*EARLY HINDOO MATHEMATICS.*

339

jects of permutations follow which are sufficiently obscure, and the treatise concludes with the neat sentiment that "joy and happiness is indeed ever increasing in this world for those who have Lílívatí clasped to their throats. . . ."

Next follows the "Vija-Ganita," a treatise on algebra, of which science the author observes: "Neither is algebra consisting in symbols, nor are the several sorts of it, analysis. Sagacity alone is the chief analysis: for vast is inference."

The methods of Hindoo algebra are rude. Positive quantities have no sign, while negative ones are distinguished by a dot. For the unknown quantities the different *colors* are used, and the initial letters of their names are placed in an equation. Equality must be expressed in words, for the sign was first used by Robert Recorde, who says, "No two things can be more equal than a pair of parallel lines."—(*Hutton*.)

Equations of the first and second degree are treated of, but with obscurity.

It is noteworthy that at least two references are made in this treatise to older authors, which deserve quotation as showing the nature of problems previously proposed.

"Example, by ancient authors. Five doves are to be had for three *drammas*; seven cranes for five; nine geese for seven; and three peacocks for nine: being a hundred of these birds for a hundred *drammas* for the prince's gratification."

"Example by an ancient author. What number multiplied by three and having one added to the product becomes a cube: and the cube root squared and multiplied by three and having one added, becomes a square?"

Enough has been given to show that the Hindoo mind was apt at mathematical logic, and to exhibit the characteristic grace of fancy with which it regarded science.

Arithmetic, when the world was young, was not inconsistent with fancy and with enjoyment. Algebra was regarded with a certain awe. We cannot better illustrate this than by one more quotation from the translation by Colebrooke of the "Vija-Ganita:"

"There is no end of instances, and therefore a few only are exhibited. Since the wide ocean of science is difficultly traversed by men of little understanding, and, on the other hand, the intelligent have no occasion for copious instruction, a particle of tuition conveys science to a comprehensive mind, and, having reached it, expands of its own impulse. . . . The rule-of-three terms constitute arithmetic; and sagacity, algebra."