# Download e-book for iPad: Mirrors, prisms and lenses: a text-book of geometrical by James P Southall

By James P Southall

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Then BP and BR are the trisectors of LABC. REFERENCE: H. T. SCUDDER, 'How to trisect an angle with a carpenter's square', American Mathematical Monthly, May 1928. Cassinian oval or ellipse If a point moves so that the product of its distances from two fixed points, F1 and F2 , is constant, its path is a Cassinian oval - named after Giovanni Domenico Cassini, who studied 26 • CATENARY them in 1680 in connection with the relative motions of the Earth and the Sun. Bernoulli's lemniscate is a special case in which the constant product is equal to the square of the distance between the fixed points.

C--------------~~~~~=-~ LAB C is the angle to be trisected. First use the wide arm of the carpenter's square to draw DE parallel to BC. Then lay the square so that one edge goes through B and the outer corner lies on DE, and so that the length P Q is double the width of the wide arm. Mark the mid-point, R, of P Q. Then BP and BR are the trisectors of LABC. REFERENCE: H. T. SCUDDER, 'How to trisect an angle with a carpenter's square', American Mathematical Monthly, May 1928. Cassinian oval or ellipse If a point moves so that the product of its distances from two fixed points, F1 and F2 , is constant, its path is a Cassinian oval - named after Giovanni Domenico Cassini, who studied 26 • CATENARY them in 1680 in connection with the relative motions of the Earth and the Sun.

Each parabola of one set is orthogonal to every parabola of the other set. Cremona-Richmond configuration The simplest configurations of points and lines, such as the Fano plane, Desargues's configuration or the eleven-three (113) configurations, all contain at least one set of three points and three lines joining them to form a triangle. Indeed, it seems quite natural that any configuration should contain some triangles. The Cremona-Richmond is a 15 3 configuration, with 15 lines, 15 points, 3 lines through every point, 3 points on every line, and not one triangle.