If a body pass, or there be generation of motion from one medium to another of different density, in a line perpendicular to the separating superficies, there will be no refraction.
For seeing on every side of the perpendicular all things in the mediums are supposed to be like and equal, if the motion itself be supposed to be perpendicular, the inclinations also will be equal, or rather none at all; and therefore there can be no cause from which refraction may be inferred to be on one side of the perpendicular, which will not conclude the same refraction to be on the other side. Which being so, refraction on one side will destroy refraction on the other side; and consequently either the refracted line will be everywhere, which is absurd, or there will be no refracted line at all; which was to be demonstrated.
Coroll. It is manifest from hence, that the cause of refraction consisteth only in the obliquity of the line of incidence, whether the incident body penetrate both the mediums, or without penetrating, propagate motion by pressure only.
Things thrown out of a thinner into a thicker medium are so refracted that the angle refracted is greater than the angle of inclination.
3. If a body, without any change of situation of its internal parts, as a stone, be moved obliquely out of the thinner medium, and proceed penetrating the thicker medium, and the thicker medium be such, as that its internal parts being moved restore themselves to their former situation; the angle refracted will be greater than the angle of inclination.
For let D B E (in the same first [figure]) be the separating superficies of two mediums; and let a body, as a stone thrown, be understood to be moved as is supposed in the strait line A B C; and let A B be in the thinner medium, as in the air; and B C in the thicker, as in the water. I say the stone, which being thrown, is moved in the line A B, will not proceed in the line B C, but in some other line, namely, that, with which the perpendicular B H makes the refracted angle H B F greater than the angle of inclination H B C.
For seeing the stone coming from A, and falling upon B, makes that which is at B proceed towards H, and that the like is done in all the strait lines which are parallel to B H; and seeing the parts moved restore themselves by contrary motion in the same line; there will be contrary motion generated in H B, and in all the strait lines which are parallel to it. Wherefore, the motion of the stone will be made by the concourse of the motions in A G, that is, in D B, and in G B, that is, in B H, and lastly, in H B, that is, by the concourse of three motions. But by the concourse of the motions in A G and B H, the stone will be carried to C; and therefore by adding the motion in H B, it will be carried higher in some other line, as in B F, and make the angle H B F greater than the angle H B C.
And from hence may be derived the cause, why bodies which are thrown in a very oblique line, if either they be any thing flat, or be thrown with great force, will, when they fall upon the water, be cast up again from the water into the air.
For let A B (in [fig. 2]) be the superficies of the water; into which, from the point C, let a stone be thrown in the strait line C A, making with the line B A produced a very little angle C A D; and producing B A indefinitely to D, let C D be drawn perpendicular to it, and A E parallel to C D. The stone therefore will be moved in C A by the concourse of two motions in C D and D A, whose velocities are as the lines themselves C D and D A. And from the motion in C D and all its parallels downwards, as soon as the stone falls upon A, there will be reaction upwards, because the water restores itself to its former situation. If now the stone be thrown with sufficient obliquity, that is, if the strait line C D be short enough, that is, if the endeavour of the stone downwards be less than the reaction of the water upwards, that is, less than the endeavour it hath from its own gravity (for that may be), the stone will by reason of the excess of the endeavour which the water hath to restore itself, above that which the stone hath downwards, be raised again above the superficies A B, and be carried higher, being reflected in a line which goes higher, as the line A G.
Endeavour, which from one point tendeth every way, will be so refracted, as that the sine of the angle refracted will be to the sine of the angle of inclination, as the density of the first medium is to the density of the second medium, reciprocally taken.