STUDY X. 301 



ducing firll, by three fradions, the triangle, which 

 of all figures, contains the fmalleft of furfaces 

 under the greateft of circuits. The triangle after- 

 ward, compofed itfelf of three triangles at the 

 centre, produces the fquare, which confifts of four 

 triangles from the central point ; the pentagon, 

 which confifts of five; the hexagon, which confifta 

 of fix ; and fo of the reft of the polygons, up to 

 the circle, which is compofed of a multitude of 

 triangles, whofe fummits are at it's centre, and 

 the bafes at it's circumference : and which, con- 

 trary to the triangle, contains the greateft of fur- 

 faces under the fmalleft of peripheries. The form 

 which has, hitherto, always been going on pro- 

 greffively, commencing with the line, relatively to 

 a centre, up to the circle, afterwards deviates from 

 it ; and produces the ellipfe, then the parabola, 

 and finally all the other widened curves, the equa- 

 tions of which may all be referred to this laft. 



So that under this afped, the indefinite line 

 has no common centre : the triangle has three 

 points in it's bounding lines, which have a com- 

 mon centre; the fquaie has four; the pentagon 

 five; the hexagon fix: and the circle has all the 

 points of it's circumference regulated conformably 

 to one common and only centre. The ellipfe be- 

 gins to deviate from this regulation, and has two 

 centres ; and the parabola, as well as the other 



curves. 



