Dissertations on Subjects of Science Connected with Natural Theology, Volume 2C. Knight, 1839 - Natural theology |
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Page 250
... equation as yet unknown ) in order to make the whole curve , for example , of the shortest length between two given points , or inclose with two given lines the largest space , or ( having some property given ) inclose within itself the ...
... equation as yet unknown ) in order to make the whole curve , for example , of the shortest length between two given points , or inclose with two given lines the largest space , or ( having some property given ) inclose within itself the ...
Page 273
... equation expressing the relations . of those first small quantities . Thus we have the origin and constitution of quantities which in the Newtonian scheme are called fluxions of different orders , because conceived to express the manner ...
... equation expressing the relations . of those first small quantities . Thus we have the origin and constitution of quantities which in the Newtonian scheme are called fluxions of different orders , because conceived to express the manner ...
Page 275
... equation , but to find dy d x in terms of or y before taking its fluxion ; yet nothing can be more clumsy than to place a dot over the fraction , whereas d dy ( ) is perfectly convenient . Several important considerations arise out of ...
... equation , but to find dy d x in terms of or y before taking its fluxion ; yet nothing can be more clumsy than to place a dot over the fraction , whereas d dy ( ) is perfectly convenient . Several important considerations arise out of ...
Page 280
... equation between randy ( the equation to the curve ) , and we get the expression for the subtangent subnormal . Thus in the common parabola , whose equation is y2 = ax , y d x dy 2 y dy = X = y 2 y2 or 2 x , and a dy a in the hyperbola ...
... equation between randy ( the equation to the curve ) , and we get the expression for the subtangent subnormal . Thus in the common parabola , whose equation is y2 = ax , y d x dy 2 y dy = X = y 2 y2 or 2 x , and a dy a in the hyperbola ...
Page 281
... equation . Again , we have seen that the ultimate ratio of the sum of all the rectangles M P , P Q , contained by the ordinates and the increments of the abscissa to the curve's area A P M is that of equality ; or , in other words ...
... equation . Again , we have seen that the ultimate ratio of the sum of all the rectangles M P , P Q , contained by the ordinates and the increments of the abscissa to the curve's area A P M is that of equality ; or , in other words ...
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Common terms and phrases
action animals apsides argument ascertained attraction axis body moves bones calculus Cél central force centre of forces centre of gravity centripetal force circle common centre conic sections coprolites curve Cuvier cycloid Deity demonstration described diameter discovery distance disturbing force doctrine earth earth's orbit eccentricity ellipse equal equation evanescent evil examination existence expression extinct feet fluxion formation former fossil genera genus given globe human hyænas ichthyosaurus inquiry inversely investigation Jupiter kind known Laplace masses matter mean motion Méc moon's move round nature observed Osteology parabola Paris Basin particle period perpendicular planets portion position Principia principles problem proportion proposition quantity question radius vector ratio rectangle remarkable respecting revolution revolve round satellites Saturn scholium Sir Isaac Newton solution space species sphere square straight line strata suppose surface syzygy theory things tion trajectory variation velocity whole wholly
Popular passages
Page 102 - So also is the resurrection of the dead. It is sown in corruption; it is raised in incorruption; it is sown in dishonour; it is raised in glory; it is sown in weakness; it is raised in power; it is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body.
Page 88 - Am I a God at hand, saith the Lord, and not a God afar off? Can any hide himself in secret places that I shall not see him ? saith the Lord. Do not I fill heaven and earth ? saith the Lord.
Page 164 - ... to an unlettered observer they may appear less strange than the tribe we have just been surveying. One of them has the muzzle of a dolphin, the teeth of a crocodile, the head and breast of a lizard, the fins or paddles of a whale, but four instead of two, and the back or vertebrae of a fish. This has been named the Ichthyosaurus. The other, being apparently nearer to the lizard, has been called the Plesiosaurus ;* and has also four paddles like those of a whale ; the head of...
Page 175 - ... bodies, he can convince himself of a truth yet more sublime than Newton's discovery though flowing from it, and must yield his assent to the marvellous position that all the irregularities occasioned in the system of the universe, by the mutual attraction of its members, are periodical, and subject to an eternal law which prevents them from ever exceeding a stated amount, and secures through all time the balanced structure of a universe composed of bodies, whose mighty bulk and prodigious swiftness...
Page 447 - ... proportion of its polar to its equatorial diameter. By a most refined process he gave this proportion upon the supposition of the mass being homogeneous. That the proportion is different in consequence of the mass being heterogeneous does not in the least affect the soundness of his conclusion. Accurate measurements of a degree of latitude in the equatorial and polar regions, with experiments on the force of gravitation in those regions, by the different lengths of a pendulum vibrating seconds,...
Page 297 - ... the squares of the periodic times are as the cubes of the distances from the common centre, the centripetal forces will be inversely as the squares of the distances.
Page 193 - ... globe, then it follows that between that period, whensoever it was, and the earliest to which the history of the world reaches back, an interposition of power took place to create those animals, and man among the rest. The atheistical argument, that the present state of things may have lasted for ever, is therefore now at an end.
Page 299 - ... that the squares of their periodic times are as the cubes of the mean distances from the focus* they are by these propositions of Sir Isaac Newton which we have been considering, shown to be deflected from the tangent of their orbit, and retained in their paths, by a force acting inversely as the squares of the distances from the centre of motion.
Page 304 - XXXV. nexion between its corollaries, and the Theory of Gravitation. The versed sine of the half of any evanescent arc (or sagitta of the arc) of a curve in which a body revolves, was proved to be as the centripetal force, and as the square of the times ; or as F x T2. Therefore the force F is directly as the versed sine, and inversely as the square of the time. From this it follows that the central force may be measured in several ways. The arc being QC, we are to measure the central force in its...
Page 174 - The reader of the Principia, if he be a tolerably good mathematician, can follow the whole chain of demonstration by which the universality of gravitation is deduced from the fact, that it is a power acting inversely as the square of the distance from the centre of attraction.