The History of Mathematical Proof in Ancient Traditions

423 13 Reading proofs in Chinese commentaries: algebraic proofs in an algorithmic context Karine Chemla Th e earliest Chinese te ...

424 karine chemla the correctness of the algorithms provided. 3 However, soon aft er its com- pletion, the book became a ‘Classi ...

Reading proofs in Chinese commentaries 425 were driving the inquiry into mathematics in ancient China. For instance, they reveal ...

426 karine chemla which the refl ection about proof developed in ancient China still awaits further study. In this chapter, I sh ...

Reading proofs in Chinese commentaries 427 base (see Figure 13.1 below). 10 Th e problem in which Th e Nine Chapters introduces ...

428 karine chemla if such is the case, as a consequence, the diameter of the lower circle of the solid to be considered is conse ...

Reading proofs in Chinese commentaries 429 lines of argumentation. Th e fi rst line consists of establishing an algorithm, for w ...

430 karine chemla Using the same notations for algorithms as above, it can be represented as follows: 14 Incidentally, this prop ...

Reading proofs in Chinese commentaries 431 To determine the ‘meaning’ of the result, that is, that one obtains the volume of the ...

432 karine chemla other. Th is operation implies inserting at this point the algorithm that Th e Nine Chapters gave for multiply ...

Reading proofs in Chinese commentaries 433 ences of the upper and lower bases were displayed, respectively in the upper and lowe ...

434 karine chemla 18 Perhaps, the layout of the fi rst step should be restored in a diff erent way. Th e middle row of the upper ...

Reading proofs in Chinese commentaries 435 thereby appears as an operation of multiplication carried out on the three lines that ...

436 karine chemla the circumscribed truncated pyramid dealt only with integers or fractions, other procedures could be used to m ...

Reading proofs in Chinese commentaries 437 Th e way in which Liu Hui describes this process is highly interesting for our purpos ...

438 karine chemla Why backtrack, one may ask, when discussing these two operations, if it leads us to start from where, in any c ...

Reading proofs in Chinese commentaries 439 with square base circumscribed to one with a circular base in case quanti- ties with ...

440 karine chemla of the ‘procedure for the fi eld with the greatest generality’ shows that, before dividing by the product of t ...

Reading proofs in Chinese commentaries 441 the commentator aims at accounting for the algorithm as described in the Classic – th ...

442 karine chemla about their motivations, when he accounts for why the order of a division and a multiplication was inverted wi ...