Contextualizing Playfair and Colebrooke 251
Th e text reads: ‘thus it is demonstrated that the diff erence of the squares
is equal to the product of the sum and the diff erence’. 93 Th e text then pro-
ceeds on the basis of this example to construct other Pythagorean triples.
Similarly, another visual demonstration follows for §149.
§149 Rule: Th e diff erence between the sum of the squares of two quantities what-
soever, and the square of their sum, is equal to twice their product; as in the case of
two unknown quantities. 94
Th e demonstration is worked out on the basis of a particular case, and pro-
vides a procedure thus for any two sets of numbers. Colebrooke’s transla-
tion of Bhaskara’s demonstration reads: ‘For instance, let the quantities be
3 and 5. Th eir squares are 9 and 25. Th e square of their sum is 64. From this
taking away the sum of the squares the remainder is 30.’ 95 And then in the
Figure 5.2 Th e square a 2 minus the square b 2.
5 × 5Figure 5.3 Th e rectangle of sides a + b and b − a.
93 C1817: 223.
94 C1817: 224.
95 C1817: 30.