"One would suppose that the relation between the pseudo-didactic and the didactic syllogism, was the same as that between the pseudo-dialectic and the dialectic; so that, if the pseudo-dialectic deserved to be called sophistic or , the pseudo-didactic would deserve these appellations also; especially, since the formal conditions of the syllogism are alike for both. This Aristotle does not admit, but draws instead a remarkable distinction. The (he says) is a dishonest man, making it his professional purpose to deceive; the pseudo-graphic man of science is honest always, though sometimes mistaken. So long as the pseudo-graphic syllogism keeps within the limits belonging to its own special science, it may be false, since the geometer may be deceived even in his own science [of] geometry, but it cannot be sophistic or eristic; yet whenever it transgresses those limits, even though it be true and though it solves the problem proposed, it deserves to be called by those two epithets. Thus, there were two distinct methods proposed for the quadrature of the circle—one by Hippokrates, on geometrical principles, the other by Bryson, upon principles extra-geometrical. Both demonstrations were false and unsuccessful; yet that of Hippokrates was not sophistic or eristic, because he kept within the sphere of geometry; while that of Bryson was so, because it travelled out of geometry. Nay more, this last would have been equally sophistic and eristic, and on the same ground, even if it had succeeded in solving the problem. If indeed the pseudo-graphic syllogism be invalid in form, it must be considered as sophistic, even though within the proper scientific limits as to [the] matter; but, if it be correct in form and within these same limits, then however untrue its premisses may be, it is to be regarded as not sophistic or eristic."