The Science of the Shulba: A Study in Early Hindu Geometry c7.27

c7.27

part. Now, when the increment happens to be equal to the given side, how is then the given side to be divided? How also the mark (should be made)? How also in the case when the increment happens to be greater (than the given side)? There also the method is exactly the same, we say. But the given side with its increment should then be reduced to common denominators; the added portion should then be divided into twice the number of parts (thus obtained) and the mark should be made in it (at a distance) less by one such part. For instance, in case of adding twice as much, the increment is one part and (in terms of it) the given side is a half part. Then on adding together the increment and the given side after reduction to common denominators, there will be three halves. On dividing the increment into twice that number of parts, there will be six halves in the denominator; so the mark will be (at a distance) less by one of these parts. In case of adding three times, the increment is one part; the given side is the third part (of that); there the increment contains three third parts. So the given side and the increment together contain four third parts. On dividing the increment into twice as many parts there will be eight third parts in the denominator. Then the mark will be (at a distance) less by one of these parts. In the cases of adding four times, etc., the divisions and the marks should be made in the same way."