"But Euclid has, demonstrated it. His demonstration has existed for two thousand years, and, during that term, has proved satisfactory to every man by whom it has been understood." I am nevertheless uninformed. The knowledge of truth lies in the perceived agreement or disagreement of the terms of a proposition. So long as I am unacquainted with the middle term by means of which they may be compared, so long as they are incommensurate to my understanding, you may have furnished me with a principle from which I may reason truly to further consequences; but, as to the principle itself, I may strictly be said to know nothing.
Every proposition has an intrinsic evidence of its own. Every consequence has premises from which it flows; and upon them, and not upon anything else, its validity depends. If you could work a miracle to prove "that the three angles of a triangle were equal to two right angles", I should still know that the proposition had been either true or false previously to the exhibition of the miracle; and that there was no necessary connection between any one of its terms and the miracle exhibited. The miracle would take off my attention from the true question to a question altogether different, that of authority. By the authority adduced I might be prevailed on to yield an irregular assent to the proposition; but I could not properly be said to perceive its truth.
But this is not all. If it were, it might perhaps be regarded as a refinement foreign to the concerns of human life. Positive institutions do not content themselves with requiring my assent to certain propositions, in consideration of the testimony by which they are enforced. This would amount to no more than advice flowing from a respectable quarter, which, after all, I might reject if it did not accord with the mature judgement of my own understanding.