# Algebra Sentence Examples

- The earliest
**algebra**consists in the solution of equations. - The
**Algebra**Joannis Naperi Merchistonii Baronis consists of two books: (I) "De nominata**Algebrae**parte; (2) De positiva sive cossica**Algebrae**parte," and concludes with the words, "There is no more of his**algebra**orderlie sett doun." - Principles of ordinary
**algebra**; B. - But when I took up
**algebra**I had a harder time still. - In
**algebra**he discovered the method of approximating to the real roots of an equation by means of continued fractions, and imagined a general process of solving**algebraical**equations of every degree. - From this formula we obtain by elementary
**algebra**1) ! - +a"aa"-1 have been much studied by Sylvester, Hammond, Hilbert and Elliott (Elliott,
**Algebra**of Quantics, ch. - When 0=4 it is clear that no form, whose partition contains a part 3, can be reduced; but every form, whose partition is composed of the parts 4 and 2, is by elementary
**algebra**reducible by means of perpetuants of degree 2. - The braille worked well enough in the languages, but when it came to geometry and
**algebra**, difficulties arose. - The theories of determinants and of symmetric functions and of the
**algebra**of differential operations have an important bearing upon this comparatively new branch of mathematics. - When
**algebra**had advanced to the point where exponents were introduced, nothing would be more natural than that their utility as a means of performing multiplications and divisions should be remarked; but it is one of the surprises in the history of science that logarithms were invented as an arithmetical improvement years before their connexion with exponents was known. - His standard work on
**algebra**, written in Arabic, and other treatises of a similar character raised him at once to the foremost rank among the mathematicians of that age, and induced Sultgn Malik-Shgh to summon him in A.H. - Young, The
**Algebra**of Invariants (Cambridge, 1903). **ALGEBRA**(from the Arab.- The principal step in the modern development of
**algebra**was the recognition of the meaning of negative quantities. - The main work of Descartes, so far as
**algebra**was concerned, was the establishment of a relation between arithmetical and geometrical measurement. - But, when I took up
**Algebra**, I had a harder time still--I was terribly handicapped by my imperfect knowledge of the notation. - From February to July, 1898, Mr. Keith came out to Wrentham twice a week, and taught me
**algebra**, geometry, Greek and Latin. - The
**Algebra**Joannis Naperi Merchistonii Baronis consists of two books: (I) "De nominata**Algebrae**parte; (2) De positiva sive cossica**Algebrae**parte," and concludes with the words, "There is no more of his**algebra**orderlie sett doun." - Special kinds of
**algebra**; C. History. - But on the night before the
**algebra**examination, while I was struggling over some very complicated examples, I could not tell the combinations of bracket, brace and radical. - He also studied the first six books of Euclid and some
**algebra**, besides reading a considerable quantity of Hebrew and learning the Odes of Horace by heart. - - The first to publish anything on Diophantus in Europe was Rafael Bombelli, who embodied in his
**Algebra**(1572) all the problems of Books I. - Heath, Diophantos of Alexandria: A Study in the History of Greek
**Algebra**(Cambridge, 1885). - At the age of eight he began Latin, Euclid, and
**algebra**, and was appointed schoolmaster to the younger children of the family. - His principal writings are Micrographia (1664); Lectiones Cutlerianae (1674-1679); and Posthumous Works, containing a sketch of his "Philosophical
**Algebra**," published by R. - After Maclaurin's death his account of Newton's philosophical discoveries was published by Patrick Murdoch, and also his
**algebra**in 1748. - For Tartaglia's discovery of the solution of cubic equations, and his contests with Antonio Marie Floridas, see
**Algebra**(History). - Each definition gives rise to a corresponding
**algebra**of higher complex numbers. - For the subjects of this general heading see the articles
**ALGEBRA**, UNIVERSAL; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; NUMBER; QUATERNIONS; VECTOR ANALYSIS. - 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. - During this period logarithms were invented, trigonometry and
**algebra**developed, analytical geometry invented, dynamics put upon a sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the differential calculus by Newton and Leibnitz and the discovery of gravitation. - Elliott,
**Algebra**of Quantics, Art. - 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. - Principles Of Ordinary
**Algebra**1. - This form of
**algebra**was extensively studied in ancient Egypt; but, in accordance with the practical tendency of the Egyptian mind, the study consisted largely in the treatment of particular cases, very few general rules being obtained. - For many centuries
**algebra**was confined almost entirely to the solution of equations; one of the most important steps being the enunciation by Diophantus of Alexandria of the laws governing the use of the minus sign. - The development of symbolic
**algebra**by the use of general symbols to denote numbers is due to Franciscus Vieta (Francois Viete, 1540-1603). - De Traytorrens, went through the elements of
**algebra**and geometry, and the three fi r st books of the Marquis de l'Hopital's Conic Sections. - Cantor's histories of mathematics, and more elaborate analyses are those of Nesselmann (Die
**Algebra**der Griechen, Berlin, 1842) and G. - But he seems to have been well cared for, and he was at the age of fourteen sufficiently advanced "in
**algebra**, geometry, astronomy, and even the higher mathematics," to calculate a solar eclipse within four seconds of accuracy. - Peirce, "Mathematics is the science which draws necessary conclusions" (Linear Associative
**Algebra**, § i. - The Leiden copy of ~Omar Khayygms work on
**algebra**was noticed as far back as i 742 by Gerald Meerman in the preface to his Specimen calculi fluxionalis; further notices of the same work by Sdillot appeared in the Nouv. - The partition method of treating symmetrical
**algebra**is one which has been singularly successful in indicating new paths of advance in the theory of invariants; the important theorem of expressibility is, directly we exclude unity from the partitions, a theorem concerning the expressibility of covariants, and involves the theory of the reducible forms and of the syzygies. - This theorem is due to Cayley, and reference may be made to Salmon's Higher
**Algebra**, 4th ed. - This led to the idea of
**algebra**as generalized arithmetic. - They teach further the solution of problems leading to equations of the first and second degree, to determinate and indeterminate equations, not by single and double position only, but by real
**algebra**, proved by means of geometric constructions, and including the use of letters as symbols for known numbers, the unknown quantity being called res and its square census. - The subject-matter of
**algebra**will be treated in the following article under three divisions: - A. **Algebra**and geometry were the only studies that continued to defy my efforts to comprehend them.- Again in January 1757 he writes: " I began to study
**algebra**under M. - It is true that I was familiar with all literary braille in common use in this country--English, American, and New York Point; but the various signs and symbols in geometry and
**algebra**in the three systems are very different, and I had used only the English braille in my**algebra**. - However, the braille worked well enough in the languages; but when it came to Geometry and
**Algebra**, it was different. - In pure
**algebra**Descartes expounded and illustrated the general methods of solving equations up to those of the fourth degree (and believed that his method could go beyond), stated the law which connects the positive and negative roots of an equation with the changes of sign in the consecutive terms, and introduced the method of indeterminate coefficients for the solution of equations.' - Fiedler, Die Elemente der neueren Geometrie and der
**Algebra**der bindren Formen (Leipzig, 1862); A. - The first, second and third sections of this publication comprise respectively the papers communicated by him to the Academies of Sciences of Turin, Berlin and Paris; the fourth includes his miscellaneous contributions to other scientific collections, together with his additions to Euler's
**Algebra**, and his Lecons elementaires at the Ecole Normale in 1795. - Consequently, I did not do so well as I should have done, if Teacher had been allowed to read the
**Algebra**and Geometry to me.