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angles base bisector bisects called centre centroid circle circumcentre circumcircle circumscribed coincide collinear complementary concurrent congruent conic considered constant construction contained corresponding curve demonstration denoted described determine diagonal diameter distance double draw drawn Edinburgh equal excentres excircle expression external FIGURE formed four Geometry given gives greater Hence incentre incircle inscribed internal intersection joining Mathematical means medians meet mid point obtained opposite sides original orthic orthocentre pairs parallel parallelogram passes perpendicular plane polar position problem produced Professor projections proof properties Proposition proved quadrilateral radii radius ratio respectively right angles sides similar Similarly situated Society spherical square straight line substance Suppose surface taken tangents temperature theorem third triangle ABC vertices volume voting
Página 50 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Página 46 - 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.
Página 13 - The perpendiculars from the vertices of a triangle on the opposite sides are concurrent.
Página 34 - Compare the area of the triangle formed by joining the centres of these squares with the area of the equilateral triangle.
Página 9 - The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles, with converse.
Página 37 - If two triangles have two sides of the one equal to two sides of the...
Página 14 - Wherefore, if the ratios &c. EXERCISES. 1. Shew that the locus of the middle points of straight lines parallel to the base of a triangle and terminated by its sides is a straight line. 2. CAB, CEB are two triangles having the angle B common and the sides CA, CE equal ; if BAE be produced to D and ED be taken a third proportional to BA , AC, then the triangle BDC is similar to the triangle BAC.
Página 6 - The straight line, joining the points of bisection of two sides of a triangle, is parallel to the base.