The motion of very small bodies when agitated by centripetal forces on Superphysics

Finding the orbits from the focus given

Mon, 01 Jan 0001 00:00:00 +0000

Proposition 94 Theorem 48

If two similar mediums be separated from each other by a space terminated on both sides by parallel planes, and a body in its passage through that space be attracted or impelled perpendicularly towards either of those mediums, and not agitated or hindered by any other force ; and the attraction be every where the same at equal distances either plane, taken towards the same hand of the plane, that the sine of incidence upon either plane will be to the sine of emcr from gence from the other plane in a given ratio.

The Sine of Incidence

Mon, 01 Jan 0001 00:00:00 +0000

Proposition 95 Theorem 49

The same things being supposed, the velocity of the body before its incidence is to its velocity after emergence as the sine of emergence to the sine of incidence.

The Reflexions and Refractions of Light

Mon, 01 Jan 0001 00:00:00 +0000

Proposition 96 Theorem 50

The same things being supposed, and that the motion before incidence is swifter than afterwards; I say, that if the line of incidence be inclined continually, the body will be at last reflected, and the angle of reflexion will be equal to the angle of incidence.

The Reflexions and Refractions of Light

Mon, 01 Jan 0001 00:00:00 +0000

Proposition 97 Problem 17

Supposing the sine of incidence upon any superficies to be in a given ratio to the sine of emergence; and that the inflection of the paths of those bodies near that superficies is performed in a very short space, which may be considered as a point; it is required to determine such a superficies as may cause all the corpuscles issuing from any one given place to converge to another given place.

Finding the orbits from the focus given

Mon, 01 Jan 0001 00:00:00 +0000

Proposition 98 Problem 48

The same things supposed, if around the axis AB any attractive superficies be described as CD, regular or irregular, through which the bodies issuing from the given place A must pass; it is required to find a second attractive superficies EF, which may make those bodies converge to a given place B.