The Science of the Shulba: A Study in Early Hindu Geometry c22.9

c22.9

*Rectilinear Figures*.—In the *Sulba*, we discern two different systems of nomenclature for the rectilinear geometrical figures.⁴ In one system the naming is according to the number of angles or corners in the figures, and the names are formed by the juxtaposition of the number names with *aśra* or *asra* which ordinarily means "corner," "angle," *e.g.*, *tryasra* ("triangle"), *caturasra* ("quadrangle"), etc. These names were introduced in the time of the *Śrauta-sūtra* (*c.* 2000-1500 B.C.). Still older names were compounds ending with *srakti* (= "angle," "corner"). Thus the name *catuḥsrakti*, which literally means, the "quadrangle," occurs in the *Vājasaneyī Saṃhitā*, *Taittirīya Saṃhitā*, *Śatapatha Brāhmaṇa*, *Āpastamba Śrauta*, *Baudhāyana Śulba* and other works. In the *Ṛgveda*, we find the term *navasrakti* referring to the "nine corners" of the heaven. In the *Kātyāyana Śulba Pariśiṣṭa*,¹ we have compound names for rectilinear figures ending with *karṇa*. The Sanskrit word *karṇa* means the "ear." Applied to geometrical figures, it implies the "angle"; hence *trikarṇa* = "triangle," *pañcakarṇa* = "pentagon." The word *karṇa* degenerated into *koṇa* in the *Prākṛta* languages. So in the Ardha Māgadhī work *Sūryaprajñapti*,² we get the names *trikoṇa* (= "trigonon"), *catuṣkoṇa* (= "tetragonon"), *pañcakoṇa* (= "pentagon") etc. These terms are, however, accepted in later Sanskrit literature.³ The term *aśra* or *asra* in a compound name sometimes denotes the "side". Thus Baudhāyana once described a square as *catuḥsrakti* ("four-cornered") and *sama-caturasra* ("equi-four-sided").⁴ So the terms *tryasra*, *caturasra*, etc., will also mean respectively "trilateral," "quadrilateral," etc.⁵ Thus we get a second system of naming retilinear geometrical figures according to the number of sides they possess.