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anharmonic ratio arc joining arcs be drawn base bisected centre of similitude chord circle touching cone conic section conjugate constant corresponding curve cut harmonically cyclic arcs diameter drawn cutting equal equation evident external centre find the locus fixed point foci follows four points geometrical given circle given in Art given lesser circle given line given right lines harmonic conjugate harmonic mean harmonic pencil hyperbola inscribed involution Lardner's Euclid last Article Lemma limiting points line joining locus meet middle point pair parallel pass perpendicular point of contact points of intersection polar pole polygon proof Prop properties Proposition proved radical axis radius reciprocal rectangle respect right angle sines sinj spherical centre spherical conic spherical ellipse spherical geometry spherical polygon spherical quadrilateral spherical triangle square subtended supposed tangent arcs theorem third diagonal transversal vertex vertical angle
الصفحة 1 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
الصفحة 211 - Find the locus of a point, the square of whose distance from a given point is proportional to its distance from a given line.
الصفحة 51 - The locus of a point from which tangents drawn to two given circles are equal...
الصفحة 1 - Hence, three quantities are said to be in arithmetical proportion, when the difference of the first and second is equal to the difference of the second and third.
الصفحة 67 - JL from the right angle on the hypotenuse of a rightangled A is a harmonic mean between the segments of the hypotenuse made by the point of contact of the inscribed circle. 10. If a line be cut harmonically by two Os, the locus of the foot of the _L, let fall on it from either centre, is a O, and it cuts any two positions of itself homographically (see Prop. 3, Cor. 2, Section VII.)11.