Attempt to Prove the Motion of the Earth https://books.google.com/books?id=JgtPAAAAcAAJ (1674) pp. 27-28, read to the Royal Society 1671, written 1670. Inserted comment (in italics) by John Aubrey, Brief Lives. Note: this statement precedes the publication of Newton's Principia by near 20 years.
Context: I should here have described some Clocks and Time-keepers of great use, nay absolute necessity in these and many other Astronomical observations, but that I reserve them for some attempts that are hereafter to follow, about the various wayes I have tryed, not without good success of improving Clocks and Watches and adapting them for various uses, as for accurating Astronomy, completing the Tables of the fixt stars to Seconds, discovery of Longitude, regulating Navigation and Geography, detecting the properties and effects of motions for promoting secret and swift conveyance and correspondence, and many other considerable scrutinies of nature: And shall only for the present hint that I have in some of my foregoing observations discovered some new Motions even in the Earth it self, which perhaps were not dreamt of before, which I shall hereafter more at large describe, when further tryalls have more fully confirmed and compleated these beginnings. At which time also I shall explaine a Systeme of the World, differing in many particulars from any yet known, answering in all things to the common Rules of Mechanicall Motions: This depends upon three Suppositions. First, that all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them, from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial Bodies that are within the sphere of their activity; and consequently that not only the Sun and the Moon have an influence upon the body and motion of the Earth, and the Earth upon them, but that Mercury also, Venus, Mars, Saturne, and Jupiter by their attractive powers, have a considerable influence upon its motion as in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodys whatsoever that are put into direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion describing a Circle, Ellipsis, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified;'—But these degrees and proportions of the power of attraction in the celestiall bodys and motions, were communicated to Mr. Newton by R. Hooke in the yeare 1678, by letters, as will plainely appear both by the coppys of the said letters, and the letters of Mr. Newton in answer to them, which are both in the custody of the said R. H., both which also were read before the Royall Society at their publique meeting, as appears by the Journall book of the said Society.—'but it is a notion which if fully prosecuted as it ought to be, will mightily assist the astronomer to reduce all the Cœlestiall motions to a certaine rule, which I doubt will never be done true without it. He that understands the natures of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having my self many other things in hand which I would first compleat, and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.
