In the last century, and at the beginning of the present, George Thibaut and A. Bürk brought to the notice of the scholarly world the mathematical significance of two sūtra texts, namely the Sulba-sūtras by Baudhāyana and Apastamba. These two works are manuals for the construction of various types of altars for fire-sacrifice, an ancient cult fully established in the time of the Samhitās. Their mathematical importance lies in a precise statement of the squared relationship of the two sides and the diagonal of a rectangle, the realization of the irrationality of numbers like √/2, efforts to determine their approximate values, formulation of rules for combining rectilinear figures, transforming squares into rectangles, triangles, trapeziums and circles and vice versa, the use of simple fractions and approximate values of π. All these arose from the mensuration of laying altars of a fixed square area but of different shapes and filling them with a fixed number of bricks necessarily of different geometrical shapes. The Greek tradition of the development of geometry from the more ancient Egyptian mensuration, the rope- stretcher’s art, appears to have its counterpart in the scriptural tradition of the Sulba-sūtras. That similar tradition obtained in other culture areas has become increasingly clear with advancing knowledge of the cuneiform texts and ancient Chinese mathematical sources.
I am happy that the authors of the present monograph have presented the full critical texts and translations of the four sulba-sūtras by Baudhāyana, Apastamba, Katyayana and Manava and modern commentaries on them. A carefully prepared introduction has dealt with: the genesis of these texts as part of the ritual literature (Kalpasūtras) constituting one of the six Vedāngas; the vexed question of the antiquity of these sūtras; the philosophical significance of performing fire sacrifices on various types of altars; and other related questions. Regarding the dating of Baudhayana, Mānava, Āpastamba and others a balanced view has been maintained between the opinions of European sanskritists like Bühler, Keith, Macdonell, Renou and Filliozat and those of Indian scholars like Kane and Ramgopal. Though the date of Baudhāyana, the earliest of sūtra writers, still varies over a range of two to three centuries, there is no doubt that the tradition of altar construction and the related sacrifices goes back to the period of the Samhitās and the Brāhmaṇas antidating the sutras, as the numerous passages in the Taittiriya, Maitrāyaṇī, and Kapiṣṭhala Samhitās and the Satapatha and other Brāhmaṇas amply indicate.
From its very inception the National Commission for the Compilation of History of Sciences in India has laid emphasis on the study of primary source materials. In astronomy and mathematics such materials are abundant. In 1966, the same two scholars along with a third carried out a bibliographical study of Sanskrit works on astronomy and mathematics. This has been followed by critical editions, translations and commentaries of the works of Aryabhața and Lalla by a number of scholars working for the National Commission. Now we have the śulba texts in the same series. We look forward to several such studies of our rich primary sources with a view to evolving a better understanding of the development of the various sciences in ancient and medieval India.
Planning Commission
Yojana Bhavan
New Delhi
14 December 1983
M. G. K. MENON