Moonlight of Mathematics, Part 1 (1936) - Page 17


Statement original: "Nyāsa"	1 — 2	1 — 4	1 — 6	1 — 12	Resulting common denominators original: "Samaccheda"	6 — 12	3 — 12


2 — 12	1 — 12	Statement	2 — 3	3 — 5	5 — 1	Resulting common denominators	10 — 15	9 — 15	75 — 15

The "class of sub-fractions" (bhāga-prabhāga) refers to finding a fraction of a fraction (e.g., 1/2 of 1/3).

A certain stingy man was asked with great devotion by someone

walking the humble path of a beggar. He gave two parts of a sixth,

a half of that, three-fifths of that, and then an eighth,

a ninth, and a sixteenth part of that. Oh learned one, if you are

expert in sub-fractions, tell me the total amount quickly! ॥ 6 ॥

Statement	1 — 2	1 — 3	1 — 6	1 — 2	3 — 5	1 — 8	1 — 9	1 — 16	The result is 1 cowrie shell. original: "Varāṭaka," a small shell used as currency.

This involves adding a fraction to an integer (bhāgānubandha) or subtracting it (bhāgāpavāha).

Three units increased by one-fifth, and

three units with six-sevenths.

Two minus one-third, and five

minus one-quarter—tell me these quickly,

friend, if you know the method of reduction. ॥ 7 ॥

Statement	3 1 5	6 3 7	Reduction original: "Savarnita" yields:	16 — 5	45 — 7

Statement	2 1̇ 3	5 1̇ 4	Reduction yields:	5 — 3	19 — 4
In Indian mathematical notation, a dot above a number (e.g., 1̇) indicates that the quantity is to be subtracted.

A half increased by its own third; a seventh decreased by its own

fifth; and one-and-a-half plus its own sixth—tell me, friend, the result.

Two-thirds minus its own half; six-fifths minus its own quarter;

and seven-ninths minus its own seventh—tell me if you know! ॥ 8 ॥

These types (svāṃśānubandha and svāṃśāpavāha) involve operations like $x + (x/y)$ or $x - (x/y)$.