Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/406

314 of incidence and emergence GH, Ik in G and K. In GH take TH equal to IK, and to the plane Aa let fall a perpendicular Tv. And (by cor. 2. of the laws of motion) let the motion of the body be reolved into two, one perpendicular to the planes Aa, Bb, Cc, &c. and another parallel to them. The force of attraction or impule, acting in directions perpendicular to thoe planes, does not at all alter the motion in parallel directions; and therefore the body proceeding with this motion will in equal times go through thoe equal parallel intervals that lie between the line AG and the point H, and between the point I and the line JK; that is. they will decribe the lines GH, IK in equal times. Therefore the velocity before incidence is to the velocity after emergence as GK to IK or TH, that is as AH or Id to vH, that is (uppoling TH or IK radius) as the force of emergence to the ine of incidence. Q. E. D.

The ame thing being uppoed, and that the motion before incidence is wifter than afterwards; I ay, that if the {{ls]]ine of incidence be inclined continually, the body will be at lat reflected, and the angle of reflexion will be equal to the angle of incidence.

For conceive the body paing between the parallel planes Aa, Bb, Cc, &c. (Pl. 25. Fig. 4.) to decribe parabolic arcs as above; and let thoe arcs be HP, PQ, QR, &c. And the obliquity