Elements of Natural Philosophy, Volume 1 |
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Page 2
... Curvature . To exemplify this , suppose P T U two tangents PT , QU , drawn to a circle , and radii OP , OQ , to the ... 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 P T U two tangents PT , QU , drawn to a circle , and radii OP , OQ , to the ... 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 1 . 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 1 . 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 co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point 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 normal section P₁ P₂ parallel parallelogram of forces particle path pendulum perpendicular plane perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular 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 theorem theory tion torsion uniform unit vertical whole wire