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 367

CHAPTER VI-XIIBD PROBLEMS.
186
The role for arriving at the square root of an unknown) number as inoroased or diminished by a known munber :
2797. The known quantity which is given is first halved and (then) Squared and then one is added (to it). The reulting quantity wither when incroased by the desired given qnantity or when diminished by the (same) quantity yiolds the square root (exactly). . .
An example in illustration thereof.
2804. Here is a number which, whou increased by 10 or diminished by the same 10, yields an exact square root. Think out and tell me that number, O mathematician.
l'he rule for arriving at the two required square quantities, with the aid of those required quantities As multiplied by a known number, and also with the aid of (tho rame known number as forming the value of the squaro root of the difference (between these products): -
281}. The given number is increased by one; and the given number is also diminished by one. The resulting quantitice when halved and then squared give rise to thu two (required) quantities. Then if these be (separately) multiplied by tho given quantity, the syuro root of the difference betwoon those (productos) becomes the given quantity.
An example in illustration thercof.
282-283. Two unknown squared quantities aro multiplied by 71. The square root of the difference between these two resulting products, is also 71. O mathematician, if you know the process of calculation known as citra-kutsikära, calculate and tell me what (those two ankuown) quantities are.
2797. This is merely a particuler cane of the rule given in ntaosa 2767 wherein a is taken to be equal to b.
281). Algebraically, wben the given number ind are the required quero quantities.