# Cayley Sentence Examples

**Cayley**, Presidential Address (Brit.- Two methods of treatment have been carried on in parallel lines, the unsymbolic and the symbolic; both of these originated with
**Cayley**, but he with Sylvester and the English school have in the main confined themselves to the former, whilst Aronhold, Clebsch, Gordan, and the continental schools have principally restricted themselves to the latter. - So the theory of the forms appertaining to a binary form of unrestricted order was first worked out by
**Cayley**and P. A. - A theory of matrices has been constructed by
**Cayley**in connexion particularly with the theory of linear transformation. - This theorem is due to
**Cayley**, and reference may be made to Salmon's Higher Algebra, 4th ed. - As modified by
**Cayley**it takes a very simple form. **Cayley**, however, has shown that, whatever be the degrees of the three equations, it is possible to represent the resultant as the quotient of two determinants (Salmon, l.c. p. 89).- Which is satisfied by every symmetric fraction whose partition contains no unit (called by
**Cayley**non-unitary symmetric functions), is of particular importance in algebraic theories. - Such quantics have been termed by
**Cayley**multipartite. - Observe the notation, which is that introduced by
**Cayley**into the theory of matrices which he himself created. - It is on a consideration of these factors of t that
**Cayley**bases his solution of the quartic equation. - We have A +k 1 f =0 2, O+k 2 f = x2, O+k3f =4) 2, and
**Cayley**shows that a root of the quartic can be xpressed in the determinant form 1, k, 0.1y the remaining roots being obtained by varying 1, k, x the signs which occur in the radicals 2 u The transformation to the normal form reduces 1, k 3, ? - Single binary forms of higher and finite order have not been studied with complete success, but the system of the binary form of infinite order has been completely determined by Sylvester,
**Cayley**, MacMahon and Stroh, each of whom contributed to the theory. - The ternary cubic has been investigated by
**Cayley**, Aronhold, Hermite, Brioschi and Gordan. - The complete covariant and contravariant system includes no fewer than 34 forms; from its complexity it is desirable to consider the cubic in a simple canonical form; that chosen by
**Cayley**was ax 3 +by 3 + cz 3 + 6dxyz (Amer. - P. 16) and by
**Cayley**(Amer. - This theory is due to
**Cayley**; its validity depends upon showing that the (w - I; 0, n) linear equations satisfied by the literal coefficients are independent; this has only recently been established by E. - A little further progress has been made by
**Cayley**, who established the two generating functions for the quintic 1 -a3s 11 -a8.1 a12. - Sylvester,
**Cayley**and MacMahon succeeded, by a laborious process, in establishing the generators for 0=5, and 0=6, viz.: 5 15 531 1 -z 2.1-z 3.1-z 4.1-z 5 ' 1-z2.1-z3.1-z4.1-z5.1-z6' but the true method of procedure is that of Stroh which we are about to explain. **Cayley**, " Memoirs on Quantics," in the Collected Mathematical Papers (Cambridge, 1898); Salmon, Lessons Introductory to the Modern Higher Algebra (Dublin, 1885); E.**Cayley**, on Matrices, Phil.**Cayley**(Memoirs of More, 2 vols., 1808).**Cayley**(2 vols., London, 1808); by Sir J.- And one of Hamilton's earliest advances in the study of his system (an advance independently made, only a few months later, by Arthur
**Cayley**) was the interpretation of the singular operator q()q1, where q is a quaternion. - The method is essentially the same as that developed, under the name of " matrices," by
**Cayley**in 1858; but it has the peculiar advantage of the simplicity which is the natural consequence of entire freedom from conventional reference lines. **Cayley**, J.- The formation of the tables of a planet has been described by
**Cayley**as " the culminating achievement of astronomy," but the gigantic task which Newcomb laid out for himself, and which he carried on for more than twenty years, was the building up, on an absolutely homogeneous basis, of the theory and tables of the whole planetary system. - ARTHUR
**CAYLEY**(1821-1895), English mathematician, was born at Richmond, in Surrey, on the 16th of August 1821, the second son of Henry**Cayley**, a Russian merchant, and Maria Antonia Doughty. - ARTHUR
**CAYLEY**(1821-1895), English mathematician, was born at Richmond, in Surrey, on the 16th of August 1821, the second son of Henry**Cayley**, a Russian merchant, and Maria Antonia Doughty. - His father, Henry
**Cayley**, retired from business in 182 9 and settled in Blackheath, where Arthur was sent to a private school kept by the Rev. G. - Degen in 1816 and Ottoris Sarti in 1823, followed
**Cayley**at moderate intervals, constructing flying models on the vertical screw principle. - Sir George
**Cayley**proposed such a machine in 1810, and W. - An investigation by means of the curve II = o, which by its intersections with the given curve determines the points of contact of the double tangents, is indicated by
**Cayley**, " Recherches sur l'elimination et la theorie des courbes " (Crelle, t. - See
**Cayley**, " On the Double Tangents of a Plane Curve " (Phil. - Lxv., 1865), and
**Cayley**, " On the Transformation of Plane Curves " (Proc. Lond. - The extension to curves of any given deficiency D was made in the memoir of
**Cayley**, " On the correspondence of two points on a curve, " - Pore. - It was thus that Zeuthen (in the paper Nyt Bydrag, " Contribution to the Theory of Systems of Conics which satisfy four Conditions " (Copenhagen, 1865), translated with an addition in the Nouvelles Annales) solved the question of finding the characteristics of the systems of conics which satisfy four conditions of contact with a given curve or curves; and this led to the solution of the further problem of finding the number of the conics which satisfy five conditions of contact with a given curve or curves (
**Cayley**, Comptes Rendus, t. - Binet in France, Carl Gustav Jacobi in Germany, and James Joseph Sylvester and Arthur
**Cayley**in England. - The farreaching discoveries of Sylvester and
**Cayley**rank as one of the most important developments of pure mathematics. - Skew-determinants were studied by
**Cayley**; axisymmetric-determinants by Jacobi, V. **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."