Ganitasara Sangraha of Mahavira

SR No.: 011112
Original Sutra Author: N/A
Author: Rangacharya
Publisher: Rangacharya
Publication Year: 1912
Total Pages: 531
Language: English
Classification: Book_English
File Size: 24 MB

Page 219

CHAPTER II-ARITA VETICAL OPERATIONS.
17
45. In an arithmetically progressive series, wherein gun is the first term ns well as the common liflorone, and the number of terms is (egnal to the riven number, multiply tho preoeding terms by the immediately following ones. The sum of the products (80 obtained), when multiplied by three and combined with the last term (in the above serios in arithmetical progression), bocomes the cubo (of the given quantity).
46. (In a given quantity, the squares of (the number reproBeutel by the figures in the last place as also (ly those in the other (remaining placos) are taken ; and cach of these (squarcs) is multiplied by the number of the other place and also by three; thu sum of the two (quantities resulting thus), when combined again with the cubes of the numbers oorrosponding to all tho (optional) places, (gives riso to) the cube (of the given quantity).
17. Or, the cubo of the last figuro (in the number counted from right to left is to be obtained); and thrior the square (of that last figure is to be pushed on to the right by ono notutional plaor) and multiplied by the number represented by the figures found in the remaining (placos); theu the Hybro of this number represented by the figures found in the remaining (placos) is to be pushed on (us above) and multiplied by thrico the Inrt figuru (above-mentioned). These three quantities are thon to bu placod in position and then summed up). Such is the rule to be carried out) here.
Framplex in illustration thereof. 48. Give out tho cubes of the numbers from 1 to 9 and of 13, 25, 35, 77 and 96.
49. Give out the cubes of 101, 172,516,717 and 1341.
........
+: 3 1x2 + 2x3+3 **+ **5+ ... +a- + -a!
40. 3ab+34) + a + ( + ) To make the rule general and applicable to numbers having more than two place, it is clearly insplied here that 3 1 +
+ 3u (b + c)* + a+(+ c) (a + b + c)', and it is obvious that any number my be represented as the sum of two other suitably chosen number
47. 'llo pnahing on of a figure here referred to in vinilar to what in exhibited in the note under stants 31 in this chapter.