The History of Mathematical Proof in Ancient Traditions

A formal system of the Gougu method 563 so c = c + a – a = 676 − x as c + b – a = 560 so, c + b = 560 + x and, b = c + b – c = 5 ...

564 tian miao Th is procedure may be represented in modern algebraic terms by the following equation: x^2 + (a + b)x − [(a + b)^ ...

A formal system of the Gougu method 565 the procedure and gets the geometrical expression of the diff erence between them, then ...

566 tian miao (4) Li Rui follows a formal and systematic way of choosing the unknown, and seeking the equation in the outline. ( ...

A formal system of the Gougu method 567 formulas in their books. Li Rui studied all of these books before he com- piled the GGSX ...

568 tian miao methods and leaving the reader with no doubt about mathematical knowl- edge were the essence of Western mathematic ...

A formal system of the Gougu method 569 yi , Li Rui argues that one has to understand the yi. 33 However, although Xu believed t ...

570 tian miao valuable suggestions. I am especially in debt to Karine Chemla and Catherine Jami. As we were discussing and worki ...

A formal system of the Gougu method 571 Problem a G i v e n F i n d O t h e r  31 a + c , c − a a , b , c Problem 2 •32 a + c , ...

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 ...

A formal system of the Gougu method 573 Gu Yingxiang ( 1553 ) Gougu Suanshu ( Mathematical Procedures on Gougu) , 1553 edn. Guo ...

Index abacus, see tool for calculation Abbenes, J. G. J., 191 abbreviation, 36–7, 328–40, 349, 355–6 absence of demonstrations, ...

Index 575 approximations, 40, 301, 452–8 Arabic science, 2, 5, 7, 21–3, 37, 43–4, 48, 274–5, 286–9 ‘Arabs’, 5, 274, 287 handling ...

576 Index Babylonian mathematics (cont.) see also mathematical education Bachet, C., 325 backtracking huan , 437–8, 447, 457–8, ...

Index 577 Cicero, 362 circle (ratio between circumference and diameter, between area and square of diameter), 427–31, 438, 444–5 ...

578 Index critical editions, 138, 261 historical analysis of critical editions, 20–6, 35–9, 136, 163–204, 336–9 history of proof ...

Index 579 iconically representing the numbers as confi gurations of units, 33, 313–16, 320, 323 indiff erence to geometric shape ...

580 Index Elements (Euclid) (cont.) divergences between proofs in the various manuscripts, 22, 90 Edition August, 82, 137 Editio ...

Index 581 E n g r o ff , J. W., 87, 106, 107, 116–18, 130 enlightenment, 228, 232, 258, 272 post-enlightenment, 228 Ennis, T. E. ...

582 Index generality (cont.) in Nicomachus’ Introduction to Arithmetic , 33–5 of diagrams, see diagram of objects, 33, 427, 460– ...