Isaac Newton

“ Because this globe is perfectly indifferent to all the axes that pass through its centre, nor has a greater propensity to one axis or to one situation of the axis than to any others it is manifest that by its own force it will never change its axis, or the inclination of it. ”

“ Suppose therefore all the accelerative attractions made towards the great body to be among themselves as the squares of the distances reciprocally; and then, by increasing the distance of the great body till the differences of the right lines drawn from that to the others in respect of their length, and the inclinations of those lines to each other, be less than any given, the motions of the parts of the system will continue without errors that are not less than any given. ”

“ For the globe, as we shall shew presently, is perfectly indifferent to the receiving of all impressions. The greatest angle of the inclination of the annulus single, is when the nodes are in the syzygies. Thence in the progress of the nodes to the quadratures, it endeavours to diminish its inclination and by that endeavour impresses a motion upon the whole globe. The globe retains this motion impressed, till the annulus by a contrary endeavour destroys that motion and impresses a new motion in a contrary direction. ”

“ If two bodies attracting each other with any kind of forces, and not otherwise agitated or obstructed, are moved in any manner whatsoever; those motion: will he the same, as if they did not at all attract each other mutually, but were both attracted with the same forces by a third body placed in their common centre of gravity; and the law of the attracting forces will be the same in respect of the distance of the bodies from the the common centre, as in respect of the distance between the two bodies. ”

“ If a body is obliged, by a force reciprocally proportional to the square of its distance from any centre, to revolve in an ellipsis round that centre; and afterwards in its descent from the upper apsis to the lower apsis, that force by a perpetual accession of new force is increased more than a duplicate ratio of the diminished distance; it is manifest that the body being impelled always towards the centre by the perpetual accession of this new force, will incline more towards that centre than if it were urged by that force alone which decreases in a duplicate ratio of the diminished distance ”

“ Therefore a homogeneous and perfect globe will not retain several distinct motions, but will unite all those that are irnpressed on it, and reduce them into one; revolving, as far as in it lies, always with a simple and uniform motion about one single given axis with an inclination perpetually invariable. And the inclination of the axis, or the velocity of the rotation will not be changed by centripetal force. ”

“ But the absolute attractive force of the body A is to the absolute attractive force of the body B, as the accelerative attraction of all the bodies towards A to the accelerative attraction of all the bodies towards B at equal distances and so is also the accelerative attraction of the body B towards A, to the accelerative attraction of the body A towards B. But the accelerative attraction of the body B towards A is to the accelerative attraction of the body A towards B as the mass of the body A to the mass of the body B ”

“ For the same reason that redundant matter in the æquatorial regions of a globe causes the nodes to go backwards, and therefore by the increase of that matter that retrogradation is increased, by the diminution is diminished, and by the removal quite ceases; it follows, that if more than that redundant matter be taken away, that is, if the globe be either more depressed, or of a more rare consistence near the æquator than near the poles, there will arise a motion of the nodes in consequentia. ”

“ In a system of bodies whose forces decrease in the duplicate ratio of the distances, if the lesser revolve about one very great one in ellipses, having their common focus in the centre of that great body, and of a figure exceeding accurate ”

“ And the case is the same if the second impulse were made upon any other place of the æquator of the first motion; and also if the first impulse were made upon any place in the equator of the motion which would be generated by the second impulse alone; and therefore also when both impulses are made in any places whatsoever; for these impulses will generate the same circular motion, as if they were impressed together and at once in the place of the intersections of the equators of those motions, which would be generated by each of them separately. ”

“ In mathematics we are to investigate the quantities of forces with their proportions consequent upon any conditions supposed; then when we enter upon physics, we compare those proportions with the phænomena of Nature; that we may know what conditions of those forces answer to the several kinds of attractive bodies. ”

“ For if the globe be supposed to be divided into two hemispheres, by any plane whatsoever passing through its own centre and the centre to which the force is directed; that force will always urge each hemisphere equally ”

“ The more distant the law of the forces is from the law in that case, the more will the bodies disturb each others motions; neither is it possible that bodies attracting each other mutually according to the law supposed in this proposition should move exactly in ellipses unless keeping a certain proportion of distances from each other. ”

“ The nodes therefore when situate in the quadratures recede perpetually, and at the syzygies, where no perturbation can be produced in the motion as to latitude, are quiescent; in the intermediate places they partake of both conditions, and recede more slowly; and therefore being always either retrograde or stationary, they will be carried backwards, or in antecedentia, each revolution.
Cor. 12. All the errors described in these corollaries are a little greater at the conjunction of the bodies P, S, than at their opposition; because the generating forces NM and ML are greater. ”

“ Cor. 4 The orbit of the body P, cæteris paribus, is more curve at the quadratures than at the conjunction and opposition. For the swifter bodies move, the less they deflect from a rectilienar path. And besides the force KL, or NM, at the conjunction and opposition, is contrary the force with which the body T attracts the body P; and therefore diminishes that force ”