Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote. A Treatise on Algebra - Page 104by George Peacock - 1830 - 685 pagesFull view - About this book
| British Association for the Advancement of Science - Science - 1834 - 562 pages
...appealed to, and some of the most important of its consequences may be pointed out. Direct proposition : Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent, whatever those symbols denote. Converse proposition : Whatever equivalent... | |
| Education - 1835 - 402 pages
...reference to this principle, as it is called, and we find the definition in page 104, as follows : — ' Whatever form is algebraically equivalent to another...their nature, the same must be an equivalent form when the symbols are general in their nature as well as in their form.' Now, we think that we here... | |
| Heat - 1841 - 280 pages
...and Symbolical Algebra, are his laws of the " Permanence of Equivalent Forms." These are — ( 1 ) " Whatever form is Algebraically equivalent to another, when expressed in general symbols, must be so whatever those symbols denote." the symbols are general in form, though specific in their nature,... | |
| Philip Kelland - Algebra - 1843 - 168 pages
...permanence of equivalent forms in both its features at the same time. The principle I allude to is this, "Whatever form is algebraically equivalent to another...in form though specific in their nature, the same " Peacock's Alg. p, 167. f Kelland's Algebra, p. 261, must be an equivalent form when the symbols are... | |
| Alfred Clebsch, Carl Neumann, Felix Klein, Adolph Mayer, David Hilbert, Otto Blumenthal, Albert Einstein, Constantin Carathéodory, Erich Hecke, Bartel Leendert Waerden, Heinrich Behnke - Electronic journals - 1911 - 622 pages
...forms" als eine unmittelbare Folge seiner Voraussetzungen ansehen zu können, dh den Doppelsatz**): „whatever form is algebraically equivalent to another when expressed in general Symbols, must continue to be equivalent, whatever those symbols denote; whatever equivalent form is discoverable... | |
| Gottfried Gabriel, Wolfgang Kienzler - Jena (Germany) - 1997 - 174 pages
...symbolischen Zugangs zur Algebra ist das "principle of the permanence of equivalent forms" (ebd., S. 198): "Whatever form is algebraically equivalent to another when expressed in general Symbols, must continue to be equivalent, whatever those Symbols denote" bzw. in der konversen Form (ebd., S. 199):... | |
| I. Grattan-Guinness - Mathematics - 2000 - 716 pages
...algebra was to be achieved via 'the principle of the permanence of equivalent forms', according to which 'Whatever form is Algebraically equivalent to another,...expressed in general symbols, must be true, whatever these symbols denote' (Peacock 1830a, 104; on p. 105 the 4 On the algebras to be discussed here, see... | |
| James Gasser - History - 2000 - 374 pages
...arithmetical algebra to the equivalences between the general forms of symbolical algebra, and conversely. (A): Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent, whatever those symbols denote. (B): Converse Proposition: Whatever equivalent... | |
| Jesper Lützen - Cartography - 2001 - 306 pages
...this principle varied slightly in the two versions of his Treatise. The 1830 version reads as follows: "Whatever form is Algebraically equivalent to another,...symbols, must be true, whatever those symbols denote. Whatever equivalent form is discoverable in arithmetical Algebra considered as the science of suggestion,... | |
| Gerard Assayag, Hans G. Feichtinger - Mathematics - 2002 - 310 pages
...into Symbolical Algebra all the general forms which have been arrived at in Arithmetical Algebra: A): Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent, whatever those symbols denote. B): Converse Proposition: Whatever equivalent... | |
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