7? ANTIENT METAPHYSICS. Book I. 



to the theorem, or problem, which is propofed to be demonftrated. 

 But I would advife the ftudent of geometry, not only to follow that 

 method, but to reverfe it, and pradice what is called the analy- 

 tic method, which begins where the other method ends, that is 

 with the propofition to be demonftrated ; and inquires whether 

 that propofition be not neceflarily conneded with fome felf- 

 evident propofition, or fome propofition, one or more, that had 

 been before demonftrated : So that, as it begins where the other 

 method ends, it ends where the other method begins. And 

 I am perfuaded, that, in this analytical way, the truth of the 

 propofitions, which Euclid has demonftrated, was firft difcovered : 

 For analyfis is the beginning of all fcience : And by going thus 

 forward and backward in the demonftration, the young ftudent more 

 perfedly comprehends the truth of it. 



It was the application of reafonlng to fubjeds fo fimple as to ht 

 prefented to the eyes, which I am perfuaded determined the Pytha- 

 goreans to make geometry the firft ftudy of their fcholars ; for they 

 thought it was teaching them in the eafieft way, to know what demon- 

 ftration was. And, further, they thought that it was the eafieft and 

 moft natural way of raifing the mind from objeds of fenfe to things 

 immaterial, which have a real and permanent exiftence ; and, there- 

 fore, were called by thefe philofophers the ra ovrag ovto,, whereas 

 things material, are always changing, and in a conftant viciflitude 

 of generation and corruption, fo that a material thing was faid by 

 them to be always becoming fomething, but never to be aflually 

 any thing : By which circumlocution we only can render in En- 

 ohfli what they exprefted in two words, 'ovx, la-rt aXXx ytyvircci. It 

 was for this reafon that geometry, and arithmetic were called Ma- 

 ■6r,'j.a.Tu,, as teaching men to reafon, and to raife their minds above 

 the perceptions of f:nfe, which was the chief objed of that ex- 

 alted philofophy. But a man, in thofe days, would have been 

 thou'^ht lidiculou?, who, becaufe he underft.ood lines and figures, 



thought 



