The History of Mathematical Proof in Ancient Traditions

(Elle) #1

572 tian miao


Problem a G i v e n F i n d O t h e r
•61 c − a , a + b + c a , b , c
 62 c − a , c + b − a a , b , c Problem 13
•63a c − a , a + c − b a , b , c c − a > a + c − b ,
( c − a ) − ( a + c − b )> a + c − b
•63b c − a , a + c − b a , b , c c − a > a + c − b ,
( c − a ) − ( a + c − b ) < a + c − b
•63c c − a , a + c − b a , b , c c − a < a + c − b , ( a + c − b ) − ( c − a ) > c − a
•63d c − a , a + c − b a , b , c c − a < a + c − b , ( a + c − b ) − ( c − a ) < c − a
 64 c − a , a − c + b a , b , c Problem 13
 65 c + b , a + b + c a , b , c Problem 8
 66 c + b , b + c − a a , b , c Problem 8
•67 c + b , a + c − b a , b , c
•68 c + b , a − c + b a , b , c
•69 c − b , a + b + c a , b , c
•70 c − b , b + c − a a , b , c
 71 c v− b , a + c − b a , b , c Problem 9
 72 c − b , a − c + b a , b , c Problem 9
 73 a + b + c , b + c − a a , b , c Problem 8
 74 a + b + c , a + c − b a , b , c Problem 12
 75 a + b + c , a − c + b a , b , c Problem 16
 76 b + c − a , a + c − b a , b , c Problem 17
 77 b + c − a , a − c + b a , b , c Problem 13
 78 a + c − b , a − c + b a , b , c Problem 9
N o t e s :
a Th e sign ‘•’ indicates problems that were also discussed by Xu Guangqi in the
Meaning of Gougu.
b Th is means ‘Solve this problem using the method of problem 1’. Similarly hereaft er.

Bibliography

Chemla , K. ( 1992 ) ‘ Résonances entre démonstration et procédure: remarques
sur le commentaire de Liu Hui aux Neuf Chapitres sur les Procédures
Mathématiques ’, in Regards Obliques sur l’Argumentation en Chine , ed.
K.  Chemla. Extrême-Orient, Extrême-Occident 14 : 91 –129.
Ch’en Liang-ts’so (Chen Liangzuo) ( 1982 ) ‘ Zhao Shuang Gougu yuanfang
tuzhu zhi yanjiu ’(Research on the commentary
by Zhao Shuang on the fi gures of the base and the height, the square and the
circle). Dalu zazhi 64 : 33 –52.
Engelfriet , P. ( 1993 ) ‘ Th e Chinese Euclid and its European context ’, in L’Europe en
Chine , ed. C. Jami and H. Delahaye. Paris : 111 –35.
( 1998 ) Euclid in China: Th e Genesis of the First Translation of Euclid’s Elements
in 1607 and its Reception up to 1723. Leiden.

Appendix Continued
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