Elements of Natural Philosophy, Volume 1 |
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Page 2
... Curvature . To exemplify this , suppose two tangents PT , QU , drawn to a circle , and radii OP , OQ , to the points ... curvature . Hence the cur- vature of a circle is inversely as its radius , and is measured , in terms of the proper ...
... Curvature . To exemplify this , suppose two tangents PT , QU , drawn to a circle , and radii OP , OQ , to the points ... curvature . Hence the cur- vature of a circle is inversely as its radius , and is measured , in terms of the proper ...
Page 3
... curvature , in the other a gauche polygon . The term ' curve of double curvature ' is a very bad one , and , though in very general use , is , we hope , not inera- dicable . The fact is , that there are not two curvatures , but only a ...
... curvature , in the other a gauche polygon . The term ' curve of double curvature ' is a very bad one , and , though in very general use , is , we hope , not inera- dicable . The fact is , that there are not two curvatures , but only a ...
Page 5
... of the centres of the circles which have at each point the same tangent and curvature as the curve PQ . And we may merely mention , as an obvious result of the B զ mode of tracing , that the arc qp is equal KINEMATICS . 5.
... of the centres of the circles which have at each point the same tangent and curvature as the curve PQ . And we may merely mention , as an obvious result of the B զ mode of tracing , that the arc qp is equal KINEMATICS . 5.
Page 10
... curvature ( perpendicular therefore to the direction of mo- tion ) , whose magnitude is proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only ...
... curvature ( perpendicular therefore to the direction of mo- tion ) , whose magnitude is proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only ...
Page 17
... curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely as the square of the ...
... curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely as the square of the ...
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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.