Treatise on Natural Philosophy, Part 1University Press, 1886 - Calculators |
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Page x
... Tangent - Surface on Surface - Both traces prescribed ; one degree of freedom Twist - Estimation of Integral Twist in a Plane Curve ; in a Curve consisting of plane portions in different Planes ; in a continuously Tortuous Curve ...
... Tangent - Surface on Surface - Both traces prescribed ; one degree of freedom Twist - Estimation of Integral Twist in a Plane Curve ; in a Curve consisting of plane portions in different Planes ; in a continuously Tortuous Curve ...
Page 2
... tangent drawn to its path , if the path be a curve , or the path itself if a straight line . 5. If the path be not ... tangents drawn to a circle , and radii to the points of contact . The angle between the tangents is the change of ...
... tangent drawn to its path , if the path be a curve , or the path itself if a straight line . 5. If the path be not ... tangents drawn to a circle , and radii to the points of contact . The angle between the tangents is the change of ...
Page 3
... tangent , at any point x , y , to OX . dy 0 = tan - 1 dx ; denote Curvature of a plane Hence curve . and , by differentiation with reference to any independent variable t , we have Also , d dy dx ---- de dy 2 1 + dx dx d'y - dy dx dx2 + ...
... tangent , at any point x , y , to OX . dy 0 = tan - 1 dx ; denote Curvature of a plane Hence curve . and , by differentiation with reference to any independent variable t , we have Also , d dy dx ---- de dy 2 1 + dx dx d'y - dy dx dx2 + ...
Page 4
... tangent to the curve . 9. Thus , as we proceed along such a curve , the curvature in general varies ; and , at the same time , the plane in which the curvature lies is turning about the tangent to the curve . The tortuosity is therefore ...
... tangent to the curve . 9. Thus , as we proceed along such a curve , the curvature in general varies ; and , at the same time , the plane in which the curvature lies is turning about the tangent to the curve . The tortuosity is therefore ...
Page 5
... tangents to a curve at points separated by an arc of length ds . We have 1 бө 2 sin 80 sin 80 = P = Ss when ds is infinitely small ; and in the same limit . ( 7 ) dz n = ; ds dz c ' - c = d . ( 8 ) ; ds & c . .... ( 9 ) ; dx 1 = m = ds ...
... tangents to a curve at points separated by an arc of length ds . We have 1 бө 2 sin 80 sin 80 = P = Ss when ds is infinitely small ; and in the same limit . ( 7 ) dz n = ; ds dz c ' - c = d . ( 8 ) ; ds & c . .... ( 9 ) ; dx 1 = m = ds ...
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Common terms and phrases
acceleration action altered angular velocity anticlastic application B₁ Cambridge centre of inertia change of direction circle co-ordinates coefficients component condition configuration constant corresponding curvature curve cycloidal cylinder degrees of freedom Demy 8vo denote diagram differential equation direction cosines distance dt dt dx dy dy dy dy dz ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed fluid force function geodetic geometrical given gyrostatic Hence infinitely small initial integral kinetic energy Laplace's equation length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes quantity radius ratio rectangular right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions simple shear solution spherical harmonic spherical surface strain suppose synclastic tangent plane theorem tion twist values whole x₁ y₁ αξ λ² аф