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Books Books 1 - 3 of 3 on The next and second step, .... consisted in treating the results of algebra as necessarily....
" 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... "
Trigonometry and Double Algebra - Page 99
by Augustus De Morgan - 1849 - 167 pages
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Imagining Numbers: (particularly the Square Root of Minus Fifteen)

Barry Mazur - Mathematics - 2004 - 288 pages
...acceptance of imaginary numbers, says that insofar as they have "no existence as . . . quantity," they are "permitted, by definition, to have an existence of...another kind, into which no particular inquiry was made."1' remind us that the idea whose birth pains we hope to reexperience did not relieve all difficulties...
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Negative Math: How Mathematical Rules Can be Positively Bent

Alberto A. Martinez - Mathematics - 2006 - 267 pages
...some relation or other, however inconsistent they might be with the suppositions from which they are deduced. So soon as it was shewn that a particular...which no particular inquiry was made, because the symbols would give true results, [which] did not differ from those previously applied to the old ones....
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A History of Mathematical Notations: Vol. II

Florian Cajori - Mathematics - 2007 - 392 pages
...particular result had no existence as a quantity, it was permitted, by definition, to have an e1ustenee of another kind, into which no particular inquiry...differ from those previously applied to the old ones When the interpretation of the abstract negative quantity shewed that a part at least of the difficulty...
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