Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page 3
... reference to any independent variable t , we have d do dy dx = 1 + ( dy dx d'y - dy d'x dx2 + dy ཆུ་ Also , ds = ( dx2 + dy3 ) . Hence , if p denote the radius of curvature , so that we conclude 1 P - 1 P = do ds dx d'y - dy d'x ( dx2 + ...
... reference to any independent variable t , we have d do dy dx = 1 + ( dy dx d'y - dy d'x dx2 + dy ཆུ་ Also , ds = ( dx2 + dy3 ) . Hence , if p denote the radius of curvature , so that we conclude 1 P - 1 P = do ds dx d'y - dy d'x ( dx2 + ...
Page 10
... reference to the other , is called the Evolute . 18. It will be observed that we speak of an involute , and of the evolute , of a curve . In fact , as will be easily seen , a curve can have but one evolute , but it has an infinite ...
... reference to the other , is called the Evolute . 18. It will be observed that we speak of an involute , and of the evolute , of a curve . In fact , as will be easily seen , a curve can have but one evolute , but it has an infinite ...
Page 37
... reference to a second point B ; if B executes any other motion with refer- ence to a third point C ; and so on - the first is said to execute , with reference to the last , a movement which is the resultant of these several movements ...
... reference to a second point B ; if B executes any other motion with refer- ence to a third point C ; and so on - the first is said to execute , with reference to the last , a movement which is the resultant of these several movements ...
Page 38
... position or the middle of its range . Epoch in angular measure is the angle described on the circle of reference in the period of time defined as the epoch . harmonic The Period of a simple harmonic motion is the 38 [ 52 . PRELIMINARY .
... position or the middle of its range . Epoch in angular measure is the angle described on the circle of reference in the period of time defined as the epoch . harmonic The Period of a simple harmonic motion is the 38 [ 52 . PRELIMINARY .
Page 86
... suspended . Two co - ordinates , 0 = A'OB , and & measured in a plane per- pendicular to 40 , from a fixed plane of reference to the plane AOB , fully specify the position of the moveable body 86 [ 109 PRELIMINARY .
... suspended . Two co - ordinates , 0 = A'OB , and & measured in a plane per- pendicular to 40 , from a fixed plane of reference to the plane AOB , fully specify the position of the moveable body 86 [ 109 PRELIMINARY .
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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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