...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...

...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....

...results of algebra as necessarily true, and as representing some relation or other, however inconsistent they might be with the suppositions from which they...quantity, it was permitted, by definition, to have an e1ustenee of another kind, into which no particular inquiry was made, because the rules under which...