Elements of Natural Philosophy, Volume 1 |
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Page 7
... give nearer and nearer approximations to the velocity at the beginning of the first second . The whole foundation of Newton's differential calculus is , in fact , contained in the simple question , ' What is the rate at which the space ...
... give nearer and nearer approximations to the velocity at the beginning of the first second . The whole foundation of Newton's differential calculus is , in fact , contained in the simple question , ' What is the rate at which the space ...
Page 14
... gives double the area described in one second about the fixed point , which has just been shown to be a constant quantity . Other examples of these principles will be met with in the chapters on Kinetics . 49. If , as in § 35 , from any ...
... gives double the area described in one second about the fixed point , which has just been shown to be a constant quantity . Other examples of these principles will be met with in the chapters on Kinetics . 49. If , as in § 35 , from any ...
Page 16
... give a complete specification of the motion . 55. The unit angular velocity is that of a point which describes , or would describe , unit angle about a fixed point in unit of time . The usual unit angle is ( as explained in treatises on ...
... give a complete specification of the motion . 55. The unit angular velocity is that of a point which describes , or would describe , unit angle about a fixed point in unit of time . The usual unit angle is ( as explained in treatises on ...
Page 18
... give the second a southward velocity of eighty miles an hour , which is the required relative motion . Or , given one train moving north at the rate of thirty miles an hour , and another relatively to it moving south at the rate of ...
... give the second a southward velocity of eighty miles an hour , which is the required relative motion . Or , given one train moving north at the rate of thirty miles an hour , and another relatively to it moving south at the rate of ...
Page 21
... give , when compounded , a single simple harmonic motion ; of the same period ; of amplitude equal to the diagonal of a parallelogram de- scribed on lengths equal to their am- plitudes measured on lines meeting at an angle equal to ...
... give , when compounded , a single simple harmonic motion ; of the same period ; of amplitude equal to the diagonal of a parallelogram de- scribed on lengths equal to their am- plitudes measured on lines meeting at an angle equal to ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centimetre centre of gravity centre of inertia circle circular cloth co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance elements ellipse ellipsoid elongation equal equations equilibrium external point Extra fcap finite flexure fluid forces acting friction geometrical given force Hence hodograph horizontal infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving Natural Philosophy normal section Oxford P₁ parallel particle path pendulum perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular resultant right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theory tion torsion uniform unit vertical whole wire
Popular passages
Page 161 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 65 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.
Page 28 - Fourier's theorem is not only one of the most beautiful results of modern analysis, but may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.
Page 161 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 66 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 68 - To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.
Page 130 - UNTIL we know thoroughly the nature of matter and the forces which produce its motions, it will be utterly impossible to submit to mathematical reasoning the exact conditions of any physical question.