Overview

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1889 Excerpt: ... are the point-circles of this system: first is the origin, which corresponds to the circle of infinite radius with centre at B, and then the point C, --, corresponding to the circle of b radius zero. All the circles of this system are conjugate with respect to these two points, which are two double points of the homographic transformation Before going farther we shall demonstrate the following geometrical theorem: Having given a circumference and n points, A, B, C, ..., L, upon this circumference which are so disposed that on making an inversion, taking for the pole a point O of the plane, t/ie corresponding points A', ', ..., L' are the vertices of a regular polygon, if 0' is the conjugate point to 0 with respect to the circumference, all the points of the circumference described upon 00' as a diameter and perpendicular to the plane of the figure will possess the same property as the point 0. Let S be a point of this circumference; then, from an elementary property of the inversion, OA OB Each of the ratios, is constant, and so the same is true of A B the ratio If the polygon A'B'C'D'E'F' has its sides equal, the same will be true of the polygon ABCDE. Q. E. D. i Returning now to the proposed question, consider the circumference described upon OC (Fig. 10) as diameter in a plane perpendicular to the plane of the figure. Let 5 and S' be the points of intersection of this circumference with the perpendicular to the plane of the figure through the point A. Conceive a sphere described upon SS' as diameter, and make a projection upon this sphere, taking 5 as the point of sight. All circles having their centres at A are projected upon circles having for poles the points 5 and S'. As to circles conjugate with respect to two points O and C, they are projected ...

Full Product Details

9781375942454

Table of Contents

Reviews

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available