436 ANTIENTMETAPHYSICS. Book V. 



CHAP. VIIL 



GtQfhetfyi according to Plato, is all built upon Hjpothefesy and does not 

 demonjhnte its oivn Principles. — // is only by means of the Firji Philo- 

 fophy that it can be made a perfetl Science. — In ivhat Sen/e Geometry 

 is founded upon Hypothefes. — Definitions and Pojiulates mere Suppofi^ 

 tions. — Nature of Definition. — Euclid does not define Magnitude^ the 

 Suhjecl of this Science ; butfuppofes both that it is known .md that it 

 ^xfis. — Neither does he define any of the three Dimenfnns ; but luppo- 

 fes them likeivife knoivn. — Euclid Juppofes Magnitude to (e tei minuted 

 by Super liciefes. Lines ^ and Points. — Definitions he gives oj ihci'e are 

 to be explained by the Firfl Philofophy. — No Definition of Equality hy 

 Euclid, but an Axiom in Place of a Definition. — Equalitv only belongs 

 to Magnitude and Number. — Magnitude, the Standard of Equality, not 

 only j or it/elf but for other Things. — That Magnitude is moved or 

 changes it s pofttion-, is another Goemetrical Hypothefis — This, and the 

 other Hypothejes above mentioned, are General Hypothefes. — The Defi- 

 nitions are particular Hypothefes. — Difference betivixt Definitions and 

 Poflulates. — The Axioms rejult from the Definitions, and have their 

 Evidence founded upon them. — All Geometry, therefore, hypothetical ; 

 andivecan only fay that its Hypothejes ate pojfible. — To make it a Real 

 Science, the Real Exiflence of the Material World miift be pr oved, 

 — The fame is true of Arithmetic. 



PLATO has faid, that the principles of geometry are all hy- 

 pothefes ; and that, therefore, a fcience founded upon fuch prin- 

 ciples, cannot be a perfed fcience * ; for no fcience can be perfect 



which 



♦ Plato de Republica, lib. 6. infnt, pag. 688. Edit. Ficini. And lib. 7. p. 704. 

 where, fpeaking of geometry, he ufes thefe words, '« y.<§ k^^c.-^ fn* 'e^n oir^, nxiuTYi h 



