Essay name: Ganitatilaka (Sanskrit text and English introduction)
Author: H. R. Kapadia
The Sanskrit text of the Ganitatilaka with an English introduction and Appendices. Besides the critically-edited text, this edition also includes the commentary of Simhatilaka Suri. The Ganitatilaka is an 11th-century Indian mathematical text composed entirely of Sanskrit verses and authored by astronomer-mathematician Shripati.
Page 23 of: Ganitatilaka (Sanskrit text and English introduction)
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External source: Shodhganga (Repository of Indian theses)
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definitely known at present being Jinabhadra Gaṇi Kṣamā-
A list of words signifying different numbers is
given in the appendix.²
s'ramaṇa.
CLASSIFICATIONS OF NUMBERS
As was the case with early Greeks, the Jaina school, too,
does not consider one as a number. This will be evident from
the following line of the 146th sutra of Anuyogadvāra:-
"से किं तं गणणासंखा [se kiṃ taṃ gaṇaṇāsaṃkhā ] ? एक्को गणणं न उबेइ, दुप्पभिइ संखा [ekko gaṇaṇaṃ na ubei, duppabhii saṃkhā] ""
While explaining this portion Maladhārin Hemacandra remarks
as under:-
When an object like a pot is seen, what one realises is only
a pot and not its number; or, he adds, it may be due to the fact
that in ordinary dealings only one thing, if given or taken, is
mostly not taken into account. Thus the Jainas begin with two
and end, of course, with the highest possible type of infinity.
All these numbers can be grouped under 21 heads. These
we shall deal with, a little bit later. For the present we shall
mention 4 types referred to in the 316th sūtra of Sthānāṃga.
THE FOUR TYPES OF NUMBERS
4 Even, in the time of the Vedas, we find the distinction
made between odd and even numbers. These are styled as
ojas (3) and yugma (ч) in Jainism. Furthermore, it is
interesting to note that they are associated with kṛta, dvāpara,
tretā and kali, the well-known names for the four yugas of
That he uses contrary moves even while expressing numbers by resorting
to Katapayādi system in its second variant is borne out by Gommaṭasāra (Jīva-
kāṇḍa, v. 158) and Trilokasāra (gāthā 98 ).
1 See Bṛhatkṣetrasamāsa I. 69.
2 While representing various numerical quantities by certain things,
S'ripati has invariably followed the decimal system of notation. The words
used by him are marked with an asterisk.
3 Sanskrit rendering:-
अथ किं सा गणनासङ्ख्या [atha kiṃ sā gaṇanāsaṅkhyā ] ? एको गणनां नोपैति, द्विप्रभृति सख्या ।
[eko gaṇanāṃ nopaiti, dviprabhṛti sakhyā |
] 4 In the following verse of Das'agitikā of Aryabhata I (499) varga means
"odd" and avarga means "even":-
"वर्गाक्षराणि वर्गेऽवर्गेऽवर्गाक्षराणि कात् इमौ यः ।
खद्विवके स्वरा नवे वर्गेऽवर्गे नवान्त्यवर्गे वा ॥ [vargākṣarāṇi varge'varge'vargākṣarāṇi kāt imau yaḥ |
khadvivake svarā nave varge'varge navāntyavarge vā ||] "
In later works the words visama and sama stand for "odd" and "even".
