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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