The Mathematical Principles of Natural Philosophy, Volumen2Benjamin Motte, 1729 |
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Página 9
... ( because QB and CK , DA and AC are pro- 2 DP2 x DA portional ) ACxCP and therefore is to 2DP , as DPX DA to CP × AC ; that is , as the refiftance to the gravity . Q.E. D. COR . 4. Hence if a body be projected from any place D , with a ...
... ( because QB and CK , DA and AC are pro- 2 DP2 x DA portional ) ACxCP and therefore is to 2DP , as DPX DA to CP × AC ; that is , as the refiftance to the gravity . Q.E. D. COR . 4. Hence if a body be projected from any place D , with a ...
Página 16
... because of the given ratio of the velocities , they will always defcribe fpaces , which are as the firft velocities and the times conjuntly . O.E.D. COR . 1. Therefore if bodies equally fwift are re- fifted in a duplicate ratio of their ...
... because of the given ratio of the velocities , they will always defcribe fpaces , which are as the firft velocities and the times conjuntly . O.E.D. COR . 1. Therefore if bodies equally fwift are re- fifted in a duplicate ratio of their ...
Página 22
... ( because the rectangle KC × KN is given ) as AP . But the ultimate ratio of the hyperbolic area KNOL to the rectangle KLX KN becomes , when the points K and L coincide , the ratio of of equality . Therefore that hyperbolic evanefcent ...
... ( because the rectangle KC × KN is given ) as AP . But the ultimate ratio of the hyperbolic area KNOL to the rectangle KLX KN becomes , when the points K and L coincide , the ratio of of equality . Therefore that hyperbolic evanefcent ...
Página 24
... ( because of the common angle D ) are in a duplicate ratio of the fides , the particle t Dv will be qDpxt D2 PD2 as that is , ( because t D is given ) as qDp PD2 But p D is AD2 --Ap2 , that is , ADAD × Ak , or ADxCk ; and q Dp is ADxpq ...
... ( because of the common angle D ) are in a duplicate ratio of the fides , the particle t Dv will be qDpxt D2 PD2 as that is , ( because t D is given ) as qDp PD2 But p D is AD2 --Ap2 , that is , ADAD × Ak , or ADxCk ; and q Dp is ADxpq ...
Página 38
... Because there can be no motion in a Parabola except in a non - refifting medium , but in the Hyperbola's here defcribed ' tis produced by a perpetual refiftance ; it is evident that the line which a projectile defcribes in an uniformly ...
... Because there can be no motion in a Parabola except in a non - refifting medium , but in the Hyperbola's here defcribed ' tis produced by a perpetual refiftance ; it is evident that the line which a projectile defcribes in an uniformly ...
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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...