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HISTORICAL NOTE: THE JAINA SCHOOL OF INDIAN MATHEMATICS
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It is Todaramala who made use of the expression alaukika ganita in the Bhāsätikā, an introduction to the mathematics appeared in the commentary of Madhavacandra Traividya on the Trilokasāra of Nemicandra (Sastri, Manoharalal 1918, pp. 122; also see Jain, L C and Trivedi, RK 1987, p. 365 and Bharilla 1999, p. 102). Long before him the expression laukikaganita was employed, in order to show how the rule for finding the meeting time of the sun and the moon can be applied on a worldly problem, by Bhaskara I (629 CE) outside the Jaina school of Indian mathematics (Shukla 1976, p. 131; also see Keller 2006, p. 127). Here it may be clearly concluded that mathematics on its own was not laukika (worldly) or lokottara (post-worldly) but because of its application it was considered to be laukika or lokottara.
Bhāskara I (629 CE) seems to have been in contact with the treatises of the Jainas as he is found to have quoted five passages in Prakrit gäthās (verses) in the Aryabhatiya-bhāsya. Two of them state the following two formulae. (1) C 10d where is the circumference of a circle of diameter d, and (2) A: V10 ch/4) where A, C and h are the area, chord and height of a segment of a circle of diameter d. The value for at implied in these formulae is 10, which was then regarded as the subtle one. His purpose of touching upon the passages was to criticizing vio and
value for it (Jadhav 2013, pp. 502-517 and 528538).
The two adjectives, laukika and lokottara, do occur in the treatises of the school but with the term māna or pramāna (measure). The Trilokasära refers to two kinds of māna (Skt. māna, measure), logiga (Skt. laukika, worldly) and loguttara (Skt. lokottara, post-worldly). The laukika māna is of six types while dravyamāna (fluent-measure), kşetramāna (space-measure), kālamāna (timemeasure and bhāvamāna (thought-measure are the four lokottara mānas (Mukhtara and Patni 1975, vv. 9-10, pp. 12-13). The Tatvārthavārtika ("Explanatory of the meaning of the fundamental principles") of Akalanka (7th century) appears to be the first treatise that contains the classification of measure in this manner (Jain, Mahendra 1999, sūtra 3.38, pp. 205-209).
One of the six laukika mänas is gani māna (or gananā māna or ganima mäna, countingmeasure). One, two, three and so on are countingmeasures (Jain, Mahendra 1999, sūtra 3.38, p. 205). Salaries, wages, provisions, income, expenditure, cost etc are, according to the Anuyogadvära Sutra, determined using it (Madhukara 1987, sūtra 327, p. 239). On the other hand, two, three and so on are samkhyāpramāna (number-measure). It is, according to the Tatvārthavārtika (Jain, Mahendra 1999, sūtra 3.38, p. 206) and the Trilokasāra (Mukhtara and Patni 1975, v. 12, p. 13), one of the two types of dravyamāna. It has three divisions: samkhyāta (numerate), asamkhyäta innumerate) and ananta (infinite). Asamkhyāta (innumerate) is further divided into three sub-classes: parita (preliminary), yukta (proper) and asamkhyāta
innumerate). Ananta (infinite) is also divided into three sub-classes: parita (preliminary), yukta (proper) and ananta (infinite). Each of samkhyāta (numerate), three sub-classes of asamkhyāta (innumerate) and three sub-classes of ananta (infinite) is again divided into jaghanya infimum), madhyama (intermediate), and utkrsta
emphasizing on Aryabhata's new value
value 20000 (Shukla 1976, p. lvi; also see below v. 2.10, pp. 72-73). He seems to have cited those five passages from some contemporary or earlier work. That work according to B B Datta, must have been of Jaina authorship (Datta 1936, p. 41). It may be noted that 10 continued to be used by one and all in the school as the value for at for the long period of more than two thousand years commencing from 500 BCE. The mathematicians of the canonical class except Virasena (816 CE) and Nemicandra (981 CE) never used any other
