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ABCD altitude axis base bisects called centre chord circle circumference circumscribed coincide common cone construct contain Corollary cylinder Definition denote describe diagonals diameter diedral angle difference distance divided draw drawn edges equal equivalent expressed extremities faces figure fixed follows formed four given circles given plane given point given straight line greater hence homologous indefinitely inscribed intersection joining lateral less limit locus mean measure meet middle point one-half opposite sides parallel parallelogram pass perimeter perpendicular plane plane MN polar pole polyedron polygon preceding prism problem proportional PROPOSITION proved pyramid quadrilateral quantities radii radius ratio rectangle respectively right angles Scholium secant segment sides similar sphere spherical square suppose surface symmetrical taken tangent tetraedron theorem third triangle ABC unit vertex vertices volume
Page 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP
Page 46 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 115 - It follows from § 259 that if through a fixed point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 216 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 74 - An angle formed by a tangent and a chord is measured by onehalf the intercepted arc.
Page 107 - If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon AB...
Page 95 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.