The Science of the Shulba: A Study in Early Hindu Geometry c21.s1.1

c21.s1.1

In the *Sulba*, as in later Hindu mathematics, the fraction is called *aṃśa*, *bhāga*, meaning "part," "portion." Once in the *Āpastamba Śulba* and *Kātyāyana Śulba* each, it is called *kalā*.¹ This term is interesting inasmuch as it was used as early as the *Ṛgveda* ² to denote particularly a sixteenth part. It is also employed symbolically for the number sixteen. The unit fraction is indicated by a compound of either of those terms with a cardinal number, *e.g.,* *pañcadaśa-bhāga* = 1/15 (*ĀpŚl*, x. 3; *KŚl*, v. 4); *tri-bhāga* = 1/3 (*KŚl*) or with an ordinal number, *e.g.,* *pañcama-bhāga* = 1/5 (*ĀpŚl*, ix. 7, x. 2; *KŚl*, v. 6). Oftentimes in the latter case, the word *bhāga* is omitted, so that we have only an ordinal to denote a fraction, *e.g.,* *pañcama* (or "fifth") = 1/5, *dvādaśa* ("twelfth") = 1/12, *trayodaśa* ("thirteenth") = 1/13, etc.³