The points in which the cutting plane intersects the sides of the triangle are the vertices of the curve; and the line joining these points is a diameter which Apollonius named the latus transversum.
The funicular or link polygon has its vertices on the lines of action of the given forces, and its sides respectively parallel to the lines drawn from 0 in the force-diagram; in particular, the two sides meeting in any vertex are respectively parallel to the lines drawn from 0 to the ends of that side of the force-polygon which represents the corresponding force.
Gomberg's triphenyl-methyl play no part in what follows), it is readily seen that the simplest hydrocarbon has the formula CH 4, named methane, in which the hydrogen atoms are of equal value, and which may be pictured as placed at the vertices of a tetrahedron, the carbon atom occupying the centre.
And at equal horizontal intervals, the vertices of the funicular will lie on a parabola whose axis is vertical.
A polyhedron (A) is said to be the summital or facial holohedron of another (B) when the faces or vertices of A correspond to the edges of B, and the vertices or faces of A correspond to the vertices and faces together of B.
It consequently has four vertices and six edges.
In Newton's method, two angles of constant magnitude are caused to revolve about their vertices which are fixed in position, in such a manner that the intersection of two limbs moves along a fixed straight line; then the two remaining limbs envelop a conic. Maclaurin's method, published in his Geometria organica (1719), is based on the proposition that the locus of the vertex of a triangle, the sides of which pass through three fixed points, and the base angles move along two fixed lines, is a conic section.
Svo - Kat- rpoieKovra, thirty-two), is a 32-faced solid, formed by truncating the vertices of an icosahedron so that the original faces become triangles.
Each of the twenty triangular faces subtend at the centre the same angle as is subtended by four whole and six half faces of the Platonic icosahedron; in other words, the solid is determined by the twenty planes which can be drawn through the vertices of the three faces contiguous to any face of a Platonic icosahedron.
Two such sets placed base to base form the octahedron, which consequently has 8 faces, 6 vertices and 12 edges.