PHYSICAL SCIENCE. 



Xlll 



of a true mathematical genius, and though not 

 familiar with the general analytical methods 

 which are now in constant use, yet his mathe- 

 matical knowledge was respectable. Mr Glen- 

 nie was another of Mr West's pupils. But the 

 man who does the highest credit to Mr West, is 

 Mr Ivory, who has raised himself to the very 

 highest rank as a mathematician ; who has 

 cultivated every branch of the higher calculus 

 with the most complete success ; who is critically 

 acquainted with the whole history of mathemati- 

 cal discoveries, and is now universally admitted 

 to be me first mathematician at present in 

 Europe. Thus he has rescued Great Britain 

 from the stigma affixed to her, of inferiority in 

 mathematical skill to the mathematicians on the 

 continent Cambridge also of late years has 

 produced different eminent mathematicians, the 

 most celebrated of whom is Sir John Herschell. 



It would be impossible in this hasty sketch, to 

 give the slightest idea of the prodigious im- 

 provements which have been made in mathematics 

 during the progress of the last century. The 

 task is an herculean one. It has been frequently 

 attempted, but never yet executed. The indi- 

 vidual best qualified for such a task, is Mr Ivory. 

 Were he to execute it, he would confer a boon 

 of no ordinary magnitude upon science, and add 

 a new wreath to those with which Great Britain 

 is already encircled. 



III. ALGEBRA. 



The word algebra is Arabic, and is derived 

 from al, the, andjebr, contortion. It was at-first 

 applied to a particular arithmetical rule, in 

 which the terms were transposed. There is 

 some reason for suspecting that what we now call 

 algebra, originated in India. Diophantus who 

 lived about 150 years after the commencement 

 of the Christian era, has left thirteen books of 

 arithmetical questions, which are treated in a 

 manner that may be considered as algebraic, 

 The science was cultivated by the Arabians 

 during the golden age of Mahomedan science. 

 And a knowledge of it was first brought to 

 Europe in the 13th century, by Leonardo, a 

 merchant of Pisa, who having made many visits 

 to the east, brought back with him a knowledge 

 of algebra, on which he wrote a treatise in 1202, 

 and another in 1223, both of which still remain 

 in manuscript. 



But the first book printed in Europe on 

 algebra, was that of Lucas de Borgo, a Francis- 

 can, who towards the end of the 15th century, 

 traveled into the East, and acquired a knowledge 

 of the principles of algebra. The characters 

 employed by him are merely abbreviations of 

 words. The letters/) and m, are used for plus and 



minus. And the rule is laid down, that in 

 multiplication, plus into minus gives minus ; but 

 minus into minus gives plus. Thus algebra was 

 originally merely an abbreviation of common 

 language, applied to the solution of arithmetical 

 problems. 



The Indians and Arabians advanced as far as 

 the solution of quadratic equations. Scipio Ferrei. 

 professor of mathematics at Bologna, had, about 

 the year 1508, found out a method of solving one 

 of the cases of cubic equations ; which he either 

 concealed, or at least communicated only to a 

 few of his scholars. One of these, Florido, 

 trusting to this secret, challenged Tartalea of 

 Brescia to contend with him in the solution of 

 algebraic problems. Florido had at first the 

 advantage ; but Tartalea being a man of inge- 

 nuity, soon discovered his rule, and likewise 

 another much more general, in consequence of 

 which he came off at last victorious. By the 

 report of this victory, the curiosity of Cardan 

 was strongly excited. For though he was himself 

 an accomplished mathematician, he had not been 

 able to discover- a method of solving equations 

 higher than the second degree. By the most 

 importunate solicitations he wrung from Tartalea 

 the secret of his rules ; binding himself at the 

 same time, by the most solemn promise, never to 

 divulge them. Though Tartalea did not communi- 

 cate the demonstration, Cardan soon found it out, 

 and extended it in a very ingenious and syste- 

 matic manner to all cubic equations whatever. 



Being thus possessed of an important disco very, 

 which was partly his own, he forgot his promises 

 to Tartalea, and published the whole in 1545, 

 not concealing, however, what he owed to the 

 latter. Thus was published the rule which still 

 bears the name of Cardan ; and which still 

 marks a point in the progress of algebraic inves- 

 tigation, which all the efforts of succeeding 

 analysts have hardly been able to pass. 



Robert Recorde, an English mathematician, 

 published about the middle of the 16th century, 

 the first English treatise on algebra, and he 

 there introduced the same sign of equality which 

 is now in use. 



The properties of algebraic equations were 

 discovered very slowly. Pelitorius, a French 

 mathematician, in 1558, first observed that the 

 root -of an equation, is the divisor of the last 

 term. Bombelli soon after published a regular 

 treatise on algebra, in which he considered with 

 particular attention the irreducible case of Car- 

 dan's rule, and pointed out the method of solving 

 problems falling under it by the trisection of an 

 arch. 



Vieta, marks an era in algebraic analysis. 

 He was a Frenchman, born at Fonterai, in 

 Poitou, in the year 1540. Though rnaitre des 



