Valentin Chirosca’s Reviews > The Principia: Mathematical Principles of Natural Philosophy > Status Update

Book I, Part XIV.Prop. XCVI, Scholium ...that light is propagated in succession, and requires about seven or eight minutes to travel from the sun to the earth.

THEOREM XXXIV.
The same things supposed, I say, that a corpuscle situate without the sphere is attracted with a force reciprocally proportional to the square of its distance from the center.

THEOREM XXXIV.

The same things supposed, I say, that a corpuscle situate without the sphere is attracted with a force reciprocally proportional to the square of its distance from the centre.

Let the bodies S and P revolve about their common centre of gravity C, proceeding from S to T, and from P to Q,. From the given point s lot there be continually drawn sp, sq, equal and parallel to SP, TQ; and the curve pqv, which the point p describes in its revolution round the immovable point s, will be similar and equal ... finally I've got the book view.

SECTION VII.

Concerning the rectilinear ascent and descent of bodies,

PROPOSITION XXXII.
PROBLEM XXIV.

Supposing that the centripetal force is reciprocally proportional to the square of the distance of the places from the centre; it is required to define the spaces which a body, falling directly, describes in given times.

finally !

It will be sufficient if that angle is found by a rude calculus in numbers near the truth...Prob XXIII, Scholium

So far concerning the finding of the orbits. It remains that we determine the motions of bodies in the orbits so found.

And after the problem is solved in the new figure, if by the inverse operations we transform the new into the first figure, we shall have the solution required...Lemma XXII

If the ellipsis, by having its centre removed to an infinite distance, degenerates into a parabola, the body will move in this parabola ; and the force, now tending to a centre infinitely remote, will become equable. Which is Galileo's theorem. And if the parabolic section of the cone (by changing the inclination of the cutting plane to the cone) degenerates into an hyperbola, the body will move in the perimeter...

A body by two forces conjoined will describe the diagonal of a parallelogram, in the same time that it wovld describe the sides, by those forces apart.