Page:Algebra, with Arithmetic and mensuration, from the Sanscrit.djvu/101

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SECTION II.

Eight Operations^[1] of Arithmetic.

12. Rule of addition and subtraction:^[2] half a stanza.

The sum of the figures according to their places is to be taken in the direct or inverse order:^[3] or [in the case of subtraction] their difference.

13. Example. Dear intelligent Lílávatí,^[4] if thou be skilled in addition and subtraction, tell me the sum of two, five, thirty-two, a hundred and ninety-three, eighteen, ten, and a hundred, added together; and the remainder, when their sum is subtracted from ten thousand.

Statement, 2, 5, 32, 193, 18, 10, 100.

[Answer.] Result of the addition, 360.

Statement for subtraction, 10000, 360.

[Answer.] Result of the subtraction, 9640.^[5]

14—15. Rule of multiplication:^[6] two and a half stanzas.

Multiply the last^[7] figure of the multiplicand by the multiplicator, and

1. Paricarmásh◌́taca, eight operations, or modes of process: logistics or algorism.
2. Sancalana, sancalita, miśrana, yuti, yóga, &c. summation, addition. Vyavacalana, vyavacalita, sód'hana, patana, &c. subtraction. Antara, difference, remainder.
3. From the first on the right, towards the left; or from the last on the left, towards the right. Gang.
4. Seemingly the name of a female to whom instruction is addressed. But the term is interpreted in some of the commentaries, consistently with its etymology, "Charming."—See § 1. and 277.
5. Mode of working addition as shown in the Manóranjana:

   Sum of the units,	2, 5, 2, 3, 8, 0, 0,	20
   Sum of the tens,	3, 9, 1, 1, 0,	140
   Sum of the hundreds,	1, 0, 0, 1,	200
   Sum of the sums		360

6. Guńana, abhyása; also hańana and any terra implying a tendency to destroy. It is denominated pratyutpannaby Brahmegupta, § 3; and by Śríd'hara, § 15—17.

   Guńya multiplicand. Guńaca multiplicator. Ghata product.

7. The digit standing last towards the left. The work may begin either from the first or the last digit, according to Śríd'hara. Ganita-sára, § 15.