ch as AB,
being in the air, and falling obliquely upon the polished surface of a
transparent body, such as FG, is broken at the point of incidence B,
in such a way that with the straight line DBE which cuts the surface
perpendicularly it makes an angle CBE less than ABD which it made with
the same perpendicular when in the air. And the measure of these
angles is found by describing, about the point B, a circle which cuts
the radii AB, BC. For the perpendiculars AD, CE, let fall from the
points of intersection upon the straight line DE, which are called the
Sines of the angles ABD, CBE, have a certain ratio between themselves;
which ratio is always the same for all inclinations of the incident
ray, at least for a given transparent body. This ratio is, in glass,
very nearly as 3 to 2; and in water very nearly as 4 to 3; and is
likewise different in other diaphanous bodies.

Another property, similar to this, is that the refractions are
reciprocal between the rays entering into a transparent body and those
which are leaving it. That is to say that if the ray AB in entering
the transparent body is refracted into BC, then likewise CB being
taken as a ray in the interior of this body will be refracted, on
passing out, into BA.

[Illustration]

To explain then the reasons of these phenomena according to our
principles, let AB be the straight line which represents a plane
surface bounding the transparent substances which lie towards C and
towards N. When I say plane, that does not signify a perfect evenness,
but such as has been understood in treating of reflexion, and for the
same reason. Let the line AC represent a portion of a wave of light,
the centre of which is supposed so distant that this portion may be
considered as a straight line. The piece C, then, of the wave AC, will
in a certain space of time have advanced as far as the plane AB
following the straight line CB, which may be imagined as coming from
the luminous centre, and which consequently will cut AC at right
angles. Now in the same time the piece A would have come to G along
the straight line AG, equal and parallel to CB; and all the portion of
wave AC would be at GB if the matter of the transparent body
transmitted the movement of the wave as quickly as the matter of the
Ether. But let us suppose that it transmits this movement less
quickly, by one-third, for instance. Movement will then be spread from
the point A, in the matter of the transparent body thr