Ganittilakam Savrtuttikam

Author(s): Hiralal R Kapadia
Publisher: Oriental Research Institute Vadodra

Page 35

XXXIV
INTRODUCTION
Dr. Datta has treated this subject in his article “The Jaina School of Mathematics" (pp. 141-142 ) as under:
“Consider a certain trough which is of the size of the Jambūdvipa whose diameter is 100,000 yojanas, and whose cir. cumference is 316, 227 yojanas, 3 gavyūti, 128 dhanus, 134 angula and a little more. Fill it up with white mustard seeds counting them one after another. Continue in this way to fill up with mustard seeds other troughs of the sizes of the various lands and seas of the Jain cosmography. Still it is difficult to reach the highest number amongst the numerables. So the highest numerable number of the early Jainas corresponds to what is called Alef-zero in modern mathematics. For numbers beyond that Anuyoga-dvāra-sätra further proceeds:
By adding unity to the higest ‘numerable', the lowest 'nearly innumerable' is obtained. After that are the intermediate numbers until the highest 'nearly innumerable' is reached. Which is the highest 'nearly innumerable'?
The lowest 'nearly innumerable' number multiplied by the lowest ‘nearly innumerable' number and then diminished by unity will give the highest 'nearly innumerable' number. Or the lowest 'truly innumerable' number diminished by unity gives the highest 'nearly innumerable' number. Which is the lowest 'truly innumerable'? The lowest 'truly innumerable' is obtained by multiplying the lowest 'nearly innumerable' number by itself; or by adding unity to the 'highest nearly innumerable' number. This number is also equivalent to Avali. After that are the intermediate numbers until the highest 'truly innumerable' number is reached. Which is this highest 'truly innumerable' number? It is the lowest 'truly innumerable' number multiplied by the Avali and then diminished by unity; or the lowest ‘innumerably innumerable' number decreased by unity. Which is the lowest innumerably innumerable' number? It is the lowest 'truly innumerable' multiplied by Avali or the highest 'truly innumerable' number increased by unity. After that, are the intermediate numbers until the highest 'innumerably
1 See "The Bulletin of the Calcutta Mathematical Society" vol. XXI, No. 2, 1929.