The History of Mathematical Proof in Ancient Traditions

Reasoning and symbolism in Diophantus 343 Text 3: Given two numbers, the fi rst greater than the second, and given the ratio of ...

344 reviel netz the third millennium bce (if not earlier), surviving, arguably, into our own time. Th ey persisted almost exclus ...

Reasoning and symbolism in Diophantus 345 elite-educated, literate form, Diophantus chose to produce not Euclidean algebra, but ...

346 reviel netz components into some kind of coherent unity then would lead to a certain transformation. Th e way this applies t ...

Reasoning and symbolism in Diophantus 347 format - not a single monolith to start with. In fi tting his text into the establishe ...

348 reviel netz geometry would be that results should be transferable from one set of numerical values to any other soluble set, ...

Reasoning and symbolism in Diophantus 349 of mathematical contents. Of course, I imagine that he would still prefer a general pr ...

350 reviel netz x and y , for sure, a confusing symbolism, as well (one would need to develop procedures to diff erentiate ‘two ...

Reasoning and symbolism in Diophantus 351 It is natural that, among the models available to him from elite literate Greek mathem ...

352 reviel netz are problems solved in the most appropriate way? Th e task, then, is to show how the off ered solution to the pr ...

Reasoning and symbolism in Diophantus 353 My interpretation of Diophantus thus relies on two theoretical contexts I developed el ...

354 reviel netz in roundabout, extremely subtle, or even paradoxical fashion, so that it is only by reading them several times o ...

Reasoning and symbolism in Diophantus 355 be lost out of sight, for otherwise the derivation would appear as a con- jurer’s tric ...

356 reviel netz (1) And if it is added to twenty, results: ς 1 Μ ο 20. (2) And if it is taken away from 100, results: Μ ο 100 la ...

Reasoning and symbolism in Diophantus 357 previous lay and school algebras, but also from the established elite literate Greek m ...

358 reviel netz to B is the same as the ratio of C to D’ one can detect three levels: the level of the proportion statement, whi ...

Reasoning and symbolism in Diophantus 359 from expressions such as ‘the ratio of A to B is the same as the ratio of C to D’. For ...

360 reviel netz Because he has a particular task, and particular tools, all refl ecting a complex historical setting. Everything ...

Reasoning and symbolism in Diophantus 361 Groningen , B. A. van ( 1955 ) Short Manual of Greek Palaeography. Leiden. Heath , T. ...

362 11 Mathematical justifi cation as non-conceptualized practice: the Babylonian example Jens Høyrup Speaking about and doing – ...