The transcription of the Suanshu Shu算數書(a bamboo book of mathematics)in simplified Chinese characters offers a new opportunity to explore the history of Chinese mathematics in ancient times.This paper analyzes the ...The transcription of the Suanshu Shu算數書(a bamboo book of mathematics)in simplified Chinese characters offers a new opportunity to explore the history of Chinese mathematics in ancient times.This paper analyzes the style and structure of the Suanshu Shu and makes comparisons with the Nine Chapters on Mathematical Procedures and a number of other texts in various social contexts.It will be shown that the Suanshu Shu was compiled from at least two sources,and that no direct textual interplay exists between the Suanshu Shu and the Nine Chapters,although both share the same origins in the Pre-Qin period when the major mathematical methods in the Nine Chapters came into being.It will also be shown that the Suanshu Shu was accomplished with the methods used in certain mathematical books in the Pre-Qin period or their results,which later led to the Nine Chapters,and by accommodating the actual conditions of the lower government administration.The Suanshu Shu is significant for establishing the evolution of algorithmic mathematics from the Warring States period to the Han dynasty.展开更多
The three-region theory,which divided the air into warm,cold,and hot strata from bottom to top,was the paramount theory for explaining meteorological phenomena in medieval Europe.Such missionaries as Matteo Ricci,Fran...The three-region theory,which divided the air into warm,cold,and hot strata from bottom to top,was the paramount theory for explaining meteorological phenomena in medieval Europe.Such missionaries as Matteo Ricci,Francisco Furtado and Alfonso Vagnone introduced it into China during the seventeenth century,where it had a significant influence on Chinese meteorological knowledge.Chinese scholars endeavored to understand and assimilate this theory based on the traditional yuanqi元氣(original substance or primal vitality)theory or yinyang陰陽(negative and positive principles)theory,so as to either broaden the range of the three regions,or to indicate that there were no definite boundaries to them.In this context,Jie Xuan揭暄drew a meteorological illustration entitled Rihuo xiajiang yangqi shangsheng tu日火下降暘氣上升圖(Illustration of the descent of the sun’s warmth and the ascent of warmed air),which epitomized how Sino-Western scientific encounters inspired new ideas.展开更多
This paper discusses the most recent case of the lost-wax process,namely,a bronze appendage with hollow snake patterns excavated in 2002 at the tomb of Duke Ning of Xu(許公寧)(a state in the Spring and Autumn period)i...This paper discusses the most recent case of the lost-wax process,namely,a bronze appendage with hollow snake patterns excavated in 2002 at the tomb of Duke Ning of Xu(許公寧)(a state in the Spring and Autumn period)in Ye County,Henan Province.Various physical and chemical analyses indicate that this artifact was cast as a whole in 547 BCE or slightly later in a high tin bronze alloy using the lost-wax process.No traces of cast joints or soldering were found.This research provides further proof that the lost-wax process was a significant technical development achieved by casters in the Pre-Qin period.展开更多
Among the bamboo slips dating to the Warring States period(475-221 BCE),stored at Tsinghua University,there is an aggregate of 21 specially shaped slips that are painted with red lines on the obverse side.Numbers are ...Among the bamboo slips dating to the Warring States period(475-221 BCE),stored at Tsinghua University,there is an aggregate of 21 specially shaped slips that are painted with red lines on the obverse side.Numbers are written on 20 slips in accordance with certain rules,and on one slip without numbers there are 20 round holes and residues of ribbon.These slips,after being compiled as a whole,serve as a practical calculator in the form of a table,which is designated as Suan Biao算表(the multiplication table).In this paper,the structure and functions of the Suan Biao are discussed by comparing it with other ancient multiplication tables.Specifically,it is noted that the core of the Suan Biao is a multiplication table comprising the numbers 9 to 1 and their products 81 to 1;the other parts are an extension of the core.The Suan Biao employs the decimal place value system and manifested the author’s knowledge of the commutative law of multiplication,the distributive law of multiplication over addition,and fractions.Not only is this table directly applicable to the multiplication of two-digit numbers,but also to division.In addition,certain computations regarding 1/2 or fractions containing 1/2 can be conducted using this table,and it may also be used for extracting roots.The Suan Biao is of great significance for research on ancient mathematics,and its discovery is enormously valuable for studies on arithmetic methods and computational tools in early China.展开更多
Chinese bronzes are both valuable archaeological remains and significant objects of study in the history of art and technology due to their unique style,complex functions,and technological sophistication.In 1928,the a...Chinese bronzes are both valuable archaeological remains and significant objects of study in the history of art and technology due to their unique style,complex functions,and technological sophistication.In 1928,the archaeological excavation in Anyang was regarded as the symbol of the establishment of the field of Chinese archaeology.By 2000,tens of thousands of bronzes,and some bronze foundries had been excavated and studied.In archaeologist-led studies,the issues involved are generic,and their scope is restricted,while in multi-disciplinary studies involving both archaeologists and historians of technology,the research is more specific,indicating that research effectiveness and scientific collaboration are closely correlated.展开更多
基金Prof.Guo Shuchun and Prof.Chen Meidong陈美东assisted with the completion of the Chinese version of this paper.In addition,Prof.Joseph W.Dauben has guided its revision in English.John Moffett copyedited the English translation.The author would like to express his heartfelt appreciation to all of them.
文摘The transcription of the Suanshu Shu算數書(a bamboo book of mathematics)in simplified Chinese characters offers a new opportunity to explore the history of Chinese mathematics in ancient times.This paper analyzes the style and structure of the Suanshu Shu and makes comparisons with the Nine Chapters on Mathematical Procedures and a number of other texts in various social contexts.It will be shown that the Suanshu Shu was compiled from at least two sources,and that no direct textual interplay exists between the Suanshu Shu and the Nine Chapters,although both share the same origins in the Pre-Qin period when the major mathematical methods in the Nine Chapters came into being.It will also be shown that the Suanshu Shu was accomplished with the methods used in certain mathematical books in the Pre-Qin period or their results,which later led to the Nine Chapters,and by accommodating the actual conditions of the lower government administration.The Suanshu Shu is significant for establishing the evolution of algorithmic mathematics from the Warring States period to the Han dynasty.
文摘The three-region theory,which divided the air into warm,cold,and hot strata from bottom to top,was the paramount theory for explaining meteorological phenomena in medieval Europe.Such missionaries as Matteo Ricci,Francisco Furtado and Alfonso Vagnone introduced it into China during the seventeenth century,where it had a significant influence on Chinese meteorological knowledge.Chinese scholars endeavored to understand and assimilate this theory based on the traditional yuanqi元氣(original substance or primal vitality)theory or yinyang陰陽(negative and positive principles)theory,so as to either broaden the range of the three regions,or to indicate that there were no definite boundaries to them.In this context,Jie Xuan揭暄drew a meteorological illustration entitled Rihuo xiajiang yangqi shangsheng tu日火下降暘氣上升圖(Illustration of the descent of the sun’s warmth and the ascent of warmed air),which epitomized how Sino-Western scientific encounters inspired new ideas.
文摘This paper discusses the most recent case of the lost-wax process,namely,a bronze appendage with hollow snake patterns excavated in 2002 at the tomb of Duke Ning of Xu(許公寧)(a state in the Spring and Autumn period)in Ye County,Henan Province.Various physical and chemical analyses indicate that this artifact was cast as a whole in 547 BCE or slightly later in a high tin bronze alloy using the lost-wax process.No traces of cast joints or soldering were found.This research provides further proof that the lost-wax process was a significant technical development achieved by casters in the Pre-Qin period.
文摘Among the bamboo slips dating to the Warring States period(475-221 BCE),stored at Tsinghua University,there is an aggregate of 21 specially shaped slips that are painted with red lines on the obverse side.Numbers are written on 20 slips in accordance with certain rules,and on one slip without numbers there are 20 round holes and residues of ribbon.These slips,after being compiled as a whole,serve as a practical calculator in the form of a table,which is designated as Suan Biao算表(the multiplication table).In this paper,the structure and functions of the Suan Biao are discussed by comparing it with other ancient multiplication tables.Specifically,it is noted that the core of the Suan Biao is a multiplication table comprising the numbers 9 to 1 and their products 81 to 1;the other parts are an extension of the core.The Suan Biao employs the decimal place value system and manifested the author’s knowledge of the commutative law of multiplication,the distributive law of multiplication over addition,and fractions.Not only is this table directly applicable to the multiplication of two-digit numbers,but also to division.In addition,certain computations regarding 1/2 or fractions containing 1/2 can be conducted using this table,and it may also be used for extracting roots.The Suan Biao is of great significance for research on ancient mathematics,and its discovery is enormously valuable for studies on arithmetic methods and computational tools in early China.
文摘Chinese bronzes are both valuable archaeological remains and significant objects of study in the history of art and technology due to their unique style,complex functions,and technological sophistication.In 1928,the archaeological excavation in Anyang was regarded as the symbol of the establishment of the field of Chinese archaeology.By 2000,tens of thousands of bronzes,and some bronze foundries had been excavated and studied.In archaeologist-led studies,the issues involved are generic,and their scope is restricted,while in multi-disciplinary studies involving both archaeologists and historians of technology,the research is more specific,indicating that research effectiveness and scientific collaboration are closely correlated.
