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" The six straight lines. joining two and two the centres of the four circles which touch the sides of a triangle pass each through one of the vertices of the triangle. "
Proceedings of the Edinburgh Mathematical Society - Page 47
by Edinburgh Mathematical Society - 1894
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The Elements of Plane and Spherical Trigonometry

John Hind - Trigonometry - 1855 - 328 pages
...ОТ «OS В and cot .V (B -A) = - : — =3- . m sin B 53. Iff/,, d2, i/3, dt be the distances, of the centres of the four circles which touch the sides of a triangle, from that of the circumscribed circle, then d,- + ¿г' + d,' + dt' = 4K2 + 2A(r,+r2 + r3-i-) = 12/2*....
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A Book of Mathematical Problems on Subjects Included in the Cambridge Course

Joseph Wolstenholme - Mathematics - 1867 - 344 pages
...is produced to meet the circle in E : prove that AE is bisected inD. 33. The straight lines joining the centres of the four circles which touch the sides of a triangle are bisected by the circumscribed circle : also the middle point of the line joining any two of the...
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Mathematical Questions and Solutions, from the "Educational Times ..., Volume 7

W. J. C. Miller - Mathematics - 1867
...I. Solution by the PBOPOSKB. 1. To show that the foci of the two imaginary parabolas drawn through the centres of the four circles which touch the sides of a given triangle ABC coincide with the circular points at infinity. The two parabolas which pass through...
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Conic Sections, Treated Geometrically

William Henry Besant - Conic sections - 1869 - 302 pages
...be of constant magnitude, the locus of P is a rectangular hyperbola. 19. Every conic passing through the centres of the four circles which touch the sides of a triangle, is a rectangular hyperbola. 20. Ellipses are inscribed in a given parallelogram, shew that their foci...
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The Geometry of Conics, Part 1

Charles Taylor - Conic sections - 1872 - 121 pages
...common points of two rectangular hyperbolas is itself a rectangular hyperbola. 206. A conic through the centres of the four circles which touch the sides of a triangle is a rectangular hyperbola, and its centre is on the circumscribing circle. 207. Any chord of a rectangular...
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The Cone and Its Sections Treated Geometrically

S. A. Renshaw - Conic sections - 1875 - 148 pages
...circle circumscribing CTQ touches the ordinate QV conjugate to CP. 101. — Every Conic passing through the centres of the four circles which touch the sides of a triangle is a rectangular Hyperbola. 102. — The foci of Ellipses inscribed in a given parallelogram lie on...
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Mathematical Problems on the First and Second Divisions of the Schedule of ...

Joseph Wolstenholme - Mathematics - 1878 - 536 pages
...is produced to meet the circle in E : prove that AE is bisected in D. 56. The straight lines joining the centres of the four circles which touch the sides of a triangle are bisected by the circumscribed circle ; also the middle point of the line joining any two of the...
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The Elementary Geometry of Conics

Charles Taylor - Conic sections - 1880 - 104 pages
...common points of two rectangular hyperbolas is itself a rectangular hyperbola. 216. A conic through the centres of the four circles which touch the sides of a triangle is a rectangular hyperbola, and its centre is on the circumscribing circle. 217. On opposite sides...
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An Introduction to the Ancient and Modern Geometry of Conics: Being a ...

Charles Taylor - Conic sections - 1881 - 384 pages
...or supplementary to the angles which they subtend at the centre. • i 477. If a conic pass through the centres of the four circles which touch the sides of a triangle it must be a rectangular hyperbola, and its centre will lie on the circumscribed circle of the triangle....
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The Doctrine of Germs, Or, The Integration of Certain Partial Differential ...

Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...equal or supplementary to the angles which they subtend at the centre. 477. If a conic pass through the centres of the four circles which touch the sides of a triangle it must be a rectangular hyperbola, and its centre will lie on the circumscribed circle of the triangle....
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