| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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.... | |
| 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... | |
| 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... | |
| 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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