Principles of Modern Geometry, with Numerous Applications to Plane and Spherical Figures: And an Appendix Containing Questions for Exercise

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1862 - 234 من الصفحات
 

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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 69 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
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.
الصفحة 73 - The middle points of the three diagonals of a complete quadrilateral are in the same straight line.

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