Elements of Natural Philosophy, Volume 1 |
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Page 5
... normal ( or per- pendicular to the tangent ) to the curve PQ . And thus the evolute of PQ is a definite curve , viz . the envelop of ( or line which is touched by ) the normals drawn at every point of PQ , or , which is the same thing ...
... normal ( or per- pendicular to the tangent ) to the curve PQ . And thus the evolute of PQ is a definite curve , viz . the envelop of ( or line which is touched by ) the normals drawn at every point of PQ , or , which is the same thing ...
Page 38
... normal at the point of contact . This is pure spin- ning , and does not change the point of contact . Let it move , so that the instantaneous axis , still passing through the point of contact , is neither in , nor perpendicular to , the ...
... normal at the point of contact . This is pure spin- ning , and does not change the point of contact . Let it move , so that the instantaneous axis , still passing through the point of contact , is neither in , nor perpendicular to , the ...
Page 39
... normal sections , curvatures oppositely directed to those in others . In the latter case , the sur- face on every side of the points bends away from the same side of its tangent plane , and the curvatures of all normal sections are ...
... normal sections , curvatures oppositely directed to those in others . In the latter case , the sur- face on every side of the points bends away from the same side of its tangent plane , and the curvatures of all normal sections are ...
Page 40
... normal planes at right angles to each other , is independent of the position of these planes . If 1 - P 1 and be the maximum and minimum curvatures at any σ point , the curvature of a normal section making an angle ✪ with the normal ...
... normal planes at right angles to each other , is independent of the position of these planes . If 1 - P 1 and be the maximum and minimum curvatures at any σ point , the curvature of a normal section making an angle ✪ with the normal ...
Page 50
... normal to the surface as one of three rectangular directions of resolution . No displacement can be effected parallel to it : and the other two displacements , at right angles to each other , in the tangent plane to the surface , are ...
... normal to the surface as one of three rectangular directions of resolution . No displacement can be effected parallel to it : and the other two displacements , at right angles to each other , in the tangent plane to the surface , are ...
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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.