Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page 1
... whole of this our first chapter ; which will form , as it were , the Geometry of our subject , embracing what can be observed or concluded with re- gard to actual motions , as long as the cause is not sought . 2. In this category we ...
... whole of this our first chapter ; which will form , as it were , the Geometry of our subject , embracing what can be observed or concluded with re- gard to actual motions , as long as the cause is not sought . 2. In this category we ...
Page 7
... whole change of direction of Integral an arc of a plane curve , is the angle through which the tangent of a curve has turned as we pass from one extremity to the other . The $ 136 ) . average curvature of any portion is its whole ...
... whole change of direction of Integral an arc of a plane curve , is the angle through which the tangent of a curve has turned as we pass from one extremity to the other . The $ 136 ) . average curvature of any portion is its whole ...
Page 8
... whole torsion , or integral of tortuosity . From this and § 12 it follows that the curvature of this plane curve at any point , or , which is the same , the projection of the curvature of the spherical curve on a tangent plane of the ...
... whole torsion , or integral of tortuosity . From this and § 12 it follows that the curvature of this plane curve at any point , or , which is the same , the projection of the curvature of the spherical curve on a tangent plane of the ...
Page 12
... second , A hundred and so on , give nearer and nearer approximations to the velocity at the beginning of the first second . The whole foundation of the differential calculus is , in fact , contained in 12 [ 23 . PRELIMINARY .
... second , A hundred and so on , give nearer and nearer approximations to the velocity at the beginning of the first second . The whole foundation of the differential calculus is , in fact , contained in 12 [ 23 . PRELIMINARY .
Page 13
... whole velocity and the steepness of the incline , or we may express the same ideas thus -- the train is moving simultaneously northward , eastward , and upward- and the motion as to amount and direction will be completely known if we ...
... whole velocity and the steepness of the incline , or we may express the same ideas thus -- the train is moving simultaneously northward , eastward , and upward- and the motion as to amount and direction will be completely known if we ...
Contents
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
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