Abstract
In the cosmography of the Jainas are found applications of certain geometrical, or rather mensuration formulae. Some of them pertaining to the geometry of circle have already been noted in my article on “The Jaina School of Mathematics”1). There are also others as regard the theory of proportional triangles and the area of the segment of a circle. It is desirable that all of them should be dealt together at one place so as to give a fairly accurate idea of the extent of the knowledge of geometry amongst the early Jainas.
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Referenzen
Bull Cal. Math. Soc., vol. 21, 1929, pp. 115 – 145; hereafter this article will be referred to as Datta, Jaina Mathematics.
Jambudvîpa-prajñapti, Sûtra 3, 10 – 16; Jîvābhigama-sûtra, Sûtra 82, 124; Sûtṛakṛtāṅga-sûtra, Sûtra 12.
Tattvārthādhigama-sûtra with the Bhāṣya of Umāsvāti, edited by K. P. Mody, Calcutta, 1903, iii. 11.
Ch. iv. This work has been published in the Appendix G of Mody’s edition of the Tattvārthādhigama-sûtra.
Jinabhadra Gani wrote two books with the title Kṣetra-samāsa, a bigger one and a smaller one. Our reference in this article is always to the bigger one, called Vrhat Kṣetra-samāsa. It has been published in 1921 by the Jaina Dharma Prasāraka Sabhā of Bhavnagar.
Vṛhat Kṣetra-samāsa, i. 36 – 41, 46.
Ibid. i. 64.
Ibid. i. 66.
Ibid. i. 122.
Malayagiri points out that by this rule the area of the base of the Vaitāḍhya mountain will come out to be 51173111/19 yojaṇa, whereas it is stated in the text (i. 76) to be 51230712/19 yojana. He then observes, “This rule for finding the area thus deviates from the truth and hence should be neglected” (i.’64 Com.).
This will be sufficiently corroborated out by the detailed workings in i. 66 – 76.
This work with English translation has been edited by M. Rangacarya. Madras, 1912.
Laghu Kṣetra-samā sa of Ratnaśekhara Sûri (1440 A. D.), Rule 192.
Datta, Jaina Mathematics, p. 145.
Ibid. p. 130.
i. 46–47.
By whom?
i. 48 (Com.).
Jambudvîpa-prajñapti, Sûtra 103.
Vṛhat Kṣetra-samāsa, i. 307–8.
Ibid. i. 309–311.
For instance see i. 13 – 4, 149–150, 229–230, 307–11; ii. 25–6, 39–40 etc.
i. 229–230.
Tattvārthādhigama-sûtra-bhāṣya, iii. 9. It shoult be noted that along with this correct rule, the available text of the work contains a few numerical data which, as has also been pointed out by the commentator, are incompatible with it and hence erroneous. The copyists of Umāsvāti’s work must be responsible for these faults.
Jamhudvîpa-samāsa, ch. iv.
Jîvābhigama-sûtra, Sûtra 172.
Sûtra 104–5.
ii. 7.
Jîvābhigama-sûtra, Sûtra 112.
ii, 79–80.
ii. 81.
i. 65.
i. 77–82.
ii. 82.
I have not seen this work. But the relevant portion has been quoted by Ma-layagiri in his commentary.
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Datta, B. (1930). Geometry in the Jaina Cosmography. In: Neugebauer, O., Stenzel, J., Toeplitz, O. (eds) Quellen und Studien zur Geschichte der Mathematik. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-38292-9_1
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