunar Year-by-year Comparison of the Five Stars and Five Years of Chinese Chronology (Compact Version)
references

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"Anyone who ever gave you confidence, you owe them a lot." - Truman Capote, Breakfast at Tiffany's

Chinese remainder theorem: the sum of the Construction of Chinese History Timeline(Chinese Edition) 中国剩余定理:总数法构建中国历史年表

Author: ZUO QUAN RU . LIU PEI JIE 左铨如
Pages: 154
Category: Mathematics 數學 道象理數 算術
Publisher: Harbin Institute of Technology Press 哈尔滨工业大学出版社
Publication Date: 2015
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目录 第0章 从“韩信点兵”到“孙子定理” §1 韩信点兵 §2 物不知总 §3 孙子定理 §4 “百鸡问题” §5 求五星会合周期的公倍数 第1章 用孙子定理证明若干竞赛题 第2章 话说祖冲之大衍法 §1 秦九韶传承了《缀术》 §2 “大衍求一术”是衍化方阵的方法 §3 连分数与商数列 第3章 从“秦一左表”到“秦一左定理” §1 更相减损求等数 §2 乘加迭代找乘率 §3 最 佳渐近分数与秦一左定理 第4章 祖冲之用最 佳逼近法开方——开差幂开差立 §1 刘徽的开方术 §2 祖冲之更开密法 §3 用古法解一元二次方程 第5章 祖冲之用内外逼近法求圆周率 第6章 用总数法、消元法解一次不定方程组 §1 从“程行相及”谈起 §2 注释“古历会积”介绍总数法 §3 用消元法(演纪法)求总数 §4 祖冲之的上元积年数 第7章 岁差“治历推闰”交食周期 §1 岁差 §2 “治历推闰” §3 日月交食周期 第8章 用总数法敲定“五星聚”的真伪 §1 岁星纪年法与岁星超辰 §2 历元定于公元1962年2月5日 §3 249个五星聚为构建《五千年中国历史年表》打基础 §4 “五星聚于房”与武王伐纣 §5 公元前2289年“辰弗集于房” §6 炎帝“七曜起于天关”在公元前2863年 第9章 万物周期旋转之道 §1 周期运动的轨道方程 §2 万物周期运动的中心力场与势函数 §3 量子数竹与原子结构 §4 万有引力斥力公式的发现过程 第10章 推广到多项式理论 §1 多项式理论中与它相似的定理 §2 交换环理论中的直和分解定理 §3 赋值论中的逼近定理 附录1 五星会合周期Ti的公倍数Ni与Ti的比值表 附录2 位于黄道附近的星宿、星座图 附录3 十二星次及二十八宿与黄道经度对照表 附录4 岁星纪年、干支纪年与公历纪年的对照表五星聚与《五千年中国历史年表》(压缩版) 参考文献 Language:Chinese.Paperback. Pub Date: 2015-1-1 Publisher: Harbin Institute of Technology Press. Dayan find a technique and total art is the ancestral magic bullet. is astronomical calculation and analysis of the indefinite article founding a small problem in mathematics Theorem series (II) Chinese remainder theorem: the sum of the Construction of Chinese chronology. first author Dayan find a technique and its operator grass transformed into useful Qin a left table. expand Remainder Theorem range of applications. highlighting the best approximation of mathematical thinking. to meet the needs of astronomy. will be on an expanded set of integers solution to the problem than equations with rational range; also describes the open square. solving a quadratic ancient equation. Application of total art to determine a common multiple of the rotation period. the search to two hundred ...
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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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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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"We were the people who were not in the papers. We lived in the blank white spaces at the edges of print. It gave us more freedom. We lived in the gaps between the stories." - Margaret Atwood, The Handmaid's Tale

(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
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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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"Maybe ever’body in the whole damn world is scared of each other." - John Steinbeck

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
Finished? No
Signed? No
First Edition? No

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Description
《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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"We cast a shadow on something wherever we stand, and it is no good moving from place to place to save things, because the shadow always follows. Choose a place where you won't do harm... yes, choose a place where you won't do very much harm, and stand in it for all you are worth, facing the sunshine." - E.M. Forster, A Room With A View

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
Finished? No
Signed? No
First Edition? No

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Description
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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挑战思维极限:勾股定理的365种证明 (The Ultimate Intellectual Challenge: 365 PROOF OF Gou Gu Theorem (Phythagoras Theorem)) ISBN: 9787302458791

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

目录
第1章分块法
1.1分块对应法
1.2镶嵌法
1.3十字分块法
第2章割补法
第3章搭桥法
第4章“化积为方”法
第5章等积变换法
第6章拼摆法
第7章增积法
第8章消去法
8.1倍积法
8.2面积比例法
第9章同积法
第10章射影法
10.1作斜边垂线的证法
10.2作直角边垂线的证法
第11章长度法
第12章方程法
第13章平方差法
第14章辅助圆法
第15章相似转化法
第16章间接证法
16.1反证法
16.2同一法
第17章解析法
17.1坐标法
17.2参数法
17.3三角函数法
第18章特例法
第19章泛化法
附录A证法出处汇总
附录B勾股定理的365种证明有用吗?
参考文献
后记

table of Contents
Chapter 1 Blocking
1.1 block correspondence method
1.2 Mosaic method
1.3 Cross block method
Chapter 2 Cant Method
Chapter 3 Bridge Method
Chapter 4 “Method of Formulating Products”
Chapter 5 Equal product transformation
Chapter 6 Plunging
Chapter 7 Accumulation
Chapter 8 Elimination
8.1 multiple product method
8.2 area ratio method
Chapter 9 Synchronous Method
Chapter 10 Projective Method
10.1 Proof of oblique vertical lines
10.2 Proof of Vertical Lines
Chapter 11 Length Method
Chapter 12 Equation Method
Chapter 13 Square Difference Method
Chapter 14 Auxiliary Circle Method
Chapter 15 Similar Transformations
Chapter 16 Indirect Proof
16.1 Anti-evidence
16.2 The same method
Chapter 17 Analysis
17.1 coordinate method
17.2 Parameter Method
17.3 Trigonometric Functions
Chapter 18 Special Cases Act
Chapter 19 Generalization
Appendix A proof of the source summary
Is the 365 kinds of proofs of Appendix B Pythagorean Theorem helpful?
references
postscript

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"It’s no use going back to yesterday, because I was a different person then." - Lewis Carroll, Alice’s Adventures in Wonderland

((The Ultimate Intellectual Challenge: 365 PROOF OF Gou Gu Theorem (Phythagoras Theorem)) 挑战思维极限:勾股定理的365种证明

Author: 李迈新
Pages: 248
Category: Mathematics 數學 道象理數 算術
Publisher: 清华大学出版社
Publication Date: 2016
Finished? No
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First Edition? No

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目录 第1章分块法 1.1分块对应法 1.2镶嵌法 1.3十字分块法 第2章割补法 第3章搭桥法 第4章“化积为方”法 第5章等积变换法 第6章拼摆法 第7章增积法 第8章消去法 8.1倍积法 8.2面积比例法 第9章同积法 第10章射影法 10.1作斜边垂线的证法 10.2作直角边垂线的证法 第11章长度法 第12章方程法 第13章平方差法 第14章辅助圆法 第15章相似转化法 第16章间接证法 16.1反证法 16.2同一法 第17章解析法 17.1坐标法 17.2参数法 17.3三角函数法 第18章特例法 第19章泛化法 附录A证法出处汇总 附录B勾股定理的365种证明有用吗? 参考文献 后记 table of Contents Chapter 1 Blocking 1.1 block correspondence method 1.2 Mosaic method 1.3 Cross block method Chapter 2 Cant Method Chapter 3 Bridge Method Chapter 4 “Method of Formulating Products” Chapter 5 Equal product transformation Chapter 6 Plunging Chapter 7 Accumulation Chapter 8 Elimination 8.1 multiple product method 8.2 area ratio method Chapter 9 Synchronous Method Chapter 10 Projective Method 10.1 Proof of oblique vertical lines 10.2 Proof of Vertical Lines Chapter 11 Length Method Chapter 12 Equation Method Chapter 13 Square Difference Method Chapter 14 Auxiliary Circle Method Chapter 15 Similar Transformations Chapter 16 Indirect Proof 16.1 Anti-evidence 16.2 The same method Chapter 17 Analysis 17.1 coordinate method 17.2 Parameter Method 17.3 Trigonometric Functions Chapter 18 Special Cases Act Chapter 19 Generalization Appendix A proof of the source summary Is the 365 kinds of proofs of Appendix B Pythagorean Theorem helpful? references postscript
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