| Bombay (India : State). Board of Education - Education - 1851 - 768 pages
...inflexion. 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 of intersection... | |
| George Salmon - Conic sections - 1852 - 338 pages
...sign, and that as we pass such a point the concavity of the curve changes to convexity, and vice versd **(see fig. p. 35). At a double point the radius of...at its extremities. For, draw any three consecutive** norinals to the original curve : let C be the point of intersection of the first and second, C' of... | |
| Bartholomew Price - Calculus - 1852
...with straight lines, whence they are said to be rectifiable ; for, from what has preceded, the length **of the evolute is equal to the difference of the radii of curvature** of the involute corresponding to its two extremities. Of this we subjoin some examples : Ex. 1. To... | |
| Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...the 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... | |
| Bombay (India : State). Board of Education - Education - 1851 - 764 pages
...inflexion. 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 of intersection... | |
| George Salmon, Arthur Cayley - Curves, Algebraic - 1873 - 379 pages
...own curvature at the point. At a cusp it will be found that the radius of curvature vanishes. 103. **The length of any arc of the evolute is equal to the...three consecutive normals to the original curve : let** G be the point of intersection of the first and second, G' of the second and third ; then since, ultimately,... | |
| Donald Francis Campbell - Calculus - 1904 - 394 pages
...establish two theorems. Theorem I. Every normal to the involute is tangent to the evolute. Theorem II. **The length of any arc of the evolute is equal to the difference** between the lengths of the radii of curvature of the involute which pass through the extremities of... | |
| Edward Harrington Lockwood - Curves - 1967 - 286 pages
...TV 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) is,... | |
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