«c*. ▼.] DISSERTATION SECOND. 171 



direct light ; the second is the foundation of Catojptricks, 

 or the theory of vision by reflected light. Dioptricks, of 

 vision by refracted light, had not yet become an object of 

 attention. 



Two other principles which Euclid adopted as postulates 

 in his demonstrations, have not met with the same entire 

 confirmation from experiment, and are, indeed, true only 

 in certain cases, and not universally, as he supposed. The 

 first of these is, that we judge of the magnitude of an ob- 

 ject altogether by the magnitude of the optical angle, or the 

 angle which it subtends at the eye. It is true that this angle 

 is an important element in that judgment, and Euclid, by dis- 

 covering this, came into the possession of a valuable truth ; 

 but by a species of sophistry, very congenial to the human 

 mind, he extended the principle too far, and supposed it 

 to be the only circumstance which determines our judg- 

 ment of visible magnitude. It is, indeed, the only measure 

 which we are furnished with directly by the eye itself; 

 but there are few cases in which we form our estimate 

 without first appealing to the commentary afforded by the 

 sensations of touch, or the corrections derived from our own 

 motion. 



Another principle, laid down by the same geometer, is in 

 circumstances nearly similar to the preceding. According 

 to it, the place of any point of an object seen by reflection, 

 is always the intersection of the reflected ray with the per- 

 pendicular drawn from that point to the reflecting surface. 

 The proof offered is obscure and defective ; the proposi- 

 tion, however, is true of plain speculums always, and of 

 spherical as far as Euclid's investigations extended, that is, 

 while the rays fall on the speculum with no great obliquity. 

 His assumption, therefore, did not affect the truth of his 

 conclusions, though it would have been a very unsafe guide 

 in more general investigations. The book is in many other 



