Elements of Natural Philosophy, Volume 1 |
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Page 9
... become OC , its change is AC , or OB . Hence , just as the direction of motion of a point is the tangent to its path ... becomes the tangent at P. Hence the direction of acceleration is that of the tangent to the curve thus described ...
... become OC , its change is AC , or OB . Hence , just as the direction of motion of a point is the tangent to its path ... becomes the tangent at P. Hence the direction of acceleration is that of the tangent to the curve thus described ...
Page 12
... become v = at , x = at2 , v2 = ax . Of course the preceding formulae apply to a constant retardation , as in the case of a projectile moving vertically upwards , by simply giving a a negative sign . 44. When there is uniform ...
... become v = at , x = at2 , v2 = ax . Of course the preceding formulae apply to a constant retardation , as in the case of a projectile moving vertically upwards , by simply giving a a negative sign . 44. When there is uniform ...
Page 21
... becomes V. 74. The acceleration of a point executing a simple harmonic motion is at any time simply proportional to the displacement from the middle point , but in opposite direction , or always towards the middle point . Its maximum ...
... becomes V. 74. The acceleration of a point executing a simple harmonic motion is at any time simply proportional to the displacement from the middle point , but in opposite direction , or always towards the middle point . Its maximum ...
Page 29
... becomes OA'B ' in the second posi- tion of the figure . 92. If from the equal angles A'OB ' , AOB of these similar triangles we take the com- 0 , mon part A'OB , we have the remaining angles AOA ' , BOB ' equal , and each of them is ...
... becomes OA'B ' in the second posi- tion of the figure . 92. If from the equal angles A'OB ' , AOB of these similar triangles we take the com- 0 , mon part A'OB , we have the remaining angles AOA ' , BOB ' equal , and each of them is ...
Page 32
... become continuous curves . Hence the theorem . From this it immediately follows , that any displacement of a rigid solid , which is in directions wholly perpendicular to a fixed line , may be produced by the rolling of a cylinder fixed ...
... become continuous curves . Hence the theorem . From this it immediately follows , that any displacement of a rigid solid , which is in directions wholly perpendicular to a fixed line , may be produced by the rolling of a cylinder fixed ...
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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.