ISBN: 1236337107

[EAN: 9781236337108], Neubuch, D. BIDDLE,HISTORY, This item is printed on demand. Paperback. This historic book may have numerous typos and missing text. Purchasers can download a free sc… Plus…

[EAN: 9781236337108], Neubuch, D. BIDDLE,HISTORY, This item is printed on demand. Paperback. 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. 1865 Excerpt: . . . is equivalent to the following theorem. The length (k) of the normal to an ellipse, from the curve to the point where it meets the minor axis, is e1 (or a: c) times the distance of this point from the focus. This can be readily proved from Taylors Conies, p. 60, or Salmons Conies, p. 164. Moreover the fixed point P is obviously one o f the two points inverse to each other with respect to both circles, and may, from this property, be easily determined. See Tovvnsends Modern Geometry, Art. 188, Cor. 1 and 2; Art. 155, Cor. 2--Editob. 1519 (Proposed by F. D. Thomson, M. A. )--ABC is a triangle having the three real points (P, Q, R) of inflexion of a cubic on the sides BC, CA, AH respectively, each of which also passes through two imaginary points of inflexion. The tangents at Q and R meet in I), those at R and P in E, and those at P and Q in F. Show that AD, BE, CF meet in a point which is fixed for all the cubics having the same nine points of inflexion. I. Solution by Professor Ceemona, of Bologna. The connectors AD, BE, CF are concurrent, since, by construction, ABC and DEF are coaxial triangles. Further, these connectors are the respective harmonic polars (see Salmons Higher Plane Curves, p. 140, or Cremonas Teoria Geometrica delle Curve Piane, p. 113) of P, Q, R, not only with respect tuthc cubic whose stationary tangents are EFP, FDQ, DER, but with rrspeot to every cubic having the same nine points of inflexion; hence the invariability of their point of concurrence. The latter, in fact, is the pole of the line PQ It with respect to every cubic of the pencil, since the harmonic polars are constituent parts of the polar conies of P, Q, It, II. Solution by Mr. W. K. Cliffobd; Mr. J. Wilson; and the Pboposbb. Taking ABC for triangle of referenc. . . This item ships from La Vergne,TN.<

2012, ISBN: 1236337107

[EAN: 9781236337108], Neubuch, [PU: Not Avail, United States], Brand New Book ***** Print on Demand *****. This historic book may have numerous typos and missing text. Purchasers can down… Plus…

[EAN: 9781236337108], Neubuch, [PU: Not Avail, United States], Brand New Book ***** Print on Demand *****. 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. 1865 Excerpt: .is equivalent to the following theorem. The length (k) of the normal to an ellipse, from the curve to the point where it meets the minor axis, is e 1 (or a: c) times the distance of this point from the focus. This can be readily proved from Taylor s Conies, p. 60, or Salmon s Conies, p. 164. Moreover the fixed point P is obviously one o f the two points inverse to each other with respect to both circles, and may, from this property, be easily determined. See Tovvnsend s Modern Geometry, Art. 188, Cor. 1 and 2; Art. 155, Cor. 2--Editob. 1519 (Proposed by F. D. Thomson, M.A.)--ABC is a triangle having the three real points (P, Q, R) of inflexion of a cubic on the sides BC, CA, AH respectively, each of which also passes through two imaginary points of inflexion. The tangents at Q and R meet in I), those at R and P in E, and those at P and Q in F. Show that AD, BE, CF meet in a point which is fixed for all the cubics having the same nine points of inflexion. I. Solution by Professor Ceemona, of Bologna. The connectors AD, BE, CF are concurrent, since, by construction, ABC and DEF are coaxial triangles. Further, these connectors are the respective harmonic polars (see Salmon s Higher Plane Curves, p. 140, or Cremona s Teoria Geometrica delle Curve Piane, p. 113) of P, Q, R, not only with respect tuthc cubic whose stationary tangents are EFP, FDQ, DER, but with rrspeot to every cubic having the same nine points of inflexion; hence the invariability of their point of concurrence. The latter, in fact, is the pole of the line PQ It with respect to every cubic of the pencil, since the harmonic polars are constituent parts of the polar conies of P, Q, It, II. Solution by Mr. W. K. Cliffobd; Mr. J. Wilson; and the Pboposbb. Taking ABC for triangle of referenc.<

2012, ISBN: 1236337107

[EAN: 9781236337108], Neubuch, [PU: Not Avail, United States], Brand New Book ***** Print on Demand *****.This historic book may have numerous typos and missing text. Purchasers can downl… Plus…

[EAN: 9781236337108], Neubuch, [PU: Not Avail, United States], Brand New Book ***** Print on Demand *****.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. 1865 Excerpt: .is equivalent to the following theorem. The length (k) of the normal to an ellipse, from the curve to the point where it meets the minor axis, is e 1 (or a: c) times the distance of this point from the focus. This can be readily proved from Taylor s Conies, p. 60, or Salmon s Conies, p. 164. Moreover the fixed point P is obviously one o f the two points inverse to each other with respect to both circles, and may, from this property, be easily determined. See Tovvnsend s Modern Geometry, Art. 188, Cor. 1 and 2; Art. 155, Cor. 2--Editob. 1519 (Proposed by F. D. Thomson, M.A.)--ABC is a triangle having the three real points (P, Q, R) of inflexion of a cubic on the sides BC, CA, AH respectively, each of which also passes through two imaginary points of inflexion. The tangents at Q and R meet in I), those at R and P in E, and those at P and Q in F. Show that AD, BE, CF meet in a point which is fixed for all the cubics having the same nine points of inflexion. I. Solution by Professor Ceemona, of Bologna. The connectors AD, BE, CF are concurrent, since, by construction, ABC and DEF are coaxial triangles. Further, these connectors are the respective harmonic polars (see Salmon s Higher Plane Curves, p. 140, or Cremona s Teoria Geometrica delle Curve Piane, p. 113) of P, Q, R, not only with respect tuthc cubic whose stationary tangents are EFP, FDQ, DER, but with rrspeot to every cubic having the same nine points of inflexion; hence the invariability of their point of concurrence. The latter, in fact, is the pole of the line PQ It with respect to every cubic of the pencil, since the harmonic polars are constituent parts of the polar conies of P, Q, It, II. Solution by Mr. W. K. Cliffobd; Mr. J. Wilson; and the Pboposbb. Taking ABC for triangle of referenc.<