6. If a body, pressing another body, do not penetrate it, it will nevertheless give to the part it presseth an endeavour to yield, and recede in a strait line perpendicular to its superficies in that point in which it is pressed.
Let A B C D (in [fig. 1]) be a hard body, and let another body, falling upon it in the strait line E A, with any inclination or without inclination, press it in the point A. I say the body so pressing, and not penetrating it, will give to the part A an endeavour to yield or recede in a strait line perpendicular to the line A D.
For let A B be perpendicular to A D, and let B A be produced to F. If therefore A F be coincident with A E, it is of itself manifest that the motion in E A will make A to endeavour in the line A B. Let now E A be oblique to A D, and from the point E let the strait line E C be drawn, cutting A D at right angles in D, and let the rectangles A B C D and A D E F be completed. I have shown (in the [8th article] of chapter XVI) that the body will be carried from E to A by the concourse of two uniform motions, the one in E F and its parallels, the other in E D and its parallels. But the motion in E F and its parallels, whereof D A is one, contributes nothing to the body in A to make it endeavour or press towards B; and therefore the whole endeavour, which the body hath in the inclined line E A to pass or press the strait line A D, it hath it all from the perpendicular motion or endeavour in F A. Wherefore the body E, after it is in A, will have only that perpendicular endeavour which proceeds from the motion in F A, that is, in A B; which was to be proved.
When a hard body, pressing another body, penetrates the same, it doth not penetrate it perpendicularly, unless it fall perpendicularly upon it.
7. If a hard body falling upon or pressing another body penetrate the same, its endeavour after its first penetration will be neither in the inclined line produced, nor in the perpendicular, but sometimes betwixt both, sometimes without them.
Let E A G (in the same [fig. 1]) be the inclined line produced; and first, let the passage through the medium, in which E A is, be easier than the passage through the medium in which A G is. As soon therefore as the body is within the medium in which is A G, it will find greater resistance to its motion in D A and its parallels, than it did whilst it was above A D; and therefore below A D it will proceed with slower motion in the parallels of D A, than above it. Wherefore the motion which is compounded of the two motions in E F and E D will be slower below A D than above it; and therefore also, the body will not proceed from A in E A produced, but below it. Seeing, therefore, the endeavour in A B is generated by the endeavour in F A; if to the endeavour in F A there be added the endeavour in D A, which is not all taken away by the immersion of the point A into the lower medium, the body will not proceed from A in the perpendicular A B, but beyond it; namely, in some strait line between A B and A G, as in the line A H.
Secondly, let the passage through the medium E A be less easy than that through A G. The motion, therefore, which is made by the concourse of the motions in E F and F B, is slower above A D than below it; and consequently, the endeavour will not proceed from A in E A produced, but beyond it, as in A I. Wherefore, if a hard body falling, &c.; which was to be proved.
This divergency of the strait line A H from the strait line A G is that which, the writers of optics commonly called refraction, which, when the passage is easier in the first than in the second medium, is made by diverging from the line of inclination towards the perpendicular; and contrarily, when the passage is not so easy in the first medium, by departing further from the perpendicular.
Motion sometimes opposite to that of the movent.
8. By the 6th theorem it is manifest, that the force of the movent may be so placed, as that the body moved by it may proceed in a way almost directly contrary to that of the movent, as we see in the motion of ships.