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adeo apse line atque adeo attraction axis body move Brewster calculations Cambridge celeritas central force centre centripetal force centrum circuli comets conic copy corporis corpus curve David Gregory density describatur describit distance distantiae diurnal motion earth ejus ellipseos ellipsis Eoyal equal Ergo erit Flamsteed fluid focus force which varies given point gravitatis haec Hooke Hooke's hyperbola hypothesis igitur Invenire inverse square ipsi Isaac Newton June 20 latus rectum lectures Lemma linea London manuscript mathematical medium moon motion motus Newton's letter orbit parallelas particle Pemberton perpendicular Planetarum planets Portsmouth Portsmouth Collection Principia printed Prop proportional propositions puncto punctum quadrata temporum periodicorum quae quam quod ratio reciproce recta resistance resistentia medii Rigaud Royal Society Scholium second edition Section semper spatium sphere straight line sunt suppose tangent temporibus theory third book third edition tract umbilicus velocity vires centripetae vis centripeta
Page 7 - I deduced that the forces which keep the Planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them to answer pretty nearly.
Page 63 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 161 - And as the earth, so perhaps may the sun imbibe this spirit copiously, to conserve his shining, and keep the planets from receding further from him ; and they that will may also suppose that this spirit affords or carries with it thither the solary fuel and material principle of life, and that the vast ethereal spaces between us and the stars are for a sufficient repository for this food of the sun and planets.
Page 77 - LAW I. Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
Page 158 - The third I now design to suppress. Philosophy is such an impertinently litigious lady, that a man had as good be engaged in lawsuits as have to do with her.
Page 140 - For my part I shall take it as a great favour if you shall please to communicate by letter your objections against any hypothesis or opinion of mine; and particularly if you will let me know your thoughts of that of compounding the celestiall motions of the planetts of a direct motion by the tangent and an attractive motion towards the centrall body...
Page 159 - Now is not this very fine ? Mathematicians, that find out, settle, and do all the business, must content themselves with being nothing but dry calculators and drudges ; and another, that does nothing but pretend and grasp at all things, must carry away all the invention, as well of those that were to follow him, as of those that went before.
Page 167 - And tho' his correcting my spiral occasioned my finding the theorem, by which I afterwards examined the ellipsis ; yet am I not beholden to him for any light into the business, but only for the diversion he gave me from my other studies to think on these things, and for his dogmaticalness in writing, as if he had found the motion in the ellipsis, which inclined me to try it, after I saw by what method it was to be done.
Page 152 - This depends upon three suppositions: — first, that all celestial bodies whatsoever have an attraction or gravitating power towards their own centres, 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 celestial bodies that are within the sphere of their activity...
Page 26 - Newton what would be the curve described by the planets on the supposition that gravity diminished as the square of the distance. Newton immediately answered, an Ellipse. Struck with joy and amazement, Halley asked him how he knew it? Why, replied he, I have calculated it; and being asked for the calculation, he could not find it, but promised to send it to him.