Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page 55
... quantities . rc dx ‚ a2 + x2 , less than F ( 3 ) a Its value is and greater than F ( 2 ) [ dx ‚ a2 + = x2 if z and z ' denote the values of x , either equal to or intermediate between the limits c and c ' , for which F ( x ) is greatest ...
... quantities . rc dx ‚ a2 + x2 , less than F ( 3 ) a Its value is and greater than F ( 2 ) [ dx ‚ a2 + = x2 if z and z ' denote the values of x , either equal to or intermediate between the limits c and c ' , for which F ( x ) is greatest ...
Page 64
... quantities , any point whose displacement is of the second order of small quantities is to be considered as rigorously at rest . Hence , for instance , if a body revolve through an angle of the first order of small quantities about an ...
... quantities , any point whose displacement is of the second order of small quantities is to be considered as rigorously at rest . Hence , for instance , if a body revolve through an angle of the first order of small quantities about an ...
Page 65
... quantities may be with rigorous accuracy neglected . This principle is of very great use , as we shall find in the sequel ; its applications are of constant occurrence . A plane figure has given angular velocities about given axes ...
... quantities may be with rigorous accuracy neglected . This principle is of very great use , as we shall find in the sequel ; its applications are of constant occurrence . A plane figure has given angular velocities about given axes ...
Page 115
... quantities which agree perfectly with the three sides and the three angles of a certain spherical triangle . A corresponding anticlastic trigonometry exists , al- though we are not aware that it has hitherto been noticed , for any ...
... quantities which agree perfectly with the three sides and the three angles of a certain spherical triangle . A corresponding anticlastic trigonometry exists , al- though we are not aware that it has hitherto been noticed , for any ...
Page 127
... quantities , of absolutely arbi- trary values , the same for all values of x , y , z . They are , of [ Xx ] , [ Yx ] , [ Zx ] denote the three final co - ordinates of a point originally at unit distance along OX , from 0 . course ...
... quantities , of absolutely arbi- trary values , the same for all values of x , y , z . They are , of [ Xx ] , [ Yx ] , [ Zx ] denote the three final co - ordinates of a point originally at unit distance along OX , from 0 . course ...
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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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