means of judicious questioning, some of the more elementary truths of geometry. As a very simple illustration, I may take a geometrical axiom, and I ask a person quite unskilled in mathematics, whether, if equals be added to equals, the wholes will be equal or unequal. If he understands the question, he will at once answer that the wholes will be equal. But I did not teach him that truth; no one imparted it to him. I merely put the question to him, and he found out for himself the right answer for himself at once. It sprang up within him; and if it had not sprung up within him, he never could have received it from without. If a student of geometry were to say, My reason for assenting to the axioms is because Euclid or my teacher has assured me that they are true, and I take their word for it—if a student, I say, were to speak thus, he would show that he had no understanding of the simplest elements of geometry. But what you have to observe is, that the whole science of mathematics is truly of the character which Socrates describes. The just inference is, that the entire science is properly, even in its most complicated demonstration, called forth from within the mind, and not communicated to the mind from without. In Plato's hands this doctrine passed into the assertion that all knowledge is reminiscence; is the recollection of what the mind knows, and actually knew in some former state of existence, and still potentially knows. Such a doctrine must be limited to what may be called rational knowledge,
