Moonlight of Mathematics, Part 1

They say a pala Pala: a traditional unit of weight is one-fiftieth part of a tulā Tulā: literally 'a balance,' here representing a large weight equal to 50 palas. A quarter of a pala is called a karṣa, and that is also known as a suvarṇa original: "suvarṇa," literally "gold-weight". A sixteenth part original: "nṛpa-bhāga." In the Indian system of word-numerals, "nṛpa" (kings) represents the number 16 of that is a māṣa, and a fraction of that is a guñjā Guñjā: the bright red seed of the Abrus precatorius, used as the fundamental smallest unit of weight. ॥ 5 ॥

Three guñjās make a valla. Sixteen vallas make a gadyāṇa. A hasta Hasta: a cubit, the distance from the elbow to the tip of the middle finger is formed by twenty-four original: "four multiplied by six" aṅgulas Aṅgula: finger-width. Ten hastas make a daṇḍa Daṇḍa: literally a "staff" or "rod," used as a standard for measuring distance and land. ॥ 6 ॥

Eight hundred daṇḍas make a krośa Krośa: a measure of distance, roughly 1.8 to 2 miles. Four of those krośas make a yojana. A square area original: "kṣetram" with sides of twenty daṇḍas and equal diagonals... ॥ 7 ॥

...is called a nivarttana Nivarttana: a traditional unit of land area. This represents a square space original: "koṣṭham," meaning a cell or field of four hundred square daṇḍas. Mathematicians define a solid volume original: "ghana" as having a width, length, and height of one hasta. ॥ 8 ॥

They say this is a ghana-hasta Cubic Cubit, which is fixed as having twelve edges. [Other volumes are defined by] the numbers 24, 16, and 16 original: "siddha-nṛpa-bhūpa" — word-symbols for the numbers 24, 16, and 16 respectively acting as the length, breadth, and height measured in aṅgulas. ॥ 9 ॥

1. Bhāskara Referring to Bhāskara II, the 12th-century mathematician whose work Nārāyaṇa often expands upon did not mention the term tulā in his own Pāṭī The Līlāvatī, the standard arithmetic text of the era.

2. Bhāskarācārya, however, considers a daṇḍa to be four hastas.

3. In Bhāskarācārya's view, the measure of a krośa in hastas is 4 × 2000 = 8000. This is the same as Nārāyaṇa’s 10 × 800. Therefore, between the two systems, there is no disagreement regarding the number of hastas contained within a krośa.