The History of Mathematical Proof in Ancient Traditions

Contextualizing Playfair and Colebrooke 243 the Bija-Ganita and Lilavati of Bhaskara, 65 as well as Brahmagupta’s (Colebrooke: ‘ ...

244 dhruv raina Colebrooke begins by pointing out that Aryabhata was the fi rst of the Indian authors known to have treated of a ...

Contextualizing Playfair and Colebrooke 245 analysis is then for Colebrooke: ‘ calculation attended with the manifestation of it ...

246 dhruv raina low’ state of one and ‘high pitch’ of the other was lost sight of and the con- trast between the two traditions ...

Contextualizing Playfair and Colebrooke 247 his homeward voyage – we are informed of this through the biography of Colebrooke wr ...

248 dhruv raina Th e really interesting feature is the convergence in the reading of Colebrooke the son and Banerji concerning t ...

Contextualizing Playfair and Colebrooke 249 off ered both algebraic and geometrical proofs. In a contemporary idiom these rules ...

250 dhruv raina In modern language this could be translated as a- 3 − 1 = c − b , where Bhaskara immediately suggests taking c − ...

Contextualizing Playfair and Colebrooke 251 Th e text reads: ‘thus it is demonstrated that the diff erence of the squares is equ ...

252 dhruv raina translation Bhaskara exhorts his reader to ‘See’ the illustration that follows (see Figures 5.4 – 5.6 ). Th us ( ...

Contextualizing Playfair and Colebrooke 253 Figure 5.6 Th e square ( a + b ) 2. 8 × 8 Figure 5.7 Th e area ( a + b )^2 minus the ...

254 dhruv raina these demonstrations, we are reminded, is similar to Wallis’ demonstration that appeared in the treatise on angu ...

Contextualizing Playfair and Colebrooke 255 99 C1817: 220–1. 100 C1817: xviii. 101 A contemporary mathematical review of the sol ...

256 dhruv raina On reading of the early responses from a French savant to the work of Colebrooke, it is possible to discern that ...

Contextualizing Playfair and Colebrooke 257 Bailly , J.-S. ( 1775 ) Histoire de l’astronomie ancienne depuis son origine jusqu’à ...

258 dhruv raina Le Gentil , G. H. J. B. ( 1779 –81) Voyages dans les mers de l’Inde, fait par ordre du roi, à l’occasion du pass ...

Contextualizing Playfair and Colebrooke 259 Teltscher , K. ( 1995 ) India Inscribed: European and British Writing on India 1600– ...

6 Overlooking mathematical justifi cations in the Sanskrit tradition: the nuanced case of G. F. W. Th ibaut Agathe Keller Introd ...

Th e Sanskrit tradition: the case of G. F. W. Th ibaut 261 Th ibaut’s intellectual background Th ibaut’s approach to the śulbasū ...

262 agathe keller Pañcasiddhānta of Varāhamihira. In 1888, he also edited and translated this treatise with S. Dvivedi and conse ...