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angles aperture arch asunder axis axle ball beam bodies move body falling breadth canal lock cast iron centre of gravity centre of gyration centrifugal force circle circumference cohesion column common centre Craigleith crushed cubes cubic foot cylinder Demonstration depth descend diameter direction distance draw elastic ends equilibrio evident experiments feet long feet per second fluid foot friction fulcrum given horizontal inch square inclined plane inversely joist lateral strength length lever motion multiplied number of teeth number of turns parabola parallel parallelogram pendulum perpendicular pinion portion pounds pressure Prop proportion PROPOSITION pulleys quantity of matter quotient radius ratio resistance rest rope rule screw side similar similar triangles sine solid space fallen specific gravity square root straight line strain substances supported surface suspended sustain Table theory tion triangle undershot uniformly vibrations waggon wheel Whence whole weight
Page 162 - The force which must be expended in order to raise the piston, is equal to the weight of a column of water, whose base is the section of the piston, and whose height is that to which the water is raised.
Page 160 - The resistance that a body sustains in moving through a fluid is in proportion to the square of the velocity. The resistance that any plane surface encounters in moving through a fluid with any velocity, is equal to the weight of a column whose height is the space a body would have to fall through in free space to acquire that velocity, and whose base is the surface of the plane.
Page 3 - The rate of change of the quantity of motion (momentum) is proportional to the force which causes it, and takes place in the direction of the straight line in which the force acts.
Page 29 - These machines are ; 1. the lever; 2. the wheel and axle ; 3. the pulley ; 4. the inclined plane ; 5. the wedge ; and 6. the screw.
Page 158 - ... feet high, the colder column presses it upwards with a force proportionate to this difference in weight, and with a velocity equal to that acquired by a body falling through a space equal to the difference in height that two columns of equal weight would occupy, which in this case is five inches.
Page 3 - If a body be at rest, it will remain at rest ; and if in motion, it will continue that motion, uniformly in a straight line, if it be not disturbed by the action of some external cause.
Page 170 - ... the mill-stone ought to have for one turn of the wheel. 7. Then, as the number of turns of the wheel in a minute is to the number of turns of the...
Page 5 - Rad. radius. S. the sine. Cos. the cosine. Tan. the tangent. Cotan. the cotangent. Sec. the secant. SECTION FIRST. THE GENERAL LAWS OF MOTION. PROPOSITION I. THE QUANTITIES OF MATTER IN ALL BODIES ARE IN THE COMPLICATE RATIO OF THEIR MAGNITUDES AND DENSITIES. FOR by Definition 3, if the magnitudes be equal, the matter will be as the densities. And if the densities be equal, the matter will be as the magnitudes. Therefore, the matter is universally in the compound ratio of both. Corollary 1.
Page 156 - principle of Archimedes*,' who enunciated it for the case of liquids. As above indicated, the argument applies to fluids of all kinds, and is not restricted to the case of uniform density. The resultant upward pressure is called the ' buoyancy ' of the body ; and the centre of gravity of the displaced fluid is called the