354 GREEK SCIENCE. 



of the shadow are equal to the object, because the extreme rays are 

 parallel. If the illuminated body be less than the luminous body, the 

 shadow will gradually diminish : on the contrary, if the illuminated 

 body be largest, the shadow will become gradually larger and larger. 



Hypothesis. Visual rays issue from the eyes in diverging right lines, 

 so as to form a pyramid, or cone, whose vertex is in the eye, and whose 

 base encircles the object which we contemplate. Objects to which 

 these rays are directed are seen by us ; but we cannot see those to- 

 wards which these visual lines do not point. 



Objects appear larger, smaller, or equal, according as the angles 

 under which we see them, are greater, less, or equal. The object is 

 always seen in the direction of the visual ray ; and those which are 

 seen by the greatest number of rays are most distinct. 



We never see the whole of an object. Of two equal objects, the 

 nearest will be seen most distinctly. Every visible object becomes 

 invisible at a certain distance. 



Of equal parts of a right line, those which are most remote are seen 

 under the smallest angle, and appear smallest. 



Equal magnitudes, seen at unequal distances, appear unequal ; that 

 which is nearest will appear greatest. 



Parallel lines, viewed from a distance, appear to converge. 

 If a horizontal surface be lower than the eye, the part which is most 

 remote will appear to be elevated : if the horizontal surface be higher 

 than the eye, the most remote portion will appear depressed. 



A circle, viewed in the direction of its own plane, will appear as a 

 right line. 



When we look at a sphere with one eye, we never see so much as 

 its half. 



Viewed from a distance, a sphere appears as a circle. 

 When we look at a sphere with both eyes, if its diameter be equal 

 to the distance between the two pupils, we see its half: if the interval 

 between the pupils be greater, we see more than half; if the said in- 

 terval be less, less than the sphere half will be seen. 



If we look at a cylinder with one eye, we shall not see its half; as 

 we approach nearer to it, we see less and less. 



If the eye be in a line that passes through the centre of a circle per- 

 pendicularly to its plane, all the radii of the circle appear equal. 

 A circle, seen obliquely, appears flattened or contracted. 

 If several objects are in motion, and only one quiescent, that one 

 will seem to move in a contrary direction. 



If several bodies move with unequal velocities, and the eye is 

 carried along in the same direction, those objects which have the same 

 velocity as the eye will appear stationary ; those which have greater 

 velocities will appear to advance, while those which have less velocities 

 will seem to recede. 



If several objects have equal velocities, those which are most remote 

 will appear to move most slowly. 



