less known makes us give our assent to the latter. But in particular and pre-eminently we call it reason, if it is the cause not only of our judgment, but also of the truth itself, which we also call reason a priori, and the cause in things corresponds to the reason in truths. This is why cause indeed is often called reason, and particularly final cause. Finally, the faculty which perceives this connection of truths, or the faculty of reasoning, is also called reason, and this is the sense you employ here. Now this faculty is really affected by man alone here below, and does not appear in other animals here below; for I have already shown above that the shadow of reason seen in the beasts is only the expectation of a similar event in a case apparently similar to the past, without knowing whether the same reason holds good. Men themselves act no differently in the cases where they are only empirical. But they raise themselves above the beasts, in so far as they see the connections of truths, the connections, I say, which themselves indeed constitute the necessary and universal truths. These connections are indeed necessary although they produce only an opinion, when after an exact research the prevalence of probability, so far as may be judged, may be demonstrated, so that then there is demonstration, not of the truth of the thing, but of the side prudence requires us to take. In dividing this faculty of reason, I think we do no wrong in recognizing two parts, according to a sufficiently received opinion which distinguishes invention and judgment. As for the four degrees which you remark in mathematical demonstrations, I find that usually the first, viz.: the discovery of proofs, does not appear therein, as is to be desired. There are syntheses, found sometimes without analysis, and sometimes the analysis has been suppressed. Geometers in their demonstrations put first the proposition which is to be proved, and in order to come to the demonstration they set forth by some figure what is given. This is called ecthesis. After this they come to the preparation and draw new lines which they need in the reasoning; and often the greatest art consists in finding this preparation. This done, they construct the reasoning itself, by drawing inferences from what was given in the ecthesis and from what has been added thereto by the preparation; and employing for this purpose truths already known or demonstrated, they reach the conclusion. But there are cases where they dispense with the ecthesis and the preparation. . Ph. It is generally believed that the syllogism is the