A History of the Canonical Literature of the Jainas c11.136

c11.136

(iii) *Bhaṅgas* are likely to remind a student of Mathematics of ‘Permutations and Combinations’. They are mentioned in *Thāṇa* (X; s. 716), and their two varieties are noted and explained by Abhayadeva Sūri in his com.² (p. 478ᵇ) to this *Aṅga*. Śīlāṅka Sūri in his com.³ (p. 9ᵇ) to *Sūyagaḍanijjutti* (v. 28) has given us 3 verses⁴ which supply us with 3 rules. The first verse enables us to determine the total number of transpositions which can be made when a specific number of things is given, whereas the other two help us in finding the actual spread of representation. The problem known as *Gāṅgeya-bhaṅga* and treated in *Viāhapaṇṇatti* (IX; s. 372–374) may be specially mentioned as one of the typical problems connected with this branch of Mathematics.