Elements of Natural Philosophy, Volume 1 |
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Page 29
... amount of the angle of rotation . 93. The lines equidistant from A and A ' , and from B and B , are parallel if AB is parallel to A'B ′ ; and therefore the construction fails , the point O being infinitely distant , and the theorem ...
... amount of the angle of rotation . 93. The lines equidistant from A and A ' , and from B and B , are parallel if AB is parallel to A'B ′ ; and therefore the construction fails , the point O being infinitely distant , and the theorem ...
Page 30
... 91 gives us at once the point 0 and the amount of rotation about it which singly gives the same effect as those about A and B in succession . But there is one case of 4 B ' exception , viz . when the rotations 30 PRELIMINARY .
... 91 gives us at once the point 0 and the amount of rotation about it which singly gives the same effect as those about A and B in succession . But there is one case of 4 B ' exception , viz . when the rotations 30 PRELIMINARY .
Page 31
... amount and in opposite directions . In this case A'B ' is evidently parallel to AB , and therefore the compound ... amounts and opposite directions , compound one of them with the given rotation by § 98 , and then compound the other with ...
... amount and in opposite directions . In this case A'B ' is evidently parallel to AB , and therefore the compound ... amounts and opposite directions , compound one of them with the given rotation by § 98 , and then compound the other with ...
Page 34
... amount of rotation about a definite axis . And hence , also , successive or simul- taneous rotations about any number of axes through the fixed point may be compounded into one such rotation . 2 X 6 107. Let OA , OB be two 34 PRELIMINARY .
... amount of rotation about a definite axis . And hence , also , successive or simul- taneous rotations about any number of axes through the fixed point may be compounded into one such rotation . 2 X 6 107. Let OA , OB be two 34 PRELIMINARY .
Page 35
... amounts of these displacements will be w , Iẞ.T and wIa.T. The point I , and therefore every point in the line OI , will be at rest during the interval 7 if the sum of these displacements is zero — i . e . if w1.IB = w.Ia . ----- 10 B Ρ ...
... amounts of these displacements will be w , Iẞ.T and wIa.T. The point I , and therefore every point in the line OI , will be at rest during the interval 7 if the sum of these displacements is zero — i . e . if w1.IB = w.Ia . ----- 10 B Ρ ...
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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.