A Study On Euclid's Elements Edited And Commentated By Christoph Clavius And Its Chinese Translation

The first 6 books of The Elements edited and commentated by Christoph Clavius(1537/1538-1612)in 1574 was translated into Chinese by Matteo Ricci(1552-1610)and Xu Guangqi(1562-1633),under a title: Jihe Yuanben.Published in 1607,this Chinese version of Elements marks a starting point for Western mathematics in China,also a starting point for Western classics in China between Ming and Qing Era,thereby signifies historically.The Chinese translation of Clavius' Elements is a tough cultural creation: on one hand,Latin differs with traditional Chinese in aspects of grammatical structure,style,words,etc;on the other hand,Euclid's system of geometry,which focuses on demonstration and deduction,is different from Chinese traditional mathematics,which focuses on utility and calculation.How a Western scientific classics gets translated from language barriers? Can traditional Chinese convey correctly Western mathematics' logic? What roles do Chinese traditional mathematics and culture play in the translation of western classics by Ricci and Xu?Former scholars studied these problems from different views,but their works do not rest on the foundation of deeply understanding Clavius' Elements,nor did they compare completely latin version and Chinese version,making their conclusions mostly incomplete and incorrect,which is a great remorse.Therefore,this dissertation focuses on the Chinese translation of Clavius' Elements.Clavius' Elements is not equal to Euclid's Elements,the nomination Clavius' Elements is a simplification of Euclid's Elements edited and commentated by Christoph Clavius,the adjective Clavius' means this version is different from Euclid's original work in aspects of number of books,text,commentary and nature,and deeply influenced by its editor and commentator: Clavius.His Elements contains lots of works by former editors and commentators,so in practical discussion,this dissertation begins with the first Latin Elements: Adelard version,scrutinizing important Latin Elements versions between 12 th to 16 th century,analysing Clavius' version into the historical context of the configuration of Latin Elements versions between 12 th to16th century,clearing its sameness and difference compared with former versions.This dissertation also compares completely Clavius' Elements and Jihe Yuanben,in two aspects of text and discourse,investigating the complex relation such as mimicking,decreasing,increasing and changing between these two versions.Specifically,except for the first introduction chapter,the second chapter investigates the configuration between Adelard's Elements and Clavius' Elements in two aspects of cultural orientation and textual form,including both eras of Medieval and Renaissance.On cultural orientation,the Medieval editors ignored the Greek cultural ingredients in Elements,which appeared as normal mathematical textbooks inMedieval times,the editors didn't make any public reference to its relation to Greek civilization.However,in Renaissance,we analyse three long prolegomenas in Zamberti's,Commandino's and Clavius' Elements,showing their common structure learns from Introduction to Mathematics by Proclus,a New-Platonist at 5th century.Its contents are: first demonstrating mathematics is a major discipline in Greek knowledge,secondly showing geometry is a major part of Greek mathematics,finally stating Euclid is a geometer,Euclid's Elements is a work of theoretical geometry,thereby making Euclid's Elements to be a feature in Greek civilization.On textual form,postulates & axioms,propositions & discourses increased greatly,making commentary a rival to text in Elements,which became a composition of text in geometry and commentary in geometry-arithmetics-algebra.Clavius' Elements followed the general developing trail of Latin Elements in aspects of thought disposition,structure,procedure of demonstration,propositions and discourses,became a cosmopolitian work in Latin Elements.The third chapter summarizes three different points between Clavius' Elements and Euclids' s Elements: 1,Difference in orientation.Euclid's Elements is a work of theoretical geometry,Clavius' Elements contains lots of ingredients of practical geometry and arithmetics.2,Difference in numbers of books.Euclid's Elements originally was composed by thirteen books,then fifteen books in general since 6th century AD,Clavius called the fifteen books Euclidis Elementorum XV,added another book,forming a version of sixteen books.3,Difference in text.Clavius' Elements increased in aspects of postulates,axioms,definitions and propositions compared with Euclid's Elements,making Clavius' Elements no more equal to Euclid's original work.However,Clavius' Elements followed structure of demonstration from Euclid's Elements completely.The fourth chapter first investigates the origin of Jihe from Jihe Yuanben,stating this word means magnitudo such as line,plane and body,also means quantitas containing both magnitudo and number.Jihe Yuanben has a meaning of theory of geometry.Then it investigates in turn the sameness and difference in definitions,propositions and structure of demonstration between Clavius' Elements and Jihe Yuanben.Generally,the translation of definition differs greatly from original version:among four definition copulatives esse,dicitur,appellatur and vocatur,only translation of esse correspondes to its original meaning;among 83 definition names,less than half correspondes to its original meaning;among 80 explanational parts,only 28 items corresponde to their original meaning.Syntax is the most similar part in translation of definitions.Translation of propositions most correspondes to its original meaning.Among 47 problemas,32 items in simple sentence keeps their original sentax,so do many items in complex sentence,making faithful translation a major part.Among five kinds of theoremas,except simple sentence,other four kinds basically contains faithful form words from tranditional Chinese,keeping original syntax of Latin propositions as possible,conditional sentences and conclusion sentences also features in its Chinese version.The translation of structure of demonstration is most influenced by Chinese traditional mathematics.Ricci and Xu borrowed words from Chinese traditional mathematics,composing referential wordsto structure of demonstration in Chinese version,such as Explation as,Procedure as,which do not exist in Clavius' Elements.Structure of demonstration in Euclid's Elements came from six-part-division by Proclus,Ricci and Xu changed it to be a four-part-division: Explation as-Demonstration as-Procedure as-Commentary as,almost deleting conclusion part in original version,changing greatly.Ricci and Xu also put lots of question sentences into the demonstration of opposing.These question sentences,though independent of Latin original version,are in common with Chinese classcis.All these features make structure of demonstration in Chinese version a special form between China and West.The fifth chapter compares four discourses in Clavius' Elements: Prolegomena mathematicae disciplinae before formal text,discourse on contingle angle in commentary of def 16 book III,discourse on classification of ratio in commentary of def 3 book V,discourse on componential ratio in commentary of def 5 book VI with their Chinese counterparts,finding out the first three pairs of discourses are different in major meaning and points,therefore not in origin-translation relation.Prolegomena mathematicae disciplinae follows transedental theory in philosophy of Plato,its chinese counterpart follows Confucian teachings of studying the things and knowing the logic.Compared with discourse on contingel angle in Clavius' Elements,the reconstruction of its chinese counterpart has two characters: 1,the weakening of the concept of angle,which is congenial to the ignorance of the concept of angle in Chinese traditional mathematics;2,reference to the significance of one-foot-long stick from Zhuangzi,stressing the contingel angle can be divided infinitely.Discourse on ratio in Clavius' Elements has contents of Aristotle logic such as the interchangement of nouns and verbs,genus with difference of linus,which are canceled and changed by Ricci and Xu,mainly keeping numeral procedure from Latin version.The comparation from first three pairs of discourses shows: specific mathematical contents from discourses in Jihe Yuanben come from Latin text,but they are explained in a Chinese traditional way.The fourth pair of discourse in this chapter makes progress between discourse in commentary of def 5 book VI in Clavius' Elements on 1574 and its Chinese counterpart in Jihe Yuanben prologed by Han Yingbi,and between discourse in commentary of def 5 book VI & prop 23 book VI in Clavius' Elements on 1589 etc and Jihe Yuanben from the first collection of the heavenly learning.The conclusion is: Jihe Yuanben prologed by Han Yingbi is the version first printed in 1607,so supports the claim that Jihe Yuanben prologed by Han Yingbi is earlier in chronology than Jihe Yuanben from the first collection of the heavenly learning by text comparation.Finally,the conclusion part in sixth chapter,from a more general view,discusses three aspects:1.the relationship among Euclid's Elements,Clavius' Elements and Jihe Yuanben;2.the two aspects of the Chinese translation of Clavius' Elements;3.the thought of harmonization of Xu Guangqi and the cultural orientation of Jihe Yuanben,so concludes the whole dissertation.