Treatise on Natural Philosophy, Volume 1, Issue 1At the University Press, 1879 - Mechanics, Analytic |
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Page 3
... Hence curve . of a plane dy 0 = tan - 1 ; dx and , by differentiation with reference to any independent variable t , we have do Also , = ( dy d dx 1 + dy dx d'y - dy d3x dx2 + dy2 dx ds = ( dx2 + dy3 ) 3 . Hence , if p denote the radius ...
... Hence curve . of a plane dy 0 = tan - 1 ; dx and , by differentiation with reference to any independent variable t , we have do Also , = ( dy d dx 1 + dy dx d'y - dy d3x dx2 + dy2 dx ds = ( dx2 + dy3 ) 3 . Hence , if p denote the radius ...
Page 15
... 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 ...
... 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
... Hence dv dt = α . It is useful to observe that we may also write ( by changing the independent variable ) dv ds Accelera- tion α = dv ds ds dt = v Since v = ds dt d28 we have a = dt and it is evident from similar reasoning that the ...
... Hence dv dt = α . It is useful to observe that we may also write ( by changing the independent variable ) dv ds Accelera- tion α = dv ds ds dt = v Since v = ds dt d28 we have a = dt and it is evident from similar reasoning that the ...
Page 18
... Hence f ƒ sin 0 = 2 v2 P Again , cos Ꮎ 1 ( dx dx dy d'y , dz d2z \ ds d's d's = + + of dt dtdt di dt dt dt2 d's = = vfdt3 - filt2 * Hence fcos 0 = = and therefore " dt2 Resolution and compo- 30. The whole acceleration in any direction ...
... Hence f ƒ sin 0 = 2 v2 P Again , cos Ꮎ 1 ( dx dx dy d'y , dz d2z \ ds d's d's = + + of dt dtdt di dt dt dt2 d's = = vfdt3 - filt2 * Hence fcos 0 = = and therefore " dt2 Resolution and compo- 30. The whole acceleration in any direction ...
Page 24
... Hence the second part of the proposition . d'x We have XC = P d'y = dt Py d'z 2 P = g dt g0 dt the fixed point being the origin , and P being some function of x , y , z ; in nature a function of r only . Hence d'y at d2x -Yats = = 0 ...
... Hence the second part of the proposition . d'x We have XC = P d'y = dt Py d'z 2 P = g dt g0 dt the fixed point being the origin , and P being some function of x , y , z ; in nature a function of r only . Hence d'y at d2x -Yats = = 0 ...
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Common terms and phrases
acceleration according action actual altered amount angle angular velocity application axes axis becomes body called Cambridge centre circle co-ordinates coefficients complete component condition configuration consider constant corresponding course curvature curve denote described determined differential direction displacement distance edition equal equations equilibrium Example expression finite fixed force function give given harmonic Hence inertia infinitely small instant integral kinetic energy length less mass matter mean measured motion moving natural negative observations parallel particle particular path period perpendicular plane position present principle problem produced proved quantity radius reference relative remain remarkable respectively resultant rigid rolling roots rotation round side simple solution space spherical strain suppose surface tangent theorem tion turn unit University values whole
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.