# Cayley sentence example

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.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).AdvertisementSuch 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.The ternary cubic has been investigated by

**Cayley**, Aronhold, Hermite, Brioschi and Gordan.The germs of the theory of determinants are to be found in the works of Leibnitz; Etienne Bezout utilized them in 1764 for expressing the result obtained by the process of elimination known by his name, and since restated by Arthur

**Cayley**.AdvertisementAnd 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.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.**Cayley**'s screws were peculiar, inasmuch as they were superimposed and rotated in opposite directions.Degen in 1816 and Ottoris Sarti in 1823, followed

**Cayley**at moderate intervals, constructing flying models on the vertical screw principle.AdvertisementAll the models referred to (

**Cayley**'s excepted') were provided with rigid screws.For the caustic by refraction of parallel rays at a circle reference should be made to the memoirs by Arthur

**Cayley**.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.The farreaching discoveries of Sylvester and

**Cayley**rank as one of the most important developments of pure mathematics.An important fact, discovered by

**Cayley**, is that these coefficients, and also the complete covariants, satisfy certain partial differential equations which suffice to determine them, and to ascertain many of their properties.AdvertisementIn England, multiple algebra was developed by j ames Joseph Sylvester, who, in company with Arthur

**Cayley**, expanded the theory of matrices, the germs of which are to be found in the writings of Hamilton (see above, under (B); and Quaternions).**Cayley**gave a matrix algebra defining addition, multiplication, scalar multiplication and inverses.