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OTAPTER I-ARITHMETICAL OPARATIONS.
CO
begin with 1 and end with 6, and then become gradually diminished, are divided between 441 persone. What is the share of each?
28. Gems (amounting to) 28483 (in number) are given in offering) to 13 Jina teinpley. Givo out the share of each (temple).
Thus ends division, the second of the oporations kuown as Parikarman.
Squaring. The rulo of work in relation to the operation of squaring, which is the third (among tho parikaman operations), is as follows:
29. The multiplication of two equal quantities: or the multi. plication of the two quantities obtained (from tho givon quantity) hy tho subtraction (therefroin), and tho addition (therounto), of any chosen quantity, together with tho addition of the square of that chosen quantity (to that product): or the sum of a series in arithmetical progrossion, of which 1 is the first torm, 2 is the common difference, and the number of terms whorein is that (of which tho square is) required : givos rise to the (roquired) square.
30. Tho square of pubers consisting of two or more places ** is equal to) the sum of the squaros of all the numbors (in all the placos) combined with twice the product of thono (vumbers) taken (two at a time) in order.
28. Here, 28483 is given a 83 + 400 + (4000 x 7). 29. Tho rule given hereiu, exproewed algebryically, comow out. thus :
(i) axa - q'; (ii) (u + a)(a -2) + x = c; (iii) 1 + 8 + 6+ 7+ ... op to a terms sal
80. The word translatod by place hero in P T; it ubviously means a pluce in notation. Here, as a commentary interpruts it, it may also denote the cons. ponent parts of rum, 4 ench kuch part han place in the sam. According to both these interpretations the rule workout correctly.
For instance, (1284)' = (100* + 200€ + 80€ + 4*) + 2 x 1000 200 + 2 x 1000 x 80 +2 x 1000 X 4+2 x 200 x 30+ 2 * 200 X 4+ 2 * 30 * .
Similarly (1+2+3+4=(1+2° +81 +4*) + 2(1 x 2+1 3+1x 4+2 3+%** +8 x 4).
