________________
No. II)
MATHEMATICS OF NEMICANDRA.
99
." वटलवणरोचगानगनजरनगंकासससघधमपरकधरं ।
farauag Uafga" = 413,452,630,308,203,177,749,512,192,000,000,000,000,000,000 with the rightward move. This way of expressing numbers by contrary moves without clearly indicating which move should be adopted in a particular instance introduces a good deal of uncertainty in the arithmetical notation.
The number 65,536 is denoted by the abbreviation qrugt of its full expression "पण्ण्टोपंचसयाछत्तीसा;" 1,294,967,296 by बादालं from "वादालं a303&t 173ra fazarITFITUE!”; and 18,446, 744,073,709,551,616 by the abbraviation game of
"एकचचउछस्सत्रयं च च य सुरणसत्ततियसत्ता। सुरणं णव पण पंच य एक्कं छक्केक्कगो य छक्कं च ॥2 --
Law of Indices
Before stating Nemicandra's definition of the Law of Indices, we should explain the technical terms employed therein. If N=2", then n is called the ardhaccheda of N. The term ardhaccheda is derived from ardha=" half," cheda="divisor" and it means “the number of times that, a particular number can be halved.” Sometimes the word ardha is deleted, and we have simply the term cheda. : In general, if N=x" then n will be the cheda
of N with regard to the base x. If N=29" then n' is called the ardhaccheda of the ardhaccheda of N. Nemicandra gives the following rules :
" The ardhaccheda of the multiplier plus the ardhaccheda of the multiplicand is the ardhuccheda of the product: it has no more cheda."4
2m x 2" =2m+n.
1 Trilokasära, Gāthā 98.
2 Ibid, Gathā 66. 3 Trilokasära. Gātha 8. 4 lbid, Gāthă 105,
