Page:A History of Mathematics (1893).djvu/111

 root extracted, addition of 8, and division by 10, gives the number 2?" The process consists in beginning with 2 and working backwards. Thus, $$\scriptstyle{(2 \cdot 10 -8)^2+52=196}$$, $$\scriptstyle{\sqrt{196}=14}$$, and $$\scriptstyle{14 \cdot \frac{3}{2} \cdot 7 \cdot \frac{4}{7} \div 3 = 28}$$, the answer.

Here is another example taken from Lilavati, a chapter in Bhaskara's great work: "The square root of half the number of bees in a swarm has flown out upon a jessamine-bush, $$\scriptstyle{\frac{8}{9}}$$ of the whole swarm has remained behind; one female bee flies about a male that is buzzing within a lotus-flower into which he was allured in the night by its sweet odour, but is now imprisoned in it. Tell me the number of bees." Answer, 72. The pleasing poetic garb in which all arithmetical problems are clothed is due to the Indian practice of writing all school-books in verse, and especially to the fact that these problems, propounded as puzzles, were a favourite social amusement. Says Brahmagupta: "These problems are proposed simply for pleasure; the wise man can invent a thousand others, or he can solve the problems of others by the rules given here. As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them."

The Hindoos solved problems in interest, discount, partnership,, summation of arithmetical and geometric series, devised rules for determining the numbers of combinations and permutations, and invented magic squares. It may here be added that chess, the profoundest of all games, had its origin in India.

The Hindoos made frequent use of the "rule of three," and also of the method of "falsa positio," which is almost identical with that of the "tentative assumption" of Diophantus. These and other rules were applied to a large number of problems.