252 dhruv raina
translation Bhaskara exhorts his reader to ‘See’ the illustration that follows
(see Figures 5.4 – 5.6 ). Th us (3 + 5)^2 = 64.. ., ( a + b)^2
From this subtract 3^2 + 5^2... a 2 + b 2
Which makes 64 – 34 = 30... ( a + b )^2 – ( a 2 + b 2 )Figure 5.4 Th e square a 2.3 × 3Figure 5.5 Th e square b 2.5 × 596 C1817: 224.Th e left -over square cells are seen to be equal to twice the product
( Figure 5.7 ). Aft er which Bhaskara concludes: ‘Here square compartments,
equal to twice the product are apparent, and (the proposition) is proved.’ 96
We have here two cases of visual demonstration (Colebrooke calls
them geometrical demonstrations) though in his translations he vacil-
lates between the terms proofs and demonstrations. But clearly both are
demonstrations from particular cases formulated within the framework of
particular cases treated in a general way.
Furthermore, Colebrooke briefl y discusses two diff erent demonstrations
of the Pythagorean theorem in Bhaskara’s Bija-Ganita (§146). Th e fi rst of