Chap. VI. ANTIENT METAPHYSICS. 425 



riable by the fame rule, viz. the greater or the lefs diftancc from the 

 Centre, upon which, as I have faid, both the Motion in the Centri- 

 petal Line, and in the Line of Projection, muft depend. 



This hypothetical method of reafoning, by which a Motion, in its 

 nature perfedtly fimple, as fimple as any Motion in one Line can 

 be, may appear to thofe who are not acquainted with the method of 

 Science, to be precarious and inconclufive ; but Euclid's whole Sy- 

 llem of Geometry is, as I have fhown, founded upon a reafoning 

 of this kind. Sir Ifaac, when, by his dodlrine of Prime and Ulti- 

 mate Ratios, he refolves the Circular or Elliptical Motion into a Po- 

 lygon of an infinite number of fides, certainly makes an hypothcfis 

 for the fake of teaching and demonftration, which has no founda- 

 tion in Nature ; for I do not believe that any Newtonian will main- 

 tain that a Circle or Ellipfis is not a Figure contained in one Line (as 

 Euclid has defined a Circle), but a Redilineal Figure of many 

 Lines*. And I am fure he will not deny the truth of the propofi- 

 tion, which Sir Ifaac, upon that hypothefis, has demonftrated, that 

 the Planet, in its Motion round its Centre, defcribes Spaces propor- 

 tional to the Times f. And there is another Theorem of his, of 

 which he makes much ufe in his Princlpia, and which, likewife, 

 proceeds upon mere hypothefis. It is the theorem of the Compo- 

 fition of Motion, by which a Motion in a Straight Line, the moll 

 fimple of any that can be imagined, and which may be produced, 

 and generally is produced, by one fingle moving Power, fuch as the 

 Impulfe of one Bcdv, is fuppofed to be produced by the action of 

 two Powers adling in the diredion of two fides of a parallelogram, 

 of which the right line, in which the Body is moved, is the diagonal; 

 and upon this hypothefis the Moving Force of the Body is de- 



VoL. II. H h h monftrated. 



* See p. 393. 



t Lib. 1. Princip. Se*.^. 2. Pfop. i. 



