Ganittilakam Savrtuttikam

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

Page 14

INTRODUCTION
XIII
It is extremely difficult to reconcile these two views especi. ally when we have at present neither any access to a comment. ary prior to the one mentioned above nor to any Mathematical work of Jaina authorship which is earlier than Ganitasāra. sangraha. So, under these circumstances, I shall be excused, if I reserve this matter for future research.
PERMUTATIONS AND COMBINATIONS Bhanga' is the name given to permutations and combina. tions as can be seen from the 716th sūtra of Sthānānga quoted on p. xii. While explaining bhangasuhume occurring in this sūtra, Abhayadeva Sūri las observed :
"भंगसूक्ष्म' भङ्गा-भङ्गका वस्तुविकल्पास्ते च द्विधा-स्थानभङ्गकाः क्रमभङ्गकाश्च तत्राद्या द्रव्यतो नामैका हिंसा न भावतः १ अन्या भावतो न द्रव्यतः २ अन्या भावतो द्रव्यतश्च ३ अन्या न भावतो नापि द्रव्यतः ४ इति इतरे तु द्रव्यतो हिंसा भावतश्च १ द्रव्यतोऽन्या नभावतः २ न द्रव्यतोऽन्या भावतः ३ अन्या न द्रव्यतो न भावतः ४ इति तल्लक्षणं सूक्ष्म भङ्गसूक्ष्म, सूक्ष्मता चास्य भजनीयपदबहुत्वे गहनभावेन सूक्ष्मबुद्धिगम्यत्वात्".
This points out two types of bhangas: (1) sthānabhanga and (2) kramabhanga.
Three verses pertaining to bhanga are noted as under by S'ilāňka Sūri in his commentary to Sūtrakrta (Samayadhyayana, Anuyogadvāra, v. 28):
"एकाद्या गच्छपर्यन्ताः परस्परसमाहताः। राशयस्तद्धि विज्ञेयं विकल्पगणिते फलम् ॥१॥ पुव्वाणुपुचि हेट्ठा समयाभेएण कुण जहाजेहें। उवरिमतुल्लं पुरओ नसेज पुव्वक्कमो सेसे ॥२॥ गणितेऽत्यन्तविभक्ते तु लब्धं शेषैविभाजयेत् । आदावन्ते च तत स्थाप्यं विकल्पगणिते क्रमात् ॥ ३॥"
1 In connoction with this bhanga, wo find in Āvas'yakasūtra-niryukti (v. 1478) a hemistich as under:
___"भंगिअसुयं गुणतो वट्टइ तिविहेण वंदामि”. In Brhatkalpabhäsya (v. 143 ) we note a line as below:
"भंगगणियाइ गमिकं”. This is explained by Malayagiri Sūri in his commentary. There he takes the word bhanga and gañiya separately and interprets the former and the latter as caturbhangi etc. and sankalana etc, respectively. 2 This is styled as karana-gatha. See p. xv.
3 गणि