THE PREFACE A BUSHS MONG all the Sciences, there is none which So much enlarges the Mind, and corrects the Judgment as that of the Mathematicks : It is, indeed, the Bafis and Foundation of all true Philofophy; and therefore PLATO wrote over the Door of his School, εδείς αγεωμέτρητος έρχετα Nor have there been wanting Perfons, in all Ages, who have cultivated this most valuable Part of Learning; and to what a confiderable Height the Ancients have advanced it, is evident from the Writings of EUCLID, ARCHIMEDES, APOLLONIUS PERGEUS, PROCLUS, DIOPHANTUS, THEON, &c. which are tranfmitted down to us. In the Practical Part likewife, there have been feveral, who have diftinguished themselves by their Care and Industry ; as ARISTYLLUS and TIMOCHARIS, who lived about 300 Tears before the Chriftian Era, HIPPARCHUS, and PTOLOMY, whofe Obfervations on the Stars have been of great Use to the Modern Aftronomers, in determining the Preceffion of the Equinoctial Points; the Quantity of which is fo fmall, that it requires an Interval of many Years to afcertain it. This was first found out by Obfervation; but bas fince been demonftrated a priori from the Laws of Gravity by the excellent Sir ISAAC NEWTON, in his Book. of the Syftem of the World: But tho the Ancients. were pretty well acquainted with the Planetary Aftro. nomy, there was one thing in which they were grofly de ficant; namely, the Aftronomy of Comets: These they look'd upon only as fublunary Vapours, or Airy Meteors, and fo never thought it worth their while to obferve their Phenomena, or write about them. But TY CHO ER AHE, by the Help of more large and ac curate Inftruments than the Ancients were poffeffed of, found that the Comet, which appeared in the Year 1577, had no diurnal Farallax that was fenfible; and confequently, that it was not only no Aerial Vapour, but also much higher than the Moon: So likewife, on the other hand, from its annual Parallax, be argued, the Descent of it into the Flanetary Regions; but yet they were ignorant of the Form of the Orbits, in which thefe Bodies moved, till, by. the help of Mr. Hamstead's most accurate Objervations on the Comet of 1680, the illuftrious NEWTON how'd that they mov'd round the Sun in Parabolical, or rather in very Eccentric Elliptical Orbits and defcribed Areas ( taken at the Centre of the Sun) proportional to the Times. Since then the Great Dr. HALLEY has compiled a Table of their Morions, (viz. fuch of them as have been hitherto obferved) and attempted to bring them under an Arithmetical Calculation, and has foretold, that in all Probability, the Comer, which appeared in the Year 1305, will return in the Year 1758: And if it should fo return, there is no Reason to doubt, but that the reft may return also; and then Aftronomers will have a large Field wherein to exercife themfelves, for many Ages, before they will be able to know the Number of thefe many and great Bodies revol ving about the common Centre of the Sun, and to reduce their Motions to certain Rules. In Question the 11th, Book the Firfi, for January, Fe bruary and March, I gave you an Example of Dr. Halley's Method of finding the Angular Motion at the Sun of a Comet in a Parabolical Orb, from the Area and peribelon Distance being given: And those, who have a Defire to fee the fame done in an Elliptical Orbit, may confult Dr. KIEL's Aftronomical Lectures in the Solution of KEPLER'S Problem. Having finished. Mr. Coris's Preface to Sir ISAAC NEWTON's Princi pia, pia, in the last Book, I fall, in this, give you the general Lares of Motion, together with fome Definitions of Matter, Space and Time, being excerpta from Mr. WHISTON'S Phyfical Lectures: And now I must inform my Readers, That as the LADIES DIARY will be published in December next, Ifball, for that Reafon, omit putting out a Book for that Quarter; because most of those, who buy this Treatife, I may fuppofe are engaged therein. ADVERTISEMENT To all LOVERS of INGENUITY, 7 T HE Author intending to publish the next Quarterly Back the Beginning of March enfuing, defires that Such Gentlemen and Ladies, &c. as think fit to encourage this Undertaking, either by promoting and recommending the Sale hereof, or by fending fuch Subjects, either in Ver fe or Profe, as are fuitable to this Defign, would please to direct their Letters to Mr. THO'. GENT, Printer, near the Star in Stone-Gate, YORK, Poft paid, before the End of February next, where they will be carefully forwarded to the Author. Whoever fend either Enigmas, or Arithmetical Questions, are defired to give the Solutions along with them, to prevent all Miftakes, or Ambiguity in the Terms: And I do affure the Buyers of this Treatise, that, in Process of Time, they Shall have Questions in all the Branches of Mathematicks, viz. Arithmetical, Nautical, Geographical, Niechanical, Trigonometrical, Aftronomical, Algebraical, and in Fluxions, tgether with exponential Equations, and the Con ftruction of Algebraic Equations, and finding their Loci; to fuit the Tafies of all Perfons, and render the Work generally useful. Mifcellanea (r.) Mifcellanea Curiofa, &c. DEFINITIONS Preparatory to B ODY, or Matter, is an extended Subftance, folid or impenetrable; ot itfelf merely paffive, and indifferent to Motion or Reit, but ca. pable of any Sort of Motions whatever, and of all Figures and Forms. I call it a Subftance extended, be. Caufe that it poffeffeth fome Part of the extended Space... but folid and impenetrable, not becaufe it cannot be pe netrated by Space, or perchance by other incorporeal Subftances, but because it is impenetrable by all other Matter and ; upon that Account, it doth eminently claim the Name of Solid. I put in the Definition, (it's being indifferent to Motion or Reft) not that I reckon Motion, as well as Reft,a Thing plainly negative or privative; bu tbecaufe the Conception of a Body as in Motion, is as ealy and familiar, as of a Body at Reft. I call it in itself paffive, becaufe we perceive nothing of Action, or Energy, or of a Power of moving itself, either in its Nature, or Affections; but, on the contrary, from all the Phænomena of Motions we every where meet with its Inactivity. But I fay, that it is capable of any Sort of Motion, and of all. Figures and Forms, fince the daily Appearances in the World, and infinite Experiments fhew this to be the Nature of it; Time, Space, Place and Motion, being Things fo well known to all, fcarce need to be defined. But, however, : |