# Vertices Sentence Examples

- This solid has 4 faces, 4
**vertices**and 6 edges. - It consequently has four
**vertices**and six edges. - 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. - Be successive
**vertices**, and let H, K... - Be situate at the
**vertices**of a triangle ABC, the mass-centre of ~ and y is at a point A in BC, such that ~. - Again, if G be the mass-centre of four particles a, $, 7, situate at the
**vertices**of a tetrahedron ABCD, we find a: ~ :~: tet GBCD: tetUGCDA: tetGDAB: tetGABC, and by suitable determination of the ratios on the left hand we can make G assume any assigned position in space. - ., and of a series of lines connecting the
**vertices**with a point 0. - And at equal horizontal intervals, the
**vertices**of the funicular will lie on a parabola whose axis is vertical. - In all cases the magnitude and direction, and joining the
**vertices**of the polygon thus formed to an arbitrary pole 0. - Through the
**vertices**A, B, C,.. - If we take any polyhedron with plane faces, the null-planes of its
**vertices**with respect to a given wrench will form another polyhedron, and the edges of the latter will be conjugate (in the above sense) to those of the former. - SX may be also divided externally at A', so that SA'/A'X = e, since e is less than unity; the points A and A' are the
**vertices**, and the line AA' the major axis of the curve. - Cayley gave the formula E + 2D = eV + e'F, where e, E, V, F are the same as before, D is the same as Poinsot's k with the distinction that the area of a stellated face is reckoned as the sum of the triangles having their
**vertices**at the centre of the face and standing on the sides, and e' is the ratio: " the angles subtended at the centre of a face by its sides /2rr." - The truncated tetrahedron is formed by truncating the
**vertices**of a regular tetrahedron so as to leave the original faces hexagons. - The truncated octahedron is formed by truncating the
**vertices**of an octahedron so as to leave the original faces hexagons; consequently it is bounded by 8 hexagonal and 6 square faces. - The truncated dodecahedron is formed by truncating the
**vertices**of a dodecahedron parallel to the faces of the coaxial icosahedron so as to leave the former decagons. - Two polyhedra are reciprocal when the faces and
**vertices**of one correspond to the**vertices**and faces of the other. - 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. - He discriminated the three species of conics as follows: - At one of the two
**vertices**erect a perpendicular (talus rectum) of a certain length (which is determined below), and join the extremity of this line to the other vertex. - 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. - 6KT6, eight, Spa, base), a solid bounded by eight triangular faces; it has 6
**vertices**and 12 edges. - Then A, A' are the 1,[ N
**vertices**of the curve. - This solid has therefore 6 faces, 8
**vertices**and 12 edges. - Two such sets placed base to base form the octahedron, which consequently has 8 faces, 6
**vertices**and 12 edges. - A connexion between the number of faces,
**vertices**and edges of regular polyhedra was discovered by Euler, and the result, which assumes the form E + 2' = F ± V, where E, F, V are the number of edges, faces and**vertices**, is known as Euler's theorem on polyhedra. - REoo-apes-KaiSEKa, fourteen) formed by truncating the
**vertices**of a cube so as to leave the original faces squares. - 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. - 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. - 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 polyhedra correspond when the radii vectores from their centres to the mid-point of the edges, centre of the faces, and to the
**vertices**, can be brought into coincidence. - Two such sets can be placed so that the free edges are brought into coincidence while the
**vertices**are kept distinct. - Denoting them by x, y, so that AB is axis of y and a perpendicular through A the axis of x, and rationalizing (26), we have 2 ax 2 - V 2 Xy 2 - V 2 aAy = o, which represents a hyperbola with
**vertices**at 0 and A. - The points thus obtained are evidently the
**vertices**of a polyhedron with plane faces. - Take the pole of each face of such a polyhedron with respect to a paraboloid of revolution, these poles will be the
**vertices**of a second polyhedron whose edges are the conjugate lines of those of the former.