CHAPTER II-ARITHMETICAL OPERATIONS. 13 begin with 1 and end with 6, and then become gradually dimi- nished, are divided between 441 persons What is the share of each? 28 Gems (amounting to) 28483 (in number) are given (in offering) to 13 Jina temples. Give out the share of each (temple) Thus ends division, the second of the operations known as Parıkarman. Squaring. The rule of work in relation to the operation of squaring, which is the third (among the parharmun operations), is as follows:- 29. The multiplication of two equal quantities: or the multi- plication of the two quantities obtained (from the given quantity) by the subtraction (therefrom), and the addition (thereunto), of: auy chosen quantity, together with the addition of the square of that chosen quantity (to that product): or the sum of a series in arith- metical progression, of which 1 is the first term, 2 is the common difference, and the number of terms wherein is that (of which the square is) required: gives rise to the (required) square. . 30. The square of numbers consisting of two or more places is (equal to) the sum of the squares of all the numbers (in all the places) combined with twice the product of those (numbers) taken (two at a time) in order 28. Here, 28 183 is given as 83 +400+ (1000 × 7). 29. The rule given here, expressed algebraically, comes out thus: (1) axa - a², (11) (+) (a-x)+= a, ()1+3+5+7+ .. up to a terms=a² 30. The word trans:ated by place here is , it obviously means a place in notation. Here, as a commentary internets it, it may also denote the com- ponent parts of a suni, as each such pait has a place in the sum. According to both these interpretations the rule works out correctly. For instance, (1234) = (100+200+30+ 1) +2 x 1000x200+2 1000 × 30 + 2 x 1000 x 4+2 x 200 x 30+ 2x 200 x4+2×30× 1. Similarly (1+2+3+4)=(1+2+3+4) +2(1 x 2+1x3+1x4+2x3+2x+ +3x+).
