## Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |

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**Hence**curve . of a plane dy 0 = tan - 1 ; dx and , by differentiation with reference to any independent variable t , we have de . = Also , dy d dx dx d'y - dy d'x ( dy dx2 + dy3 1 + ds = ( dx2 + dy3 ) 3 .**Hence**, if p denote the radius ... Page 15

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**Hence**the resultant of velocities represented by the sides of any closed polygon whatever , whether in one plane or not , taken all in the same order , is zero .**Hence**also the resultant of velocities represented by all the sides of a ... Page 17

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**Hence**dv = α . dt It is useful to observe that we may also write ( by changing the independent variable ) dv ds Accelera- tion a = dv ds ds dt = v Since vπ ds dt d's we have a = dt , and it is evident from similar reasoning that the ... Page 18

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**Hence**f ƒ sin 9 = 2 . 1 / dx d2x Again , cos 0 dy d'y dz dz = + + = vfdt dt dt dt dt dt2 ds d's vfilt filt d's**Hence**fcos 0 d's = and therefore dt2 and compo- Resolution 30. The whole acceleration in any direction is the sum of sition ... Page 24

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**Hence**the second part of the proposition . We have d'x dt = P d'y dts = Py d'z 2 = P dts the fixed point being the origin , and P being some function of x , y , z ; in nature a function of r only .**Hence**d3y d2x OC -Y- dt * dt = = 0 ...### Contents

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### Common terms and phrases

acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф

### Popular passages

Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.