Proceedings of the Edinburgh Mathematical SocietyScottish Academic Press, 1893 |
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Resultat 1-5 av 22
Side 23
... inscribed and escribed circles is equal to three times the diameter of the circumscribing circle . A geometrical solution is given in the Diary for 1854 , p . 56 , where the following results are established : and hence MI R - r MIR + ...
... inscribed and escribed circles is equal to three times the diameter of the circumscribing circle . A geometrical solution is given in the Diary for 1854 , p . 56 , where the following results are established : and hence MI R - r MIR + ...
Side 24
... inscribed and escribed to triangles drawn according to a given law . Or the theorem may be expressed more fully : If the radical centres of the inscribed and escribed circles of any triangle be taken , and circles be inscribed and ...
... inscribed and escribed to triangles drawn according to a given law . Or the theorem may be expressed more fully : If the radical centres of the inscribed and escribed circles of any triangle be taken , and circles be inscribed and ...
Side 25
... inscribed in a conic , and if through each vertex there be drawn a transversal respectively conjugate to the opposite side , then ( 1 ) These three transversals will intersect in the same point O. ( 2 ) The middle points of the lines OA ...
... inscribed in a conic , and if through each vertex there be drawn a transversal respectively conjugate to the opposite side , then ( 1 ) These three transversals will intersect in the same point O. ( 2 ) The middle points of the lines OA ...
Side 26
... inscribed circle is given by the equation Hence d2 = 2r2 - 4R2cos Acos BcosC . D2 - 2d2 R2 - 4r2 . = ( 3 ) It follows that if the two circles be fixed , the locus of the intersection of perpendiculars is a circle whose radius is R - 2r ...
... inscribed circle is given by the equation Hence d2 = 2r2 - 4R2cos Acos BcosC . D2 - 2d2 R2 - 4r2 . = ( 3 ) It follows that if the two circles be fixed , the locus of the intersection of perpendiculars is a circle whose radius is R - 2r ...
Side 27
... inscribed and escribed circles of a plane triangle , are all touched by another circle . See also Lachlan's Elementary Treatise on Modern Pure Geo- metry , pp . 251-7 ( 1893 ) . There are other demonstrations of Feuerbach's theorem ...
... inscribed and escribed circles of a plane triangle , are all touched by another circle . See also Lachlan's Elementary Treatise on Modern Pure Geo- metry , pp . 251-7 ( 1893 ) . There are other demonstrations of Feuerbach's theorem ...
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Vanlige uttrykk og setninger
A₁ algebra angle B.Sc B₁ bisects centre centroid circumcentre circumcircle College concyclic cône conic convergence coordonnées corresponding D.Sc denote diameter Dirichlet's drawn Edinburgh elastic equal equation Euler excircles expression finite Fourier series function Gentleman's Diary geometrical George Watson's College given straight line Glasgow h₁ h₂ Hamilton's Heaviside Hence incentre incircle infinite number inscribed circle integral intersection isogonal isogonally conjugate l'équation Lady's and Gentleman's layer Lemoine locus m₁ Mathématiques memoir method mid point n₁ nine-point circle notation orthocentre parallel pedal triangle plane point of BC Professor Professor Gibbs proof quantities quaternion r₁ r₂ radial stress radius reciprocal respectively scalar solution square suppose surface symmedian symmedian point tangent theorem touches triangle ABC trigonometric series trilinears uniform convergence Vaß vector analysis versor vertices
Populære avsnitt
Side 5 - To draw a straight line perpendicular to a given straight line from a given point without it . 26 4.
Side 7 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 14 - ABC be the given rectilineal figure, to which the figure to be described is required to be similar, and D that to which it must be equal. It is required to describe a rectilineal figure similar to ABC, and equal to D. Upon the straight line BC describe (cor.
Side 166 - Review is to be conducted, and it may be of interest to the members of the Society to have these presented in outline.
Side 9 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Side 9 - SEGMEBTT of a circle being given to describe the circle of which it is the segment.* Let ABC be the given segment of a circle ; it is required to describe the circle of which it is the segment.
Side 60 - must be ranked as one of the retarders of quaternion progress, in virtue of his pamphlet on Vector Analysis; a sort of hermaphrodite monster, compounded of the notations of Hamilton and Grassmann.
Side 76 - ... the sum of the squares on half the line and on the line between the points of section*.
Side 24 - The circle which passes through the middle points of the sides of a triangle touches the four circles which touch the three sides.
Side 67 - Va/3 than any which depend on the definition of a quaternion, will appear in a strong light if we try to extend our formulae to space of four or more dimensions. It will not be claimed that the notions of quaternions will apply to such a space, except indeed in such a limited and artificial manner as to rob them of their value as a system of geometrical algebra.