# Trigonometry and Double Algebra (Google eBook)

Taylor, Walton and Maberly, 1849 - Algebra - 167 pages

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Page vi - Syllabus of a Course of Lectures upon Trigonometry and the Application of Algebra to Geometry. 8vo. 7*. 6d. MECHANICS AND HYDROSTATICS. Elementary Hydrostatics. By WH BESANT, MA, Late Fellow of St John's College. [Preparing. Elementary Hydrostatics for Junior Students. By R. POTTER, MA late Fellow of Queens...
Page vi - O'Brien (Rev. M.) Treatise on Plane Coordinate Geometry ; or the Application of the Method of Coordinates to the Solution of Problems in Plane Geometry.
Page 101 - C, etc., might stand for virtues and vices, the reader might believe him, or contradict him, as he pleases, but not out of this chapter. The one exception above noted, which has some share of meaning, is the sign placed between two symbols, as in A B. It indicates that the two symbols have the same resulting meaning, by whatever steps attained. That A and B, if quantities, are the same amount of quantity ; that if operations, they are of the same effect, etc.
Page v - J.) on the objections against the geometrical representation of the square roots of negative quantities ii. 371 ; on the geometrical representation of the powers of quantities whose indices involve the square roots of negative quantities, ii.
Page 104 - De Morgan professes to give a complete inventory of the laws which the symbols of algebra must obey, for he says ' ' Any system of symbols which obeys these rules and no others, except they be formed by combination of these rules, and which uses the preceding symbols and no others, except they be new symbols invented in abbreviation of combinations of these symbols, is symbolic algebra.
Page 41 - Frend's papers, and dated November 16, 1801, distinctly lays it down that, in these matters, it is not the principles which prove the conclusions, but the truth of the conclusions which proves that there must, somewhere or other, be principles. " Whether or not," says he, " I have found a logic, by the rules of which operations with imaginary quantities are conducted, is not now the question ; but surely this is evident, that, since they lead to right conclusions, they must have a logic.
Page 92 - As soon as the idea of acquiring symbols and laws of combination, without given meaning, has become familiar, the student has the notion of what I will call a symbolic calculus; which, with certain symbols and certain laws of combination, is symbolic algebra: an art, not a science; and an apparently useless art, except as it may afterwards furnish the grammar of a science.
Page 101 - It is a mode of combination represented by -)• ; when + receives its meaning, so also will the word addition. It is most important that the student should bear in mind that, with one exception , no word nor sign of arithmetic or algebra has one atom of meaning throughout this chapter, the object of which is symbols, and their laws of combination, giving a symbolic algebra which may hereafter become the grammar of a hundred distinct significant algebras. If any one were to assert that + and —...
Page 99 - The next and second step, .... consisted in treating the results of algebra as necessarily true, and as representing some relation or other, however inconsistent they might be with the suppositions from which they were deduced. So soon as it was shewn that a particular result had no existence as a quantity, it was permitted, by definition, to have an existence of another kind, into which no particular inquiry was made, because the rules under which it was found that the new symbols would give true...
Page 98 - Ignorance, the necessary predecessor of knowledge, was called nature ; and all conceptions which were declared unintelligible by the former, were supposed to have been made impossible by the latter. The first who used algebraical symbols in a general sense, Vieta, concluded that subtraction was a defect, and that expressions containing it should be in every possible manner avoided. Vitium negationis, was his phrase.

### References from web pages

Trigonometry and Double Algebra (work by De Morgan) -- Britannica ...
In his Trigonometry and Double Algebra (1849) he gave a geometric interpretation of the properties of complex numbers (numbers involving a term with a ...
www.britannica.com/ eb/ topic-605291/ Trigonometry-and-Double-Algebra

De Morgan and Laws of Algebra
those of Trigonometry and Double Algebra as T1-14. All these are .... Trigonometry and Double Algebra. seems to have had little success. The reviewer in the ...
www.blackwell-synergy.com/ doi/ pdf/ 10.1111/ j.1600-0498.1981.tb00639.x

Augustus De Morgan - Wikipedia, the free encyclopedia
The best presentation of his view of algebra is found in a volume, entitled Trigonometry and Double Algebra, published in 1849; and his earlier view of ...
en.wikipedia.org/ wiki/ Augustus_De_Morgan

Who was Augustus De Morgan?
He wrote many books and articles, including Trigonometry and Double Algebra and Formal Logic. He is perhaps best known as the creator of De Morgan's Laws: ...
www.demorgan.com/ demorgan.htm

Trigonometry and Double Algebra - Augustus De Morgan - Merchant Books
Trigonometry and Double Algebra. Augustus De Morgan. Prezzo: € 19.61. Disponibilità: Spedito normalmente in 6/8 giorni lavorativi ...
www.webster.it/ book_usa-trigonometry_and_double_algebra_augustus-9781933998718.htm

JSTOR: Augustus De Morgan's Algebraic Work: The Three Stages
Later, in Trigonometry and Double Algebra, he concentrated on developing one particular logical algebra, that including the imaginaries, which he called ...

Michael Schroeder A BRIEF HISTORY OF THE NOTATION OF BOOLE’S ...
his “Trigonometry and Double Algebra”:. Given symbols M, N, +, and one sole relation of combination, namely that. M + N is the same as N + M. Here is a ...
www.hf.uio.no/ ifikk/ filosofi/ njpl/ vol2no1/ history/ history.pdf

Augustus De Morgan: Trigonometry And Double Algebra - Unabridged ...
Trigonometry And Double Algebra - Unabridged. Merchant Books (United States), 2007 Hardback, 188 stran Velikost: 229x152 mm ISBN: 9781933998718 (1933998717) ...
www.bookfayre.cz/ books/ item/ 9781933998718.html.cs

Augustus De Morgan - Wikipedia
De beste weergave van zijn visie op de Algebra is te vinden in een werk getiteld Trigonometry and Double Algebra uit 1849. Zijn voorgaande kijk op de logica ...
nl.wikipedia.org/ wiki/ Augustus_De_Morgan

voltar www.matematica.br Augustus De Morgan Período: 1806 a 1871 ...
Augustus De Morgan. Período: 1806 a 1871 dc. Assuntos matemáticos envolvidos:. Álgebra: álgebra abstrata; Análise: indução; cálculo; números complexos ...
www.ime.usp.br/ ~leo/ imatica/ historia/ demorgan.html