# Quantics Sentence Examples

- Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of
**quantics**; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers. - This notion is fundamental in the present theory because we will find that one of the most valuable artifices for finding invariants of a single quantic is first to find simultaneous invariants of several different
**quantics**, and subsequently to make all the**quantics**identical. - In addition, and transform each pair to a new pair by substitutions, having the same coefficients a ll, a12, a 21, a 22 and arrive at functions of the original coefficients and variables (of one or more
**quantics**) which possess the abovedefinied invariant property. - Such
**quantics**have been termed by Cayley multipartite. - +a"aa"-1 have been much studied by Sylvester, Hammond, Hilbert and Elliott (Elliott, Algebra of
**Quantics**, ch. - An important reference is " The Differential Equations satisfied by Concomitants of
**Quantics**," by A. - Elliott, Algebra of
**Quantics**, Art. - Of the Memoir he discusses bi-ternary
**quantics**, and in particular those which are lineo-linear, quadrato-linear, cubo-linear, quadrato-quadratic, cubo-cubic, and the system of two lineo-linear**quantics**. - 1-a'5 Accounts of further attempts in this direction will be found in Cayley's Memoirs on
**Quantics**(Collected"Papers), in the papers of Sylvester and Franklin (Amer. - I.-iv.), and in Elliott's Algebra of
**Quantics**, chap. viii. - Cayley, " Memoirs on
**Quantics**," in the Collected Mathematical Papers (Cambridge, 1898); Salmon, Lessons Introductory to the Modern Higher Algebra (Dublin, 1885); E. - Elliott, Algebra of
**Quantics**(Oxford, 1895); F. - Among his most remarkable works may be mentioned his ten memoirs on
**quantics**, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of ellipsoids; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.