The Science of the Shulba: A Study in Early Hindu Geometry c23: Bibliography of the Śulba

The Science of the Śulba: A Study in Early Hindu Geometry c23

Language: English

Bibliography of the Śulba

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The following works on the *Śulba* and their commentaries, published and unpublished, have been made use of in this book.¹

¹ In the collection of the Calcutta University, there is a good number of transcripts of the works on the *Śulba* and their commentaries. We have noted below, along with them, the original manuscripts from which they have been transcribed. The key to the abbreviations used is as follows : Ady. Lib. = Library of the Theosophical Society at Adyar, Southern India. Asiat. Soc. Ben. = Asiatic Society of Bengal, Calcutta. Bhand. O. Inst. = Bhandarkar Oriental Institute, Poona. Bom. Br. Roy. Asiat. Soc. = Bombay Branch of the Royal Asiatic Society, Bombay. Bom. Univ. = Bombay University. Ind. Off. Lib. = Library of the India Office at London. Mad. O. Ms. Lib. = Government Oriental Manuscripts Library, Madras. Mys. O. Ms. Lib. = Government Oriental Manuscripts Library, Mysore. Tanj. Pal. Lib. = Palace Library of the Mahāraja of Tanjore.

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1 . *Baudhāyana Śulba* :

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This work was published by G. Thibaut with English translation, critical notes, extracts from the commentary of Dvārakanātha Yajvā and a few diagrams, in the *Paṇḍit*, a monthly journal, now defunct, of the Sanskrit College of Benares: Old Series, IX and X, 1874-5; New Series, I, 1877. The text is printed in the *Baudhāyana Śrauta Sūtra*, being the 30th Chapter of it, edited by W. Caland, in three volumes, Calcutta, 1904, 1907, 1913. Besides these printed works, the manuscripts consulted are:

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(1·1) Text only:

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C. U. 21

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(1·2) Text with the commentary, entitled *Śulba-dīpikā*, of Dvārakanātha Yajvā:

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C. U. 15 (= Tanj. Pal. Lib., No. 3743B). C. U. 15 (a) (= Tanj. Pal. Lib., No. 3742, collated with No. 3743B). C. U. 21 (= Tanj. Pal. Lib., No. 9160(*b*), collated with No. 3743B),

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(1·3) Text with the commentary, *Śulba-mīmāṁsā*, of Veṅkaṭeśvara Dīkṣita:

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C. U. 42 (= Bhand. O. Inst., No. 96 of 1891-95).

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2. *Āpastamba Śulba*:

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This has been edited and published by A. Bürk, with German translation, notes and comments, helpful extracts from the commentaries of Kapardisvāmī, Karavindasvāmī and Sundararāja, and diagrams, together with a masterly introduction, in the *Zeitschrift der deutschen morgenländischen Gessellschaft*, LV, 1902, pp. 543-591; LVI, 1903, pp. 327-391. Manuscripts consulted are:

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(2·1) Text only:

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C. U. 16 (= Tanj. Pal. Lib., No. 3846). C. U. 27 (= Bom. Univ.). C. U. 34 (= Ady. Lib.).

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(2·2) Text with the commentary, *Śulba-vyākhyā*, of Kapardisvāmī:

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C. U. 1 (= Mad. O. Ms. Lib., No. 777 collated with No. 151 (*b*)).

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C. U. 17 (=Tanj. Pal. Lib., No. 3851). C. U. 52 (=Mad. O. Ms. Lib.). C. U. 54 (=Mys. O. Ms. Lib.).

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(2.3) Text with the commentary, *Śulba-pradīpikā*, of Karavindasvāmī : C. U. 18 (=Tanj. Pal. Lib., No. 3852), C. U. 31 (=Ms. of Pandit Gopal Desikacarya of Kumbhakonam). C. U. 49 (=Mad. O. Ms. Lib.). C. U. 50 (=Do. another copy). C. U. 53 (=Mys. O. Ms. Lib.),

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(2·4) Text with the commentary, *Śulba-pradīpa*, of Sundararāja : C. U. 10 (=Ms. of Pandit Gopal Desikacarya of Kumbhakonam). C. U. 19 (=Tanj. Pal. Lib., No. 9160 (a)̄). C. U. 20 (=Tanj. Pal. Lib., No. 9160 (a) collated with 9172 (a) ). C. U. 32 (=Ady. Lib.). C. U. 33 (=Do., another copy). C. U. 43 (=Bhand. O. Lib., No. 23 of A 1879-80). C. U. 44 (=Mad. O. Ms. Lib. No. R 911 (a). C. U. 51 (=Mad. O. Ms. Lib., No. 5812). C. U. 55 (=Mys. O. Ms. Lib.).

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(2·5) Text with the commentary, *Āpastambīya Śulba-bhāṣya*, of Gopāl.

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(3) *Kātyāyana Śulba* :

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A portion of this work, only the first two chapters, was published by G. Thibaut with English translation and the commentary, entitled the *Śulba-sūtra-vṛtti* of Rāma (c. 1450 A.D.) in the *Paṇḍit*, New Series, IV, 1882. Manuscripts consulted are:

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(3.1) Text only :

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C. U. 41 (= Bhand. O. Inst., No 74 of A 1881-82). It contains also the transcript of the MS. of the *Pariśiṣṭa* of Kātyāyana Śulba in the Ind. Off. Lib., No. E 363.

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C. U. 45 (= Bom. Br. Roy. Asiat. Soc. Lib.).

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(3·2) Text with the commentary, *Śulba-Sūtra-vivaraṇa*, of Mahīdhara (1589 A.D.):

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C. U. 41 (= Bhand. O. Inst., No. 363 of 1883-84).

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C. U. 46 (= Bom. Br. Roy. Asiat. Soc. Lib.).

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4. *Mānava Śulba*:

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C. U. 23 (= Asiat. Soc. Ben., No. I. E. 17); the text with the commentary of Śivadāsa.

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C. U. 29 (= Bom. Univ.); the text only.

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5. *Maitrāyanīya Śulba*:

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C. U. 47 (= Bom. Br. Roy. Asiat. Soc.); the text with the commentary of Śaṅkara.

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6. *Varāha Śulba*:

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C. U. 30 (= Mys. O. Ms. Lib.).

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Following is a list of articles dealing primarily with the mathematics in the *Śulba*:

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(1) Bürk, A.—"Das Āpastamba Śulba-sūtra," *Zeitschrift der deutschen morgenländischen Gesellschaft*, LV, 1901, pp. 543-591; LVI, 1902, pp. 327-391.

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(2) Cantor, M.—"Über die älteste indische Mathematik," *Archiv der Mathematik und Physik*, VIII (3), 1905, pp. 63-72.

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(3) ,, — "Gräko-indische Studien," *Zeitschrift für Mathematik und Physik*, XXII, Hist. Lit.

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(4) Datta, B—"The Origin of Hindu Indeterminate Analysis," *Archion*, XIII, 1931, pp. 401-7.

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(5) Levi, B.—"Observazioni e congetture sopra la geometria degli Indiani," *Bibliotheca Mathematica*, IX (3), 1909/10, p. 97.

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(6) Mazumdar, N. K.—"Mānava Śulba Sūtram," *Journal of the Department of Letters in the Calcutta University*, VIII, 1922.

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(7) ,,—"On the Different Śulba Sūtras," *Proceedings and Transactions of the Second Oriental Conference, Calcutta*, 1922, pp. 561-4.

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(8) Milhaud, G.—"La geometric d'Āpastamba," *Revue générale des Sciences*, XXI, 1910, pp. 512-520.

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(9) Müller, C.—"Die Mathematik der Śulvasūtra," *Abhand. a. d. Math. Sem. d. Hamburg. Univ.*, Bd. VII. 1929, pp. 173-204.

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(10) Thibaut, G.—"On the Śulva-sūtras," *Journal of the Asiatic Society of Bengal*, XLIV, 1875, pp. 227-275.

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(11) ,, —"The Baudhāyana Śulva-sūtra, *The Paṇḍit, Old Series*, IX, X; *New Series*, I.

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(12) ,, —"The Kātyāyana Śulva-sūtra; " *The Paṇḍit, New Series*, IV.

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(13) Vogt, H.—"Der Pythagoreischen Lehrsatz in der ältesten Geometrie der Inder," *Schlesiche Gesellschaft, Jahresberichte der Math. Sec*, LXXXIV, 1906, pp. 3-4.

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(14) ,, —"Haben die alten Inder den Pythagorsischen Lehrsatz und das Irrationale gekant?" *Bibliotheca Mathematica*, VII. (3), 1906/7, pp. 6-23.

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(15) Weber, A.—"Zur Kenntniss des vedischen Opferrituals," *Indische Studien*, XIII, pp. 215-292.

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(16) Zeuthen, H. G.—"Sur l'Arithmétique Géometrique des Grecs et des Indiens," *Bibliotheca Mathematica*, 1904, pp. 97-112.

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(17) Zeuthen, H. G.—"Theorème dé Pythagore, Origine de la Geometrie scientifique," *Comptes Rendus du IIme Congrés internationale de Philosophie*, Genéve, 1904.

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III

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Valuable information on the subject can also be had from the following standard works and articles:

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(1) Cantor, M.—*Geschichte der Mathematik*, I₃, pp. 635-645.

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(2) Datta, B.—"Hindu Contribution to Mathematics," *Bulletin of the Mathematical Association of the University of Allahabad*, I to II, pp. 1ff.

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(3) ,, —"The Scope and Development of the Hindu Gaṇita," *Indian Historical Quarterly*, V, 1929, pp. 479-512.

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(4) Dutt, R. C.—*A History of Civilisation in Ancient India*, revised edition, London 1893, I, pp. 260 ff.

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5) Hankel, H.—*Zur Geschichte der Mathematik im Alterthum und Mittelalter*, Leipzig, 1874.

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(6) Heath, T.—*The Thirteen Books of Euclid's Elements*, I, Cambridge, 1908, pp. 352-364.

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(7) Von Schroeder, L.—*Indien Literatur und Kultur*, Leipzig, 1887.

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(8) ,, —*Pythagoras und die Inder*, Leipzig, 1884.