102 PHYSICAL SCIENCES IN ANCIENT GREECE. 



conditions of successful physical speculation, -which we have laii 

 down. 



It is proper to notice more distinctly the nature of the Geometrical 

 Propositions contained in Euclid's work. The Optica contains Propo- 

 sitions concerning Vision and Shadows, derived from the principle that 

 the rays of light are rectilinear : for instance, the Proposition that the 

 shadow is greater than jhe object, if the illuminating body be less, and 

 vice versa. The Catoptrica contains Propositions concerning the effects 

 of Reflection, derived from the principle that the Angles of Incidence 

 and Reflection are equal : as, that in a convex mirror the object appears 

 convex, and smaller than the object. We see here an example of the 

 promptitude of the Greeks in deduction. When they had once ob- 

 tained a knowledge of a principle, they followed it to its mathematical 

 consequences with great acuteness. The subject of concave mirrors is 

 pursued further in Ptolemy's Optics. 



The Greek writers also cultivated the subject of Perspective specula- 

 tively, in mathematical treatises, as well as practically, in pictures. 

 The whole of this theory is a consequence of the principle that vision 

 takes place in straight lines, drawn from the object to the eye. 



" The ancients were in some measure acquainted with the Refrac- 

 tion as well as the Reflection of Light," as I have shown in Book ix. 

 Chap. 2 [2d Ed.] of the Philoso2^hy. The current knowledge on this 

 subject must have been very slight and confused ; for it does not ap- 

 pear to have enabled them to account for one of the simplest results 

 of Refraction, the magnifying effect of convex transparent bodies. I 

 have noticed in the passage just referred to, Seneca's crude notions on 

 this subject; and in like manner Ptolemy in his Optics asserts that an 

 object placed in water must always appear larger then when taken 

 out. Aristotle uses the term avaxX&Wij (Meleorol. iii. 2), but appa- 

 rently in a very vague manner. It is not evident that he distinguished 

 Refraction from Reflection. His Commentators however do distin- 

 guish these as ^axXatfis and dvaxXatfj^. See Olympiodorusin Schnei- 

 der's Edogce Physicce, vol. i. p. 397. And Refraction had been the 

 subject of special attention among the Greek Mathematicians. Archi- 

 medes had noticed (as we learn from the same writer) that in certain 

 cases, a ring which cannot be seen over the edge of the empty vessel 

 in which it is placed, becomes visible when the vessel is filled with 

 water. The same fact is stated in the Optics of Euclid. We do not 

 find this fact explained in that wcrk as we now have it ; but in Ptol- 

 emy's Optics the fact is explained by a flexure of the visual ray : it is 



