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" As shown on p. 84 for the cycloid, the arc of the evolute is equal to the difference of the radii of curvature at its end-points. "
A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... - Página 396
de Bartholomew Price - 1852 - 540 páginas
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Examples of the processes of the differential and integral calculus

Duncan Farquharson Gregory - 1841 - 566 páginas
...= a. 27 When a curve is the evolute of another curve, the length of its arc is best found by taking the difference of the radii of curvature of the involute, corresponding to the extremities of the arc. (8) To find the length of the evolute of the ellipse. The radius of curvature...
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Report of the Board of Education

Bombay (India : State). Board of Education - 1851 - 768 páginas
...24. Show geometrically that the normals to a curve are tangents to the evolute. 25. Also that an arc of the evolute is equal to the difference of the radii of curvature at its extremities. 26. If an ellipse and circle intersect in four points, the lines joining the points...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - 1852 - 338 páginas
...point. At a cusp it will be found that the radius of curvature vanishes. 115. The length of any arc of the evolute is equal to the difference of the radii of curvature at its extremitics. For, draw any three consecutive normals to the original curve : let C be the point...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - 1855 - 592 páginas
...normals are more or less numerous. . This property, taken in connection with the property that any arc of the evolute is equal to the difference of the radii of curvature of the involute through its extremities, enables us to construct the involute when the evolute and one point arc given....
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - 1855 - 628 páginas
...or less numerous. This property, taken in connection with the property that any arc of the evolutc is equal to the difference of the radii of curvature of the involute through its extremities, enables us to construct the involute when the evolute and one point arc given....
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Report of the Board of Education

Bombay (India : State). Board of Education - 1851 - 764 páginas
...24. Show geometrically that the normals to a curve are tangents to the evolute. 25. Also that an arc of the evolute is equal to the difference of the radii of curvature at its extremities. 26. If an ellipse and circle intersect in four points, the lines joining the points...
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A Treatise on the Stability of Ships

Sir Edward James Reed - 1885 - 414 páginas
...which he adopts is based upon the principle that the length of an arc of the evolute or " metacentric " is equal to the difference of the radii of curvature of the involute corresponding to the extremities of the arc. After having found the length of the radii of curvature (instead of the...
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A Book of Curves

Edward Harrington Lockwood - 1967 - 290 páginas
...is the centre of curvature for the original spiral at P. As shown on p. 84 for the cycloid, the arc of the evolute is equal to the difference of the radii of curvature at its end-points. The length of the new spiral from N to the pole (or as near to the pole as may be)...
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