Principles of Modern Geometry: With Numerous Applications to Plane and Spherical Figures : and an Appendix Containing Questions for Exercise : Intended Chiefly for the Use of Junior StudentsHodges, Smith, 1862 - 227 ページ |
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多く使われている語句
anharmonic ratio arc joining arcs be drawn bisected centre of similitude chord circle touching circumscribed coincident cone conic section conjugate constant corresponding curve cut harmonically cyclic arcs diameter equal equation Euclid evident external centre find the locus fixed point foci follows four points geometrical given circle given in Art given lesser circle given line given point given right line harmonic conjugate harmonic mean harmonic pencil hyperbola inscribed involution last Article Lemma limiting points line joining locus meet middle point pair parallel Pascal's theorem pass perpendicular points of contact points of intersection pole polygon Prop properties Proposition proved radical axis radius reciprocal rectangle respect right angle segments sin AB sines sphere spherical centre spherical conic spherical ellipse spherical polygon spherical triangle square subcontrary subtended tangent arcs theorem third diagonal three given transversal vertex vertical angle
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1 ページ - 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...
69 ページ - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
211 ページ - Find the locus of a point, the square of whose distance from a given point is proportional to its distance from a given line.
51 ページ - The locus of a point from which tangents drawn to two given circles are equal...
1 ページ - 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.
67 ページ - 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.
73 ページ - The middle points of the three diagonals of a complete quadrilateral are in the same straight line.