26 DISSERTATION SECOND. ^part i. 



ced (he same characters for plus and minus which are at 

 present employed. 



Robert Recorde. an English mathematician, published 

 about this time, or a few years later, the first English trea- 

 tise on Algebra, and he there introduced the same sign of 

 equality which is now in use. 



The properties of algebraick equations were discovered, 

 however, very slowly. Pelitarius, a French mathemati- 

 cian, in a treatise which bears the date of 1558, is the first 

 who observed that the root of an equation is a divisor of 

 the last term ; and he remarked also this curious property 

 of numbers, that the sum of the cubes of the natural 

 numbers is the square of the sum of the numbers them- 

 selves. 



The knowledge of the solution of cubick equations was 

 still confined to Italy. Bombelli, a mathematician of that 

 country, gave a regular treatise on Algebra, and consi- 

 dered, with very particular attention, the irreducible case 

 of Cardan's rule. He was the first who made the remark, 

 that the problems belonging to that case can always be re- 

 solved by the trisection of an arch. ' 



1 A passage in Bombelli's book, relative to the Algebra of 

 India, has become more interesling, from the information con- 

 cerning the science of that country, which has reached Europe 

 within the last twenty years. He tells us, that he had seen in 

 the Vatican library, a manuscript of a certain Diophantus, a 

 Greek author, which he admired so much, that he had formed 

 the design of translatins; it. He adds, that in this manuscript he 

 had found the Indian authors often quoted ; from which it ap- 

 peared, (bat Algebra was known to the Indians before it was 

 known to the Arabians. Nolhing, however, of all this is to be 

 found in the work of Diophantus, which was publ'^hed about 

 three years after the time when Bombelli wrote. As it is, at 

 the same time, impossible that he could be so much mistaken 

 about a manuscript which he had particularly examined, this 

 passage remains a mystery, which those who are curious about 

 the ancient history of science would be very glad to have un- 

 ravelled. See Hutton's History of Algebra. 



