The Mathematical Principles of Natural Philosophy, Volumen2Benjamin Motte, 1729 |
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Página 3
... Prop . 1. Book 2. ) and therefore are alfo as the wholes . Q. E. D. COROL . Hence if to the rectangular afymptotes AC , CH , the Hyperbola B G is defcribed , and AB , DG be drawn perpendicular to the afymptote AC , and both the velocity ...
... Prop . 1. Book 2. ) and therefore are alfo as the wholes . Q. E. D. COROL . Hence if to the rectangular afymptotes AC , CH , the Hyperbola B G is defcribed , and AB , DG be drawn perpendicular to the afymptote AC , and both the velocity ...
Página 7
... Prop . 2. Book 2. ) as the line DR , and the height ( by Prop . 3. Book 2. ) as the area DRXAB- RDGT , that is , as the line Rr . But in the very be- ginning of the motion the area RDGT is equal to the rectangle DRXAQ , and therefore ...
... Prop . 2. Book 2. ) as the line DR , and the height ( by Prop . 3. Book 2. ) as the area DRXAB- RDGT , that is , as the line Rr . But in the very be- ginning of the motion the area RDGT is equal to the rectangle DRXAQ , and therefore ...
Página 17
... Prop . ) is augmented in the ratio of motion directly , and the space described in the ratio of the time . COR . 5. And if the globes move in different me- diums , the space , in a medium which , cateris paribus , refifts the moft ...
... Prop . ) is augmented in the ratio of motion directly , and the space described in the ratio of the time . COR . 5. And if the globes move in different me- diums , the space , in a medium which , cateris paribus , refifts the moft ...
Página 47
... Prop . 11. ) the velocity is given from the given time , and ( by this Prop . ) the fpace is given from the given velocity ; the space will be given from the given time : and the contrary . THEOREM X. PROPOSITION XIII . Suppofing that a ...
... Prop . 11. ) the velocity is given from the given time , and ( by this Prop . ) the fpace is given from the given velocity ; the space will be given from the given time : and the contrary . THEOREM X. PROPOSITION XIII . Suppofing that a ...
Página 54
... Prop . foregoing , and their Corollaries . For in thofe Propofitions , instead of the uniform resistance made to an afcending body arifing from its gravity , one may fubftitute the uniform refiftance which arifes from the tenacity of ...
... Prop . foregoing , and their Corollaries . For in thofe Propofitions , instead of the uniform resistance made to an afcending body arifing from its gravity , one may fubftitute the uniform refiftance which arifes from the tenacity of ...
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Términos y frases comunes
afcending afymptote alfo angle aphelion apogee arifing axis becauſe body cafe caufe centre centripetal force circle Comet cycloid cylinder defcend defcrib'd defcribed denfity diameter difference diftance diminiſhed diurnal motion duplicate ratio Earth ecliptic ellipfis equal equation faid fame ratio fatellite fecond feen femidiameter fide fimilar fince firft fluid folid fome force of gravity fpace fquare fubduplicate fuch fuperficies fuppofe furface fyzygies given globe gravity greater greateſt horary motion Hyperbola inches increaſed Jupiter latitude latus rectum leaft leffer lefs length let fall mean diſtance mean motion meaſure medium Moon Moon's move muſt nearly nodes obfervations ofcillations orbit paffing Parabola particles pendulum perihelion perpendicular Planets pofition preffure progreffion prop proportion PROPOSITION pulfes quadratures radius reciprocally rectangle refiftance refpect reprefent revolve right line Saturn ſpace Sun's tail tangent thefe themſelves THEOREM theſe thofe thoſe thro tion veffel velocity vortex weight whofe whole
Pasajes populares
Página 385 - ... all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles.
Página 385 - And now we might add something concerning a certain most subtle Spirit which pervades and lies hid in all gross bodies: by the force and action of which Spirit the particles of bodies mutually attract one another at near distances, and cohere, if contiguous...
Página 198 - In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.
Página 68 - B, from B to C, from C to D, from D to E, and from E to A ; and measure the distances AB, BC, CD, DE, and EA.
Página 213 - ... upon all the gold to the action of the same upon all the wood; that is, as the weight of the one to the weight of the other: and the like happened in the other bodies. By these experiments, in bodies of the same weight, I could manifestly have discovered a difference of matter less than the thousandth part of the whole, had any such been.
Página 207 - IV. THAT THE MOON GRAVITATES TOWARDS THE EARTH, AND BY THE FORCE OF GRAVITY IS CONTINUALLY DRAWN OFF FROM A RECTILINEAR MOTION, AND RETAINED IN ITS ORBIT.
Página 217 - ... to every action corresponds an equal reaction; therefore the planet B will, on the other hand, gravitate towards all the parts of the planet A; and its gravity towards any one part will be to the gravity towards the whole as the matter of the part to the matter of the whole.
Página 287 - Moon, the inclination of the Moon's orbit, to the plane of the ecliptic, the...
Página 198 - ... matter of observation; and, in the particles that remain undivided, our minds are able to distinguish yet lesser parts, as is mathematically demonstrated. But whether the parts so distinguished, and not yet divided, may, by the powers of Nature, be actually divided and separated from one another, we cannot certainly determine. Yet, had we the proof of but one experiment that any undivided particle, in breaking a hard and solid body, suffered a division, we might by virtue of this rule, conclude...
Página 213 - For, should we imagine our terrestrial bodies removed to the orb of the moon, and there, together with the moon, deprived of all motion, to be let go, so as to fall together towards the earth, it is certain, from what we have demonstrated' before, that, in equal times, they would describe equal spaces with the moon, and of consequence are to the moon, in quantity of matter, as their weights to its weight. Moreover...