This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1912 Excerpt: ...R" are the corresponding points on a coaxal ellipsoid, OP," OQ," OR" are conjugate diameters. Ex. 4. An umbilic on an ellipsoid corresponds to an umbilic on any confocal ellipsoid. Ex. 5. P and Q are any points on a generator of a hyperboloid and P' and Q' are the corresponding points on a second hyperboloid. Prove ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1912 Excerpt: ...R" are the corresponding points on a coaxal ellipsoid, OP," OQ," OR" are conjugate diameters. Ex. 4. An umbilic on an ellipsoid corresponds to an umbilic on any confocal ellipsoid. Ex. 5. P and Q are any points on a generator of a hyperboloid and P' and Q' are the corresponding points on a second hyperboloid. Prove that P' and Q' lie on a generator, and that PQ = P'Q'. THE FOCI OF CONICOIDS. 129. '(I) The locus of a point such that the square on its distance from a given point is in a constant ratio to the rectangle contained by its distances from two fixed planes is a conicoid. The equation to the locus is of the form (x-a_y+(y-Pf+z-yf--k2(lx + my + nz +p)(l'x + m'y + n'z +p'), which represents a conicoid. 1(II) The locus of a point whose distance from a fixed point is in a constant ratio to its distance, measured parallel to a given plane, from a given line, is a conicoid. 1 That a conicoid could be generated by the method (I) was first pointed out by Salmon. The method (II) is due to MacCullagh. Choose rectangular axes so that the given plane is the xy-plane and the point of intersection of the given line and given plane is the origin. Let the fixed point be (x, 8, y) and the fixed line have equations y =--=--. The '7 I m n plane through ( rj, f) parallel to the ajy-plane meets the given line in the point, j, and therefore the distance of ( rj, ) from the line measured parallel to the given plane is given by Hence the equation to the locus is which represents a conicoid. In (I) the equation to the locus is of the form j--uv = 0, and in (II) of the form X0--(u2+v2) = 0, where and u = (), v = 0 represent planes. In either case, if S = 0 is the equation to the locus, the equation S--X0 = O represents a pair of pla...
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Add this copy of An Elementary Treatise on Coordinate Geometry of Three to cart. $22.29, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of An Elementary Treatise on Coordinate Geometry of Three to cart. $33.45, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of An Elementary Treatise on Coordinate Geometry of Three to cart. $35.34, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
Add this copy of An Elementary Treatise on Coordinate Geometry of Three to cart. $46.21, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.