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.

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.

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 or Ramachandra (Shulba-sutra-vrtti)
Krishna Yajurveda	Taittriya	Baudhayana	3 Adhyayas	Dvarakanatha Yajva (Sulba-dipika), Venkatesvara Dikshita (Shulba-mimamsa)
		Apastamba	6 Patalas (21 Adhyayas and 223 Sutras)	Kapardisvami (Shulba-vyakhya), Karavindasvami (Shulba-pradipika), Sundararaja (Shulba-pradipa or Sundararajiya),
		Varaha	3 Adhyayas
		Hiranyakeshi
	Vadhula	Vadhula (वाधूलः)
	Maitrayani	Manava by Manu	7 Khandas	Narada
		Maitrayana	4 Khandas	Shankarabhatta
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.

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

1. mensuration - the act and process of measuring
2. line - the result obtained by measuring
3. measure - the instrument of measuring
4. geometry - the art of measuring

In the Shulbas the measuring tape is called "Rajju", so is "a line". One who is well-versed in the science of Shulba (geometry) is called Shulbavijnana, a Shulbavid (expert in geometry), a Sulbapariprcchaka (an inquirer into the Shulba), a Samkhyaajna (expert in numbers), Parimaanajna (expert in measuring). A special term sama-sutra-niranchaka (meaning uniform rope stretcher) is also used, this rope plays a very significant role and we find many references of similar words rajjuka, rakku-grahaka, sutra-grahaka - all used to denote a maharaja's land surveyor. A sutra-grahaka is further described as an expert in alignment, a rekajna, one who knows "the line".

It is extremely interesting to note that land surveying is an ancient procedure followed by our ancestors.

Relationship between Shulba and Yajnas

Yajnas are of two main classes: Nitya (obligatory) and Kamya (optional or performed with a special intent). NItya yajnas are indispensible and not performing them will incur papam (sin) to the yajamana. The Kamya yajnas are, however, optional and those who do not have any specific aims to achieve any such object need not perform them. Every yajna must be made in an altar of prescribed shape and size.

These sutras give a compilation of principles in geometry that were used in designing the altars (called vedi or citi) where the Vedic sacrifices (yaj˜na) were to be performed. The platforms of the altars were built with burnt bricks and mud mortar. It is stated that even a slight irregularity and variation in the form and size of the chiti (Citi) will nullify the object of the whole ritual and may even lead to an adverse effect. So ancient adhvaryus took utmost care in building a chiti of right shape and size.

The Vedic altars had rich symbolic significance and their designs were often intricate. For instance, the Syenacit has the shape of a falcon in flight (a symbolic representation of the aspiration of soaring upward); the Kurmachit is shaped as a tortoise, with extended head and legs, the rathacakracit as a chariot wheel with spokes, and so on.