10 DISSERTATION SECOND. [part i. 



may be found out, and which, when skill in using it has 

 been acquired by practice, may be applied to an unlimited 

 exlent. 



A similar process enables us to discover the demonstra- 

 tions of propositions, supposed to be true, or, if not true, 

 to discover that they are false. 



This method, to the consideration of which we shall 

 again have an opportunity of returning, was perhaps the 

 most valuable part of the ancient matheraaticks, inasmuch 

 as a method of discovering truth is more valuable than the 

 truths it has already discovered. Unfortunately, how- 

 ever, the fragments containing this precious remnant had 

 suffered more from the injuries of time than almost any 

 other. 



In the fifteenth century, Regiomontanus, already men- 

 tioned, is the mathematician who holds the highest rank. 

 To him we owe many translations and commentaries, to- 

 gether with several original and valuable works of his own. 

 Trigonometry, which had never been known to the Greeks 

 as a separate science, and which took that form in Arabia, 

 advanced, in the hands of Regiomontanus, to a great degree 

 of perfection, and approached very near to the condition 

 which it has attained at the present day. He also intro- 

 duced the use of decimal fractions into arilhmetick, and 

 therebv save to that scale its full extent, and to numerical 

 computation the utmost degree of simplicity and enlarge- 

 ment which it seems capable of attaining. 



This eminent man was cut off in the prime of life ; and 

 his untimely death, says Mr. Smith, amidst innumerable 

 projects for the advancement of science, is even at this 

 day a matter of regret. ' He was buried in the Pantheon 

 at Rome ; and the honours paid to him at his death prove 



1 History of Astronomy, p. 90. Regiomontanus was born in 

 i 1450. and died in 1496. 



