Shulbasutras (शुल्बसूत्राणि)
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Shulbasutras (Samskrit: शुल्बसूत्राणि) are manuals for the construction of yajnas. They are sections of the Kalpasutras, associated in particular with the Shrautasutras. Each Shrautasutra seemed to have their own Shulbasutra section based on literary data; however, in the present days, only seven of these sutra works, Baudhayana, Apastamba, Katyayana, Manava, Maitayana, Varaha and Vadhula are available.
Introduction
Recognized as the oldest and earliest treatises on mathematical problems, Shulbasutras give us a glimpse of the knowledge of geometry that the vedic people possessed. Incidentally they furnish us with a few other subjects of much mathematical interest.[1]
One of the prime occupations of the vedic people, performing yajnas, required altars or yajna-vedis of prescribed shapes and sizes. It was primarily in connection with the construction of altars that problems of geometry and also of arithmetic and algebra presented themselves to these ancient rshis, which led to the development of these texts.
Authors and Commentators
Unlike the other Sutra charanas, there are a very few Shulbasutra texts available at present and all of them belong to Yajurveda. The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava are the main sources of the knowledge of geometry. The Kalpa texts of Vedangas clearly outline that astronomy on one hand and geometry on the other were cultivated under different circumstances by different rtviks based on the duties apportioned to them in the conduct of yajnas.[2]
| Vedas | Shakas | Shulbasutra | Contents | Commentators |
|---|---|---|---|---|
| Rigveda | Shakala | None available | ||
| Kaushitaki | ||||
| Shukla Yajurveda | Vajasaneya | Katyayana | Purvabhaga (7 Kandikas with 90 Sutras)
Uttarabhaga (40 or 48 shlokas) |
Rama |
| Krishna Yajurveda | Taittriya | Baudhayana | 3 Adhyayas | |
| Apastamba | 6 Patalas (21 Adhyayas and 223 Sutras) | |||
| Varaha | 3 Adhyayas | |||
| Hiranyakeshi | ||||
| Vadhula | Vadhula (वाधूलः) | |||
| Maitrayani | Manava by Manu | 7 Khandas | ||
| Maitrayana | 4 Khandas | |||
| Samaveda | Kauthuma | None available | ||
| Rananiya | ||||
| Jaimini | ||||
| Atharvaveda | None available | |||
Etymology
The word Shulba (शुल्ब) means a 'cord', 'a rope', 'a string'. A Sutra refers to a short rule. The commentators refer to this subject matter as Shulba as the true name, Shulba-parishista, Shulbi Kriya etc.[1]
In few other instances the word "rajju (रज्जुः) has been used. B. B. Datta states that the words "shulba (शुल्ब)" "shulva (शुल्व)" and "rajju (रज्जुः) may be used synonymously to mean a rope or cord. However, shulba or shulva is derived from the dhatu "शुल्ब्" in the meaning "to measure" and hence its etymological significance is "measuring" or act of measurement. The terms Shulba and Rajju have four meanings
- mensuration - the act and process of measuring
- line - the result obtained by measuring
- measure - the instrument of measuring
- geometry - the art of measuring