Page:Indian mathematics, Kaye (1915).djvu/64

 17. The number of terms less one multiplied by the common difference and added to the first term is the amount of the last. Half the sum of the last and first terms is the mean amount, and this multiplied by the number of terms is the sum of the whole.

21. The product of half the sides and opposite sides is the rough area of a triangle or quadrilateral. Half the sum of the sides set down four times and each lessened by the sides being multiplied together—the square-root of the product is the exact area.

40. The diameter and the square of the radius respectively multiplied by three are the practical circumference and area. The square-roots extracted from ten times the square of the same are the exact values.

62. The integer multiplied by the sexagesimal parts of its fraction and divided by thirty is the square of the minutes and is to be added to the square of the whole degrees.

101. These questions are stated merely for gratification. The proficient may devise a thousand others or may solve by the rules taught problems set by others. 102. As the sun obscures the stars so does the expert eclipse the glory of other astronomers in an assembly of people by reciting algebraic problems, and still more by their solution. Mahāvīra's Gaņita-Sāra-Sangraha—(Circa. A.D. 850). i. 13–14. The number, the diameter and the circumference of islands, oceans and mountains; the extensive dimensions of the rows of habitations and halls belonging to the inhabitants of the world, of the interspace, of the world of light, of the world of the gods and to the dwellers in hell, and miscellaneous measurements of all sorts—all these are made out by means of computation.