Excerpt from The Mathematical Principles of Natural Philosophy, Vol. 1 of 3: To Which Are Added, Newton's System of the World; A Short Comment on and Defence of the Principia

XI 'in the publication of this:vvork the moﬂ: acute and univer fally learned Mr. Edmund. Halley not only' aﬂilted me with1 his pains in correcting the prefs and taking care of the, fchemes, but it was to his folicitations that its becoming pub lie is owing; 'for when he had obtained 'of me my demon {trations of the figure of the celeftial orbits, he continually prefi'ed me to communicate the fame to the Royal, Society, who afterwards, by their kind encouragement and entreaties, engaged me to think of publiihi/ng them But after I had begun to confider the inequalities of the lunar motions, and had entered upon fome other things relating to the laws and meafures of gravity, and other forces; and the figures that would be defcribed by bodies attracted, according to given laws; andﬂthe motion of feveral bodies moving among themfelves the motion of bodies in refitting mediums the forces, denfities, and motions, of mediums; the orbits of the comets, and fuch like; I put off that publication till I had made a fearch into thofe matters, and could put out the whole together. What relates to the lunar motions (being Imper fect) I have put all together 111 the corollaries of prop. 66, to avoid being obliged to propofe and diftin�tly demonfir ate the feveral things there contained in a method more prolix than the fubje�t deferved, and' interrupt the feries of the feveral propofrtions. Some things, found out after the refs, I chofe to infert in places lefs fuitable, rather than change the num ber of the propofitions and the citations. I heartily beg that what I have here done may be read with candour; and that the defects Iihave been guilty of upon thrs difiicult fub jec't may be not fo much reprehended a's kindly fupplied, and invefiigated by newendeavours of my readers.

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