Ill 



CHAP. XIX. 



Of the many Discoveries of the Ancients in, Mathe- 

 matics* &c. 



maticS) 



1. JLJL LARGE book might becomposed,were we but 

 cursorily to mention all tire important discoveries in 

 geometry, mathematics, and philosophy, for which we 

 are indebted to the ancients* Wherefore, not to swell 

 this volume we shall just point at the principal of them, 

 without insisting at length ; because it is generally 

 acknowledged that they owe their origin to those 

 philosophers of antiquity. 



2. All tfee learned agree, that Thales was the first 

 we know of who predicted eclipse* ; pointed out 

 the advantage that must arise from a due obftcrva. 

 tion of the Little Bear, or polar star ; taught that the 

 earth was round, and the ecliptic in an obliquo posi- 

 tion, IIiMlid no less service to geometry than astro- 

 nomy, lie instructed in that science the Kgyptuns 

 themselves, to whom he went to be taught, ll^snew. 

 ed them how to " measure the pyramids by the length 

 of their shades, and (o determine the measure of inac- 

 cessible heights and distances, by the proportion of the 

 sides of a triangle." He demonstrated the various 

 properties of the circle; particularly that whereby it 

 appears, * that all triangles which have the di*rnetiT 

 for their base, the subtending angle of which totuM s 

 the circumference, are in that point of contact rigiit- 

 angled," He discovered respecting the isosceles trian- 

 gle, that the angles at its base were enual ; and was 



