Now when the body is considered but as a point, it is all one whether the superficies or line in which the reflection is made be strait or crooked; for the point of incidence and reflection C is as well in the crooked line which toucheth D G in C, as in D G itself.
The same happens in the generation of motion in the line of incidence.
9. But if we suppose that not a body be moved, but some endeavour only be propagated from A to C, the demonstration will nevertheless be the same. For all endeavour is motion; and when it hath reached the solid body in C, it presseth it, and endeavoureth further in C I. Wherefore the reaction will proceed in C H; and the endeavour in C H concurring with the endeavour in H E, will generate the endeavour in C E, in the same manner as in the repercussion of bodies moved.
If therefore endeavour be propagated from any point to the concave superficies of a spherical body, the reflected line with the circumference of a great circle in the same sphere will make an angle equal to the angle of incidence.
For if endeavour be propagated from A (in [fig. 6]) to the circumference in B, and the centre of the sphere be C, and the line C B be drawn, as also the tangent D B E; and lastly if the angle F B D be made equal to the angle A B E, the reflection will be made in the line B F, as hath been newly shown. Wherefore the angles, which the strait lines A B and F B make with the circumference, will also be equal. But it is here to be noted, that if C B be produced howsoever to G, the endeavour in the line G B C will proceed only from the perpendicular reaction in G B; and that therefore there will be no other endeavour in the point B towards the parts which are within the sphere, besides that which tends towards the centre.
And here I put an end to the third part of this discourse; in which I have considered motion and magnitude by themselves in the abstract. The fourth and last part, concerning the phenomena of nature, that is to say, concerning the motions and magnitudes of the bodies which are parts of the world, real and existent, is that which follows.
Vol. 1. Lat. & Eng.
C. XXIV.
Fig. 1-6
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