XVI 



O N T E N T S. 



the Exiftence of External Objeas from a Principle acknowledged by the Sceptics, 

 viz. Confcioufnefs.— Proof from the Cafe of Blind and Deaf Men— Proof from the 

 Mind being paflive in the Perceptions of Senfe—Objeaion anfwered— Mr Locke's 

 Diftinaion of Primary and Secondary Qiialities defended— Objeaion from our 

 Dreams anfwered— The Mind then has not the entire Ufe of its Faculties — There- 

 fore not able to diftinguifli betwixt lUufion and Reality Page 414 



CHAP. VII. 



Of the Nature of Reafoning by Induaion — This Reafoning ufed both in Natural Phi- 

 Jofophy, and in the Ordinary Affairs of Life — From this Way of Reafoning in Na- 

 tural rhilofuphy, the Laws of the Motions of Bodies are inferred — From thefe Laws 

 we leafon downwards, and demonflrate — This is the Science of modern Natural 

 Philofophy — ^The Evidence of thofe Laws of Nature very different from that of 

 Axioms — The Reafon for our Belief in thefe Laws twofold — Every Experimental 

 Philofopher is, in fome refpea, a Theift, though he may not know it — Of Induaion 

 in the common Affairs of Life— -of the fame Kind with Induaion in Natural Philo- 

 fophy, but not near fo certain — Reafon of the Difference — Speculations concerning 

 the Duration of this Syftcm of Nature and of Man do not belong to this Part of the 

 Work P- 430 



CHAP. VIII. 



Geometry, according to Plato, is all built upon Hypothefes, and does not demonflrate 

 its own Principles — It is only by Means of the Firfl Philofophy that it can be made a 

 perfta Science — In what Senfe Geometry is founded upon Hypothefes — Definitions 

 and Poflulates mere Suppofitions — Nature of Definition — Euclid does not define 

 Magnitude, the Subjea of this Science ; but fuppofes both that it is known, and 

 that it exifts — Neither does he define any of the three Dimenfions ; bur fuppofes 

 them likewife known — Euclid fuppofes Magnitude to be terminated by Superficiefes, 

 Lines, and Point!! — Definitions he gives of thefe are to be explained by the Firfl Phi- 

 lofophy — No Definition of Equality by Euclid, but an Axiom in place of a- Defini- 

 tion — Equality only belongs to Magnitude and Number — Magnitude, the Standard 

 of Equality, not only for itfelf, but for other things — That Magnitude is moved or 

 changes its Pofition, is ar.other Geometrical Lypothefis — This, and the other Hypo- 

 tbtfcs above mentioned, are General Hypothefes — The Definitions are particular 

 Hypothefes — Difterence betwixt Definitions and Poflulates — The Axioms refultfrom 

 the Definitions, and have their Evidence founded upon them — All Geometry, there- 

 fore, hypothetical •, and we can only fay that its Hypothefes are pofllble — To- make 



it 



