The History of Mathematical Proof in Ancient Traditions

Reading proofs in Chinese commentaries 463 kinds of units – cash and persons. In correlation with these changes, the algorithm d ...

464 karine chemla One should not forget, however, that the modern symbolism erases the fact that the two fractions are fractions ...

Reading proofs in Chinese commentaries 465 on the other hand, share a common sub-procedure and, in the context of division, whic ...

466 karine chemla Whatever the literal interpretation of this expression may be, there is no doubt that the result is understood ...

Reading proofs in Chinese commentaries 467 sharing’, this transformation is carried out on the dividend and the divisor jointly ...

468 karine chemla Th e key point that Liu Hui stresses is that by the very fact that these quantities are taken as dividend and ...

Reading proofs in Chinese commentaries 469 Th e consequences of such a state are made explicit in the commentary following probl ...

470 karine chemla in correlation with each other. In the case of a division, by a simultaneous dissection of the units of the di ...

Reading proofs in Chinese commentaries 471 (a+ )/( + )=( + )/( + )=( + )/( + ) b c d e f ca b cd ec f fca fb fcd ec (fi rst mult ...

472 karine chemla each other. 61 In the context of dividing between quantities with fractions, the last analysed sentence of Liu ...

Reading proofs in Chinese commentaries 473 exact. On the other hand, as Liu Hui shows, the ‘procedure for directly sharing’ amou ...

474 karine chemla of Mathematical Procedures contains in relation to this operation, which provides a hint that this was how the ...

Reading proofs in Chinese commentaries 475 is, the rule of three, it guarantees precisely that the number by which one multiplie ...

476 karine chemla If ‘the denominators of the parts respectively multiply the integer corresponding to them and the numerators o ...

Reading proofs in Chinese commentaries 477 in various ways, and the proof of the correctness of the former may as well incorpora ...

478 karine chemla In each of the cases when a dividend does not fi ll up a divisor, they hence have the names of denominator and ...

Reading proofs in Chinese commentaries 479 cates the reason why it must be used: earlier in the fl ow of computations, one multi ...

480 karine chemla Th e problem in Th e Nine Chapters asks to compute the product of a / b by c / d. On the basis of the previous ...

Reading proofs in Chinese commentaries 481 We saw how proofs relied on algorithms, which had already been estab- lished as corre ...

482 karine chemla lianchu ‘dividing at a stroke’, bingchu ‘dividing together’. 81 Th ese terms refer to the three fundamental tr ...