The Mathematical Principles of Natural Philosophy, Volumen2Benjamin Motte, 1729 |
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Página 24
... radius be- ing of a fit magnitude ; all the time of the afcent to the highest place will be as the Jector of the circle , and all the time of de- fcending from the highest place as the fector of the hyperbola . Pl . 2. Fig . 2 . To the ...
... radius be- ing of a fit magnitude ; all the time of the afcent to the highest place will be as the Jector of the circle , and all the time of de- fcending from the highest place as the fector of the hyperbola . Pl . 2. Fig . 2 . To the ...
Página 55
... radius SQ in T ; draw PO , QO perpendicular to the spiral , and meeting in O , and join SO . Ifay , that if the points P and Q approach and coincide , the angle PSO will become a right angle , and the ultimate ratio of the rectangle TQ ...
... radius SQ in T ; draw PO , QO perpendicular to the spiral , and meeting in O , and join SO . Ifay , that if the points P and Q approach and coincide , the angle PSO will become a right angle , and the ultimate ratio of the rectangle TQ ...
Página 59
... radius PS be any how changed ; the number of revolutions which the body can compleat in the space between the circumfe- rences of thofe circles , going round in the spiral from one circumference to another , will be as PS OS > or as the ...
... radius PS be any how changed ; the number of revolutions which the body can compleat in the space between the circumfe- rences of thofe circles , going round in the spiral from one circumference to another , will be as PS OS > or as the ...
Página 60
... radius AS into parts AS , BS , CS , DS , & c . that are continually proportional . But the times of the revolutions ... radius AS , is in the fame ratio to the fecant of the angle in which the new fpiral , in the propofed medium , cuts ...
... radius AS into parts AS , BS , CS , DS , & c . that are continually proportional . But the times of the revolutions ... radius AS , is in the fame ratio to the fecant of the angle in which the new fpiral , in the propofed medium , cuts ...
Página 62
... radius SP , whofe index is greater than the number 3 , the affirmative refiftance will be changed into a negative . SCHOLIUM . This Propofition and the former which relate to me- diums of unequal denfity , are to be understood of the ...
... radius SP , whofe index is greater than the number 3 , the affirmative refiftance will be changed into a negative . SCHOLIUM . This Propofition and the former which relate to me- diums of unequal denfity , are to be understood of the ...
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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...