The History of Mathematical Proof in Ancient Traditions

Reading proofs in Chinese commentaries 443 Figure 13.5 Th e basic structure of algorithms 1 and 2, for the truncated pyramid wit ...

444 karine chemla Th e fi rst division ends the ‘procedure for the fi eld with the greatest gen- erality’. Th e reason underlyin ...

Reading proofs in Chinese commentaries 445 the outline of a problem asks to fulfi l. Th is detail indicates that, in ancient Chi ...

446 karine chemla Transforming algorithms as lists of operations Th e goal, from this point onwards, is the transformation of th ...

Reading proofs in Chinese commentaries 447 Although the transformation seems comparable to transformation 3 discussed earlier, i ...

448 karine chemla expectation is all the more natural when we know that in a second part of his commentary, Liu Hui relies on hi ...

Reading proofs in Chinese commentaries 449 grouped into a unique division. Th e technical term chosen for this division refers t ...

450 karine chemla equalities are reshaped, whereas, in the commentaries, what is rewritten are instead algorithms. 31 In correla ...

Reading proofs in Chinese commentaries 451 ii. Inverting the order of divisions and multiplications We saw that this very inve ...

452 karine chemla were conceived. Th ese suggestions seem to be natural on the basis of the previous discussion. Indeed, on seve ...

Reading proofs in Chinese commentaries 453 Th e reason Liu Hui adduces for explaining why it was necessary to give the result in ...

454 karine chemla introduction of certain kinds of numbers and the line of proof that made use of transformations carried out on ...

Reading proofs in Chinese commentaries 455 types of proof. 39 Th e introduction of such quantities is hence related to a specifi ...

456 karine chemla as a kind of division – the fact that they are exact guarantees that inverse operations which follow each othe ...

Reading proofs in Chinese commentaries 457 more interesting is that, although in the Book of Mathematical Procedures the aim of ...

458 karine chemla fact that a value was used earlier in the fl ow of computations, that it was interpreted as having been expand ...

Reading proofs in Chinese commentaries 459 with the greatest generality’. And the nature of the division as being ‘in return’ is ...

460 karine chemla dividend and divisor of a division to be carried out, or as the numerator and denominator of a completed divis ...

Reading proofs in Chinese commentaries 461 fractions discussed in Th e Nine Chapters. Th ere, the commentary discusses the reaso ...

462 karine chemla We can now turn to examining in greater detail the relationship between proving the correctness of procedures ...