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 Lilivati clasped 

 to their throats. . . ." 



Next follows the " Vija-Ganita," a treatise on algebra, of which 

 science the author observes : " Neither is algebra consisting in sym- 

 bols, 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 un- 

 known 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, 

 11 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 pea- 

 cocks 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, be- 

 comes 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 ex- 

 hibited. 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 con- 

 veys science to a comprehensive mind, and, having reached it, ex- 

 pands of its own impulse. . . . The rule-of-three terms constitute 

 arithmetic ; and sagacity, algebra." 



