115 



enables us to find the tnith we are in quest of, 

 out of the proposition itself which, we want to resolve." 

 He it was who at length solved the famous problem, 

 respecting the duplication of the cube, on account of 

 which so much honour is paid, by all the philosophers 

 of his school, to Euxodus, Archytus, and Menechmus, 

 To him also is ascribed the solution of the problem 

 concerning the trisection of an angle ; and the disco- 

 very of the conic sections. Pappus hath given us the 

 sirm.mary of a great many analytic works. In the 

 preface to his seventh book, we meet with this princu 

 pie of Guldinus, * ; that whatever figure arises from 

 the circumfolution of another, is produced by the re* 

 folutionof the latter about its centre of gravity. 1 ' 



5. Geometry is indebted to Hipparchus for the first 

 elements. of plain and spherical trigonometry ; and to 

 Diophantes, who lived 360 years before Jesus Christ, 

 we owe the invention of algebra. That the ancients 

 laid the first foundations of algebra, is a thing out of 

 doubt, and shewn by the celebrated Wallis in his his* 

 to ry of that science. He makes DO question but al- 

 gebra was known to the artcienU,and that they thence 

 drew those long and difficult demonstrations which we 

 meet with in their works. He supports his opinion 

 by the testimonies of Scjioten, Oughtred, and Bar- 

 row ; and makes mention of a manuscript in the Sa. 

 Tilian library, which treats of this science and bears 

 the name of Apollonius. But he thinks the ancients 

 carefully concealed a method, which furnished them 

 jvith so many beautiful and difficult demonstrations ; 

 and that they chose rattier to prove their proposu 

 lions by reasonings ad absurdum, than to hazard the 

 discovery of that method, which brought them more 

 directly to the result of what .they demonstrated. One 

 to whom algebra is much indebted, Leibnitz,, forms the 

 same judgment. Speaking of the higher operations of 

 it, he says, ' in perusing the arithmetic of Diophantes, 

 and the geometrical books of Apollouius and Pappus, 

 we cannot doubt but the aacients hadsome kuowiedge 



