Elements of Natural Philosophy, Volume 1 |
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Page 8
... square root of the sum of their squares ; and the cosines of its inclination to the given direc- tions are the ratios of the components to the resultant . 32. The velocity of a point is said to be accelerated or retarded according as it ...
... square root of the sum of their squares ; and the cosines of its inclination to the given direc- tions are the ratios of the components to the resultant . 32. The velocity of a point is said to be accelerated or retarded according as it ...
Page 10
... square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject to an acceleration ...
... square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject to an acceleration ...
Page 16
... square of the distance from this point . The same proposition is true for any path , when the acceleration is towards the point about which the angles are measured : being merely a different mode of stating the result of § 48 . 60. The ...
... square of the distance from this point . The same proposition is true for any path , when the acceleration is towards the point about which the angles are measured : being merely a different mode of stating the result of § 48 . 60. The ...
Page 17
... square of the distance of the moving point from the fixed point . 62. From §§ 61 , 52 , it follows that when a particle moves with acceleration towards a fixed point , varying inversely as the square of the distance , its orbit is a ...
... square of the distance of the moving point from the fixed point . 62. From §§ 61 , 52 , it follows that when a particle moves with acceleration towards a fixed point , varying inversely as the square of the distance , its orbit is a ...
Page 35
... square of the resultant angular velocity is the sum of the squares of its components , and the ratios of the three components to the resultant are the direction - cosines of the axis . Hence also , an angular velocity about any line may ...
... square of the resultant angular velocity is the sum of the squares of its components , and the ratios of the three components to the resultant are the direction - cosines of the axis . Hence also , an angular velocity about any line may ...
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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.