The Science of the Shulba: A Study in Early Hindu Geometry c7.26

c7.26

" In case of all additions, as many times the added portion as the sum of the given side and the added portion is, into twice so many parts the added portion is divided; make the mark there (*i.e.*, in the added portion, at a distance) less by one such part. For instance, in case of adding to the given side its half, (consider) that half as one part; the given side contains two such parts. So the given side with its increment contains three parts like the increment. Dividing the added portion into twice as many parts, that mark will be (at a distance) less by one-sixth the added portion. So in case of increasing the given side by itself, the increment is one part ; the given side has one part like it. So the given side with its increment has two parts. On dividing the increment into twice as many parts, it will be divided into four parts; then the mark will be (at a distance) less by the fourth part. Similarly in case of adding the third part, the added portion is one part; the given side contains three such parts. On dividing the added portion into twice as many parts, the mark will be (at a distance) less by its one-eighth part. In the same way in case of adding the fourth and other parts, the sum of the given side and its increment should be divided into parts in the same way and the mark should be made (at a distance) less by one such