Elements of Natural Philosophy, Volume 1 |
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Page 10
... equal ( to V ) , and there- fore PQS is a circle whose centre is 0. The direction of acceleration at A is parallel to S the tangent at P , that is , is per- pendicular to OP , i.e. to Aa , and is therefore that of the radius AC . Now P ...
... equal ( to V ) , and there- fore PQS is a circle whose centre is 0. The direction of acceleration at A is parallel to S the tangent at P , that is , is per- pendicular to OP , i.e. to Aa , and is therefore that of the radius AC . Now P ...
Page 13
... equal to OBD . Hence the sum of the two half - moments together with half the area of the parallelogram is equal to AOB together with BOD , that is to say ; to the area of the whole figure OABD . But ABD , a part of this figure , is equal ...
... equal to OBD . Hence the sum of the two half - moments together with half the area of the parallelogram is equal to AOB together with BOD , that is to say ; to the area of the whole figure OABD . But ABD , a part of this figure , is equal ...
Page 14
... equal to the amount of the acceleration of the moving point . When the hodograph and its origin , and the velocity ... equal areas in equal times , that is ( § 48 ) , let the velocity be inversely as the perpendicular SY from S to the ...
... equal to the amount of the acceleration of the moving point . When the hodograph and its origin , and the velocity ... equal areas in equal times , that is ( § 48 ) , let the velocity be inversely as the perpendicular SY from S to the ...
Page 21
... 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 their difference of epochs ; and of epoch differing from their epochs by angles equal to those ...
... 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 their difference of epochs ; and of epoch differing from their epochs by angles equal to those ...
Page 22
... equal , but the amplitude of one of them much greater than that of the other . To find the time and the amount of the maximum acceleration or retardation of phase , let CA be equal to the greater half - amplitude . From A as centre ...
... equal , but the amplitude of one of them much greater than that of the other . To find the time and the amount of the maximum acceleration or retardation of phase , let CA be equal to the greater half - amplitude . From A as centre ...
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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.