The History of Mathematical Proof in Ancient Traditions

Archimedes’ writings: through Heiberg’s veil 203 accessible; Archimedes had to be diffi cult. While perfectly explicit and consi ...

204 reviel netz much of the argument for Heiberg’s excisions – his major editorial inter- vention in the text of Archimedes – di ...

Archimedes’ writings: through Heiberg’s veil 205 ( 1996 ) ‘ Th e method of indivisibles in ancient geometry ’, in Vita Mathemati ...

206 4 John Philoponus and the conformity of mathematical proofs to Aristotelian demonstrations Orna Harari One of the central is ...

Philoponus and Aristotelian demonstrations 207 certain mathematical proofs to Aristotelian demonstrations is questioned. 2 Accor ...

208 orna harari Aristotelian demonstrations. As a corollary to this discussion, I conclude my chapter with an attempt to trace t ...

Philoponus and Aristotelian demonstrations 209 are two right angles? We know it from the defi nition of right angles, [stating] ...

210 orna harari formulates this question in response to Aristotle’s contention that sentences whose subject is an attribute, suc ...

Philoponus and Aristotelian demonstrations 211 them from divine entities, which are also capable of knowledge but are not mortal ...

212 orna harari include the attributes that are present in matter. 12 In this interpretation, then, the ontological distinction ...

Philoponus and Aristotelian demonstrations 213 of natural things cannot be separated in existence from matter, but he disa- gree ...

214 orna harari of an object are not physical defi nitions, but are dialectical or empty. His example of such an empty defi niti ...

Philoponus and Aristotelian demonstrations 215 In his comments on the Posterior Analytics ii .2, Philoponus presents the followi ...

216 orna harari understanding the distinction made in this passage, Philoponus clearly does not follow Aristotle here in assimil ...

Philoponus and Aristotelian demonstrations 217 term and the conclusion of a demonstration are related according to the fourth se ...

218 orna harari demonstrative derivation rests on two relations: the transitivity of the pre- dicative relation that the premise ...

Philoponus and Aristotelian demonstrations 219 Proclus on the conformity between mathematical proofs and Aristotelian demonstrat ...

220 orna harari Proclus’ reason for regarding this Euclidean proof as based on signs rather than on causes concerns the relation ...

Philoponus and Aristotelian demonstrations 221 up to their intersection point, is also presented by Proclus in his comments on p ...

222 orna harari Causal considerations are employed with regard to mathematical dem- onstrations, when mathematical objects are c ...