An Essay on Newton's "Principia"Macmillan and Company, 1893 - 175 sider |
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Side 40
... linea HI , ipsi FC parallela , ob aequales CS , CH aequentur ES , EI , adeo ut EP semisumma sit ipsarum PS , PI , id est ( ob parallelas HI , PR et angulos aequales IPR , HPZ ) ipsarum PS , PH quae conjunctim totum axem 2AC adaequant ...
... linea HI , ipsi FC parallela , ob aequales CS , CH aequentur ES , EI , adeo ut EP semisumma sit ipsarum PS , PI , id est ( ob parallelas HI , PR et angulos aequales IPR , HPZ ) ipsarum PS , PH quae conjunctim totum axem 2AC adaequant ...
Side 44
... linea PH , in qua umbilicus alter H locatur . Demisso ad PH perpendiculo SK et erecto semiaxe minore BC , est SP - 2KP × PH + PH¶ = SH¶ -4CH 4BH - 4BC¶ = = ( SP + PH ) quad - L × ( SP + PH ) SPq + 2SP × PH + PHq − Lx ( SP + PH ) ...
... linea PH , in qua umbilicus alter H locatur . Demisso ad PH perpendiculo SK et erecto semiaxe minore BC , est SP - 2KP × PH + PH¶ = SH¶ -4CH 4BH - 4BC¶ = = ( SP + PH ) quad - L × ( SP + PH ) SPq + 2SP × PH + PHq − Lx ( SP + PH ) ...
Side 45
... linea recta , determinanda est ejus via rectilinea . Sit ea APBD , sintque A , P , B , D loca cometae in via illa temporibus observationum , et S locus solis . Ea celeritate qua cometa uniformiter percurreret rectam AD , finge ipsum ...
... linea recta , determinanda est ejus via rectilinea . Sit ea APBD , sintque A , P , B , D loca cometae in via illa temporibus observationum , et S locus solis . Ea celeritate qua cometa uniformiter percurreret rectam AD , finge ipsum ...
Side 49
... linea N ad EG ut est DC ad CP , et ad rectae DC punctum quodvis R erecto perpendiculo RT , quod occurrat hyperbolae DR × DE - DRTBG in T , et rectae EH in t , in eo capiatur Rr = N projectile tempore DRTBG perveniet ad punctum r ...
... linea N ad EG ut est DC ad CP , et ad rectae DC punctum quodvis R erecto perpendiculo RT , quod occurrat hyperbolae DR × DE - DRTBG in T , et rectae EH in t , in eo capiatur Rr = N projectile tempore DRTBG perveniet ad punctum r ...
Side 52
... linea recta semper pergere si nil impediat . Lex 2. Mutationem status movendi vel quiescendi proportionalem esse vi impressae et fieri secundum lineam rectam qua vis illa im- primitur . Lex 3. Corporum dato spatio inclusorum eosdem esse ...
... linea recta semper pergere si nil impediat . Lex 2. Mutationem status movendi vel quiescendi proportionalem esse vi impressae et fieri secundum lineam rectam qua vis illa im- primitur . Lex 3. Corporum dato spatio inclusorum eosdem esse ...
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Vanlige uttrykk og setninger
adeo apse line atque adeo attraction axis body describes body moves Brewster Cambridge celeritas central force centripeta centripetal force centrum circuli comets conic copy corporis corporum corpus Cotes Correspondence curve David Gregory density distance distantiae diurnal motion earth ellipseos ellipsis equal erit Flamsteed fluid focus force varying inversely force which varies geometrical progression given point given straight lines gravitatis Halley Hooke Hooke's hyperbola hypothesis Invenire inverse square Isaac Newton June 20 latus rectum law of force lectures Lemma linea manuscript mathematical medii medium whose resistance moon moon's motion of bodies motus Newton Newton's letter orbit parabola particle Pemberton pendulum perpendicular planets Portsmouth Portsmouth Collection Principia printed Prop proportional proportionalis propositions punctum quadrata quadrature quae quam quod ratio reciproce recta resistentia Rigaud Royal Society Scholium second edition SECTION spatium sphere sunt tangent temporis theory third book third edition umbilicus velocity
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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...
Side 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.