GREEK MATHEMATICS. 



AT the time when the state of eloquence and the arts among the Greek 

 Greeks showed most strongly the extraordinary powers of their geometry, 

 minds, they were employed in forming and advancing the singularly 

 beautiful and intellectual structure of the GREEK GEOMETRY. This 

 science, associated in its birth with their earliest philosophy, generally 

 continued combined with their favourite speculations ; and in its pro- 

 gress was more rapid, or at least more certain, than any of them. In 

 the school of PLATO it had already engaged in the most intricate and 

 difficult researches; and when transferred to the college of Alexandria, 

 it produced those profound investigations, on which the first intellects 

 of later times have been content to employ themselves without hoping 

 to add to its discoveries. 



Among the names which the history of this subject offers, that of 

 ARCHIMEDES has been, by the suffrage of all judges, considered as 

 standing highest; and possessing the same pre-eminence in the 

 ancient world with that of Newton in modern times. It will, there- 

 fore, be natural to combine with what can be collected of his biography, 

 some account of the history, about that time, of the sciences which he 

 cultivated. This sketch of what was then known, may be considered 

 as the only view which we can give of that which is generally the 

 most interesting part in the life of a mathematician, his education : 

 for it is clear that Archimedes was familiar with all that had been 

 done in mathematics up to his time. Without such knowledge, few 

 have been fortunate enough to extend, as he did, the limits of their 

 province in the world of science. 



THALES of Miletus, the first of the Greeks who is mentioned as Thaies. 

 having turned his attention to geometry, is to be looked on as the B< c - 60 - 

 father of their mathematical science, as indeed he appears to have 

 been of the rest of their philosophy. The discoveries attributed to 

 him are of the most elementary kind; but enough was done to give 

 an impulse to the subject; and his followers in the Ionic school 

 imitated him also in these researches. ANAXIMANDER is said to have Anaximan. 

 written an * Introduction to Geometry.' PYTHAGORAS was a scholar of J er t ' h orag 

 Thaies ; and did much for the progress of mathematics, besides the B. c. 540'. 

 discovery of his celebrated theorem, for which he is said, it must be 

 acknowledged with little probability, to have sacrificed a hetacomb. 

 The theories of which he was the author, and the reception which 

 they met with, show the strong tendency of the Greeks to such 

 inquiries. In his hands and those of his successors, music became a 



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