This paper is principally based on the following general theorem, which is a remarkable extension of Pascal's hexagram: "If a polygon move so that each of its sides passes through a fixed point, and if all its summits except one describe curves of the degrees m, n, p, &c., respectively, then the free summit moves on a curve of the degree 2mnp. ..   anvd [Please select]

V LATENT GEOMETRY [Illustration 51: THE HEXAGRAM AND EQUILATERAL TRIANGLE IN NATURE] It is a well known fact that in the microscopically minute of nature, units everywhere tend to arrange themselves with relation to certain simple geometrical solids, among which are the tetrahedron, the cube, and the sphere.   anvd [Please select]

The number 3 is of course the triangle; the irregular and vital beauty of the number 5 appears clearly in the heptalpha, or five-pointed star; the faultless symmetry of 6, its relation to 3 and 2, and its regular division of the circle, are portrayed in the familiar hexagram known as the Shield of David.   anvd [Please select]