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mentators upon them, began to multiply; and the rapidprogress of the art of printing gave an additional im-pulse, by the facilities it created for the disseminationof learning. Amongst these numerous writers we mayparticularly notice Venatorius, distinguished by histranslation of Archimedes , and Commadine by that ofEuclid , and various other ancient mathematicians, en-riched with commentaries.

The Greek mathematicians, in particular, now beganto attract the attention of students, and the value oftheir geometrical labours to be rightly appreciated. Theelementary treatises had been already adopted as thebasis of mathematical study; and the more difficult andabstruse parts of the ancient systems were now beginningto be studied with all the zeal and ardour which iscommonly inspired by the acquisition of a new treasure,and the discovery of a fresh source of intellectual gra-tification.

We have before adverted to that beautiful portion ofthe ancient mathematics known by the name of thegeometrical analysis : this may, perhaps, be fairly calledthe most valuable part of the ancient geometry, inas-much as a method of discovering truth is more valuablethan the particular truths it has already discovered.Unfortunately, but few works of the ancients on thesubject have come down to us; and those few havesuffered more from the injuries of time than almost anyother remnants of their writings. Among the first ofthe moderns who turned their attention to the subjectof these methods, and to unfolding the contents of some,of the ancient treatises, was Werner, who lived aboutthe end of the fifteenth century : his works are nowvery rare. He first studied the data of Euclid ; and,from the elementary notions of the subject there im-parted, he proceeded, without further help, except thatof his own powerful and original genius, to pursue theprinciples of the system, and to apply it to the solutionof several recondite problems. The work of Apollonius,entitled “ Sectio Rationis,” was known to him only ini 4