 | George Salmon - Conic sections - 1852 - 329 pages
...envelopes, is that of the evolutes of curves. We have defined the evolute of a curve (Conies, p. 329) as the locus of the centres of curvature of the curve...the locus of all the centres of curvature must be the same as the envelope of all the normals. We add the investigation of the evolutes of the conic... | |
 | George Salmon - Conic sections - 1855 - 376 pages
...[l>fi"(aa + cy - 6/3)} + \/ (cy"(«a + 6/3 - cy)} = 0, the equation of a conic touching the lines joining the middle points of the sides of the triangle formed' by the given tangents. If the conic touch a fourth given line, Aa + B/3 + Cy = 0, we must (p. 237) have the... | |
 | William Walton - Mechanics - 1858 - 294 pages
...jointed together at their extremities, are laid on a smooth horizontal table; and forces are applied at the middle points of the sides of the triangle formed by the rods, respectively perpendicular to them : to shew that, if these forces produce equilibrium, the strains... | |
 | Robert Henry Wright - Coordinates, Trilinear - 1865 - 174 pages
...6/3)} + V{C7* (aa + 6/3 - с7)} = 0, the equation indicating that the conic touches the lines joining the middle points of the sides of the triangle formed by the given tangents. Let Aa + Bß + Су = 0 be a fourth line. The locue of the center will be a right line... | |
 | Norman Macleod Ferrers - Conic sections - 1866 - 208 pages
...centres, -2gh (z+xy) (x+yz)- 2hf(x + yz) (z + x -y) a conic touching the three straight lines which join the middle points of the sides of the triangle formed by the three given tangents. Its asymptotes are parallel to those of the curve /V +зУ + hV - 2ghyz - 2hfzx... | |
 | George Salmon - Curves, Algebraic - 1879 - 424 pages
...points /, J, and wherever, in our theorems lines at right angles occur, substitute lines cutting I, J harmonically. One of the most important and the...the locus of all the centres of curvature must be the same as the envelope of all the normals. Ex. 1 . To find the evplute of j* + ^ = 1. The normal... | |
 | George Salmon - Curves, Algebraic - 1879 - 424 pages
...class of envelopes is that of the evolutes of curves. We have defined the evolute of a curve (Conics, Art. 248) as the locus of the centres of curvature...the locus of all the centres of curvature must be the same as the envelope of all the normals. ; X* V* Ex. 1. To find the evolute of -, + IT = 1. o*... | |
 | George Albert Wentworth - Geometry, Analytic - 1886 - 346 pages
...the origin to those points of the given line whose ordinates are — 1 and 19. 49. The lines joining the middle points of the sides of the triangle formed by the lines x — 5y-f-ll=0, I1x-\-Gy — 1=0, 50. Find the area of the quadrilateral whose vertices are... | |
 | Edward John Routh - Elastic rods and wires - 1891 - 428 pages
...jointed together at their extremities, are laid on a smooth horizontal table ; and forces are applied at the middle points of the sides of the triangle formed by the rods, and respectively perpendicular to them. Show that, if these forces produce equilibrium, the strains... | |
 | George Albert Wentworth - 1894 - 362 pages
...and its altitude is —^; and therefore its area is 49. Find the area included by the lines joining the middle points of the sides of the triangle formed by the lines x — 5y + 11 = 0, Пx + 6у — 1 = 0, x + y + 4 = 0. The intersection of x — 5 у +ll = 0... | |
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Art. 248) as the locus of the centres of curvature of the curve ; but the evolute may also be defined as the envelope of all the normals of the curve. For the circle of curvature is that which passes through three consecutive points of the curve, and... 
