246 THE MATHEMATICAL PRINCIPLES IBoOK 1 SCHOLIUM. These attractions bear a great resemblance to the reflexions and refrac tions of light made in a given ratio of the secants, as was discovered h} Siiellius ; and consequently in a given ratio of the sines, as was exhibited by Hes Cortes. For it is now certain from the phenomena of Jupiter's ^satellites, confirmed by the observations of different astronomers, that light is propagated in succession, and requires about seven or eight minutes to travel from the sun to the earth. Moreover, the rays of light that are in our air (as lately was discovered by Grimaldus, by the admission of light into a dark room through a small hole, which 1 have also tried) in their passage near the angles of bodies, whether transparent or opaque (such aa the circular and rectangular edges of gold, silver and brass coins, or of knives, or broken pieces of stone or glass), are bent or inflected round those bodies as if they were attracted to them ; and those rays which in their passage come nearest to the bodies are the most inflected, as if they were most attracted : which tiling I myself have also carefully observed. And those which pass at greater distances are less inflected ; and those at still greater distances are a little inflected the contrary way, and form three fringes of colours. In the figure 5 represents the edge of a knife, or any tl \ / K", \ / ^•::^ x -^» . v ^--:V J V U W~"~a~" "~a C: O la kind of wedge AsB : and gowog,fmnif,emtme, dlsld, are rays inflected to wards the knife in the arcs owo, nvn, mtm, Isl ; which inflection is greater or less according; to their distance from the knife. Now since this inflec tion of the rays is performed in the air without the knife, it follows that the rays which fall upon the knife are first inflected in the air before they touch the knife. And the case is the same of the rays falling upon glass. The refraction, therefore, is made not in the point of incidence, but gradually, by a continual inflection of the rays ; which is done partly in the air before they touch the glass, partly (if [ mistake not) within the glass, after they have entered it ; as is represented in the rays ckzc, bujb^ ahxa, falling upon r, q, p, and inflected between k and z, i and y, h and x. Therefore because of the analogy there is between the propagation of the rays f light and the motion of bodies, I thought it not amiss to add the followi »g Propositions far optical uses ; not at all. considering the nature of the rays of .light, or inquiring whether they are bodies or not ; but only determining the tra jectories of bodies which are extremely like the trajectories of the rays.