The Mathematical Principles of Natural Philosophy, Tom 2H.D. Symond, 1803 |
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Strona 8
... ratio of the gravity to the refiftance , the point A will be given . And hence the curve DraF is also given . COR ... duplicate of that ratio , it is plain that the length 2DP is augmented in that fimple ratio only ; and is therefore ...
... ratio of the gravity to the refiftance , the point A will be given . And hence the curve DraF is also given . COR ... duplicate of that ratio , it is plain that the length 2DP is augmented in that fimple ratio only ; and is therefore ...
Strona 9
... ratio of the refiftance to the gra- vity , which was to be found . From this ratio the length DF is to be collected ... duplicate ratio of the velocities . For by the action of a swifter body , a greater motion in proportion to a greater ...
... ratio of the refiftance to the gra- vity , which was to be found . From this ratio the length DF is to be collected ... duplicate ratio of the velocities . For by the action of a swifter body , a greater motion in proportion to a greater ...
Strona 11
... proportion of this re- fiftance to the force of gravity , or any other given centripetal force . COR . 5. And , vice ... duplicate ratio of the velocities , and moving on by their innate force only , will , in times which are reciprocal ...
... proportion of this re- fiftance to the force of gravity , or any other given centripetal force . COR . 5. And , vice ... duplicate ratio of the velocities , and moving on by their innate force only , will , in times which are reciprocal ...
Strona 12
... duplicate ratio of their velocities , in times which are as the first motions directly , and the first refiftances inversely , they will lofe parts of their mo- tions proportional to the wholes , and will defcribe fpaces pro- portional ...
... duplicate ratio of their velocities , in times which are as the first motions directly , and the first refiftances inversely , they will lofe parts of their mo- tions proportional to the wholes , and will defcribe fpaces pro- portional ...
Strona 19
... duplicate ratio of the fides , qDp x tD2 PD2 the particle tDy will be as that is ( because tD is given ) , as qDp pD2 But pD2 is AD2 + Ap2 , that is , AD2 + AD x pq . There- AD × Ak , or AD x Ck ; and qDp is fore tDv , the particle of ...
... duplicate ratio of the fides , qDp x tD2 PD2 the particle tDy will be as that is ( because tD is given ) , as qDp pD2 But pD2 is AD2 + Ap2 , that is , AD2 + AD x pq . There- AD × Ak , or AD x Ck ; and qDp is fore tDv , the particle of ...
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afcent alfo alſo angle aphelion arifing axis becauſe body cafe centre centripetal force circle comet conjunctly cylinder decrement defcend defcribed denfity diameter diminiſhed diſtance diurnal motion duplicate ratio earth ecliptic ellipfis equal equator fame ratio fatellite fecond feet femi-diameter fhould fide fimilar fince firft firſt fituated fixed ftars fluid folid fome force of gravity fpace fquare fubduplicate ratio fuch fun's fuperficies fuppofe furface fyzygies given globe greater greateſt horary motion hyperbola inches increaſed Jupiter latitude latus rectum lefs length 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 reafon reciprocally rectangle refiftance refpect repreſent reſiſtance revolve right line Saturn SCHOLIUM ſpace ſtars tail thefe themſelves THEOREM theſe thofe thoſe tion veffel velocity vortex weight whofe whole
Popularne fragmenty
Strona 160 - 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.
Strona 158 - Upon this subject I had, indeed, composed the third Book in a popular method, that it might be read by many; but afterwards, considering that such as had not sufficiently entered into the principles could not easily discern the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent the disputes which might be raised upon such accounts, I chose to reduce...
Strona 312 - ... 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.
Strona 310 - Whence also He is all similar, all eye, all ear, all brain, all arm, all power to perceive, to understand, and to act ; but in a manner not at all human, in a manner not at all corporeal, in a manner utterly unknown to us.
Strona 309 - And from his true dominion it follows that the true God is a living, intelligent, and powerful Being; and from his other perfections, that he is supreme, or most perfect. He is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things, and knows all things that are or can be done.
Strona 309 - He is not eternity or infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures for ever, and is every where present; and by existing always and every where, he constitutes duration and space.
Strona 92 - If the figure DNFG be such a curve, that if, from any point thereof, as N, the perpendicular NM be let fall on the axis AB, and from the given point G there be drawn...
Strona 310 - As a blind man has no idea of colours, so have we no idea of the manner by which the all-wise God perceives and understands all things. He is utterly void of all body and bodily figure, and can therefore neither be seen nor heard nor touched ; nor ought He to be worshipped under the representation of any corporeal thing. We have ideas of His attributes, but what the real substance of anything is, we know not.
Strona 158 - The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
Strona 54 - 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.