Mathematical Questions and Solutions, from the "Educational Times.", Volum 3F. Hodgson, 1865 |
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asymptotes axes bisecting bisectors centre Ceva's theorem chord circumscribed circle circumscribing coefficients conics which pass connectors coordinates corresponding cos² cosec Cr+1 Crelle's Journal critical conic curve denote determined diameter double point draw drawn ellipse envelope equal equation F. D. THOMSON FITZGERALD fixed points given angle given in position given line given triangle harmonic conjugate hence homographic hyperbola inscribed intersection involution line at infinity line joining locus meet middle points nine-point circle parabola parallel perpen perpendiculars plane points of contact polar Proposed prove quadric quadrilateral radius respectively right angles segments semicircle sin² square straight line subtends tan² tangent tetrahedron theorem touch triangle ABC triangle of reference trilinear trilinear coordinates vertices whence
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Side 16 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Side 41 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Side v - There are n points in a plane, no three of which are in the same straight line with the exception of p, which are all in the same straight line; find the number of lines which result from joining them.
Side 71 - CE is equal to the difference of the segments of the base made by the perpendicular.
Side xii - Construct a triangle, having given the base, tho vertical angle, and the length of the straight line drawn from the vertex to the base bisecting the vertical angle. 551. A, B, C are three given points in the circumference of a given circle : find a point P such that if AP, BP, CP meet the circumference at D, E, F respectively, the arcs DE, EF may be equal to given arcs. 552. Find...
Side xv - If from the intersection of the diagonals of a quadrilateral inscribed in a circle perpendiculars be...
Side 63 - Cc in r; and so on. Prove that, after going twice round the triangle in this way, we always come back to the same point. Show that the theorem is its own reciprocal. Find the analogous properties of a skew quadrilateral in space, and of a polygon of n sides in a plane. Solution by PBOFESSOE CAYLEY.
Side 23 - Let nCr denote the number of combinations of n things taken r at a time.
Side 90 - A-sin2 o) = &c. ; and its quasi-reciprocal and polar, cos b cos c, cos b, cos c cos a, cos c cos a, cos c cos a, cos b, cos a cos...
Side 8 - PROBLEM VIII. It is required to Investigate a Theorem, by means of which, Spherical Triangles, whose Sides are Small compared with the radius, may be solved by the rules for Plane Trigonometry, without considering the Chords of the respective Arcs or Sides.