obtained by Means of imaginary Quantities. 119 
mathematicians, neglecting to exercise mental superintendance, 
are too prone to trust to mechanical dexterity ; and that some, 
instead of establishing the truth of conclusions on antecedent 
reasons, have endeavoured to prop it by imperfect analogies or 
mere algebraic forms. On the other hand, there are mathema- 
ticians, whose zeal for just reasoning has been alarmed at a 
verbal absurdity ; and, from a name improperly applied, or a 
definition incautiously given, have been hurried to the precipi- 
tate conclusion, that operations with symbols of which the 
mind can form no idea, must necessarily be doubtful and unin- 
telligible. * 
I have endeavoured to establish a logic for impossible quan- 
tities; to fix the meaning of certain ambiguous expressions ; and 
to reconcile the contradictions in the doctrine of logarithms. I 
indulge the hope that what I have . said may deter mathema- 
ticians from attempting to found demonstration on so frail and 
narrow a basis as analogy ; or from reposing in the dangerous 
notion, that there are either unaccountable paradoxes, or inex- 
plicable mysteries, in a system of characters entirely of their 
own invention. 
* It is to be desired, that the charges of paradox and mystery, said to be introduced 
into algebra by negative and impossible quantities, should be proposed distinctly, ire 
a precise form, fit to be apprehended and made the subject of discussion. 
