...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...

...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...

...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,...

...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...

...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...

...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):...

...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...

...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...

...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,...

...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...