The History of Mathematical Proof in Ancient Traditions

Mathematical justifi cation: the Babylonian example 363 meant to agree with such norms as are refl ected in the philosophical pr ...

364 jens Høyrup 3 I use the translations from H2002 with minor corrections, leaving out the interlinear transliterated text and ...

Mathematical justifi cation: the Babylonian example 365 [a surface] I have built. [So] much as the length over the width wen ...

366 jens Høyrup Igi 6^12 detach: 10 ́. 10 ́ to 10the surface raise, 140. Th e equalside of 1`40 what? 10. Obv. ii 1. 10 to 3 w ...

Mathematical justifi cation: the Babylonian example 367 Th e one who follows the procedure on the diagram and keeps the exact (g ...

368 jens Høyrup Figure 11.2 Th e procedure of BM 13901 #1, in slightly distorted proportions. 1 2 1 2 1 2 1 2 1 2 1S S ...

Mathematical justifi cation: the Babylonian example 369 20 Actually, both Neugebauer and Th ureau-Dangin knew that this was not ...

370 jens Høyrup operations were confl ated, etc. All in all, the text was thus interpreted as a numerical algorithm: Halve 1: ½. ...

Mathematical justifi cation: the Babylonian example 371 Most explicit are some texts from late Old Babylonian Susa: TMS vii , TM ...

372 jens Høyrup Figure 11.3 Th e confi guration discussed in TMS ix #1. 30 ′ 20 ′ 1 Figure 11.4 Th e confi guration of TMS ix #2 ...

Mathematical justifi cation: the Babylonian example 373 statement but identifying the area as 10 ́. In line 3, this is told to b ...

374 jens Høyrup Th ereby, the problem has been reduced to a standard rectangle problem (known area and sum of sides), and it is ...

Mathematical justifi cation: the Babylonian example 375 Th e dimensions of the rectangle are not stated directly, but from the n ...

376 jens Høyrup is the width of an imagined ‘real’ fi eld, which could be 20 rods (120  m), whereas the width simpliciter is tha ...

Mathematical justifi cation: the Babylonian example 377 Justifi ability and critique Whoever has tried regularly to give didacti ...

378 jens Høyrup Rev. 1. 3°30 ́, the made-hold, 2. from one tear out, 3. to one append. 4. Th e fi rst is 12, the second is 5. 5. ...

Mathematical justifi cation: the Babylonian example 379 back in its original position) must fi rst be at disposition, that is, i ...

380 jens Høyrup explicit, this notion underlies the determination of areas by ‘raising’; 34 i t is widespread in pre-modern prac ...

Mathematical justifi cation: the Babylonian example 381 trade, the teaching of mathematics. None the less, the social raison d’ê ...

382 jens Høyrup by explanations of the reasons for what they were asked to do? If the rules used by practitioners were regarded ...