The History of Mathematical Proof in Ancient Traditions

Polygonal numbers in ancient Greek mathematics 323 But now Diophantus is only interested in OB ( j + 2 = 1 + (1 + j )), KB ( j ) ...

324 ian mueller Th ere is no more basis for this generalization than for the generalizations we have seen in Nicomachus; indeed, ...

Polygonal numbers in ancient Greek mathematics 325 8 × KB) the square of what is less than it by 4 is added (that is NB), it pr ...

326 ian mueller Bibliography Bachet , C. (ed. and trans.) ( 1621 ) Diophanti Alexandrini Arithmeticorum Libri Sex et De Numeris ...

327 10 Reasoning and symbolism in Diophantus: preliminary observations Reviel Netz In memoriam D. H. F. Fowler 1. Introducing th ...

328 reviel netz ( 1842 ), it has been widely recognized that Diophantus’ symbols are not the same as those of modern algebra: hi ...

Reasoning and symbolism in Diophantus 329 by such connectors as ‘since’, ‘therefore’, etc. Since the text is at the inter- secti ...

330 reviel netz scribe’s discretion, and no pattern was assumed at the outset. Th e two – full word and its abbreviation – acted ...

Reasoning and symbolism in Diophantus 331 ‘lacking’, roughly an upside-down Ψ (I shall indeed represent it in what follows by Ψ, ...

332 reviel netz Th e alphabetic numerals themselves. While Greek numbers are very oft en written out by alphabetic numerals, the ...

Reasoning and symbolism in Diophantus 333 abbreviation is used inside the noun-phrase of the specifi c form of example (2) above ...

334 reviel netz consonant–vowel syllable), which he then turned into a symbol by placing the vowel as a superscript on the conso ...

Reasoning and symbolism in Diophantus 335 Th e symbols for square, and for sides in a right-angled triangle, are the exception, ...

336 reviel netz ‘number’. It is only the second number – the one counted as ‘1’ - which serves as an unknown in this problem. On ...

Reasoning and symbolism in Diophantus 337 Tannery: Let the which is added and taken away from each number <sc. of the two ot ...

338 reviel netz Tannery has all as alphabetical numerals. Th e most we can say is that, in the manuscripts, there is an overall ...

Reasoning and symbolism in Diophantus 339 abbreviation as against a fully spelled out word, are tenuous. Sometimes one discerns ...

340 reviel netz used in Sanskrit mathematics. 10 Indo-European words are a concatena- tion of prefi xes, roots and suffi xes. Ea ...

Reasoning and symbolism in Diophantus 341 codex, and with the overall tenor of the culture with which it is associated: a cultur ...

342 reviel netz To two given ςς: to add to the smaller of them, and to take away from the greater, and to make the resulting < ...