Outlines of Natural Philosophy: Being the Heads of a Course of Lectures, Delivered in Columbia College, New-York, المجلدات 1-2

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C.S. Van Winkle, 1822

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الصفحة 56 - The product of the mass of a body into the square of its velocity is what has been called the Vis Viva of the body.
الصفحة 90 - ... be necessary to include among the forces the resistances exercised by the curves or surfaces. As a corollary, we may deduce from the above proposition, that the motion of the centre of gravity of a system of bodies will be uniform and rectilineal, whenever no accelerating force affects the system, except the mutual action of the several bodies upon each other. This will be true, whether the mutual action be produced by an attractive or a repulsive force, or by actual collision. See § 216.
الصفحة 64 - ... observed that this investigation, as well as the inverse problem for the case of rectilinear motion in the preceding section, is conducted more analytically than the greater part of the Principia, the reasoning of the demonstration conducting to the solution and not following it synthetically. A is the height from which a body must fall to acquire the velocity at any point D, which the given body moving in the trajectory VIK (sought by the investigation) has at the corresponding point I ; DI,...
الصفحة 61 - ... governs the variation of the "sun's attraction from point to point of such orbit ; but beyond this orbit it proves nothing. It remains, therefore, to show from the planetary motions round the sun, and from the motions of the satellites round their primaries, that the same law of attraction by which the intensity decreases as the square of the distance from the " centre of attraction increases, and vice versa., is universal.
الصفحة 7 - In experimental philosophy, propositions collected from the phenomena by induction, are to be deemed {notwithstanding contrary hypotheses) either exactly, or very nearly true, till other phenomena occur, by which they may be rendered more accurate, or liable to exception.
الصفحة 26 - There is an equilibrium upon the wheel and axle when the power is to the weight as the radius of the axle to the radius of the wheel.
الصفحة 70 - For since the time of vibration is to the time of descent through half the length of the pendulum, as the circumference of a circle to its diameter, that is, as 3.14159 to 1?
الصفحة 57 - B (b'— b) ; and since a + a' = b' + b, [75] therefore A (a* — of*) = B (6'1 + 6Z), or A a* + B b1 — A a'* + B 6". ' See another demonstration, Maclaurin's Account of Newton's Discoveries, Book ii. chap. iv. § 12. ' 77. If between two unequal elastic bodies A and C, a third B be interposed;, and if the least A, be made to strike with any given velocity on B, the motion communicated to C will be the greatest possible, when B is a mean proportional between A and C. It is easily shewn from §...
الصفحة 15 - The moment of a force about any point is the product of the force into the perpendicular let fall from that point on the direction of the force. The point is called the origin of moments. The moment of a force measures the tendency of the force to produce rotatory motion about a fixed point. 31. PROP.
الصفحة 66 - ... as the height of the plane is to its length, or as the thickness of the head of the wedge is to the length of the slanting side. The only difference will be in the greater friction, and difficulty in moving the plane or wedge instead of the weight. A common wedge is two inclined planes placed together, as the dotted line in figure 32 represents. Therefore...

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