Des Cartes, speaking as a naturalist, and in imitation of Archimedes, said, give me matter and motion and I will construct you the universe. We must of course understand him to have meant; I will render the construction of the universe intelligible. In the same sense the transcendental philosopher says; grant me a nature having two contrary forces, the one of which tends to expand infinitely, while the other strives to apprehend or find itself in this infinity, and I will cause the world of intelllgences with the whole system of their representations to rise up before you. Every other science presupposes intelligence as already existing and complete: the philosopher contemplates it in its growth, and as it were represents its history to the mind from its birth to its maturity. The venerable sage of Koenigsberg has preceded the march of this master-thought as an effective pioneer in his essay on the introduction of negative quantities into philosophy, published 1763. In this he has shown, that instead of assailing the science of mathematics by metaphysics, as Berkeley did in his ANALYST, or of sophisticating it, as Wolf did, by the vain attempt of deducing the first principles of geometry from supposed deeper grounds of ontology, it behoved the metaphysician rather to examine whether the only province of knowledge, which man has succeeded in erecting into a pure science, might not furnish materials, or at least hints, for establishing and pacifying the unsettled, warring, and embroiled domain of philosophy. An imitation of the mathematical method had indeed been attempted with no better success than attended the essay of David to wear the armour of Saul. Another use however is possible and of far greater promise, namely, the actual application of the positions which had so wonderfully enlarged the discoveries of geometry, mutatis mutandis, to philosophical subjects. Kant having briefly illustrated the utility of such an attempt in the questions of space, motion, and infinitely small quantities, as employed by the mathematician, proceeds to the idea of negative quantities and the transfer of them to metaphysical investigation. Opposites, he well observes, are of two kinds, either logical, that is, such as are absolutely incompatible; or real, without being contradictory. The former he denominates Nihil negativum irrepraesentabile, the connection of which produces nonsense. A body in motion is something--Aliquid cogitabile; but a body, at one and the same time in motion and not in motion, is nothing, or, at most, air articulated into nonsense. But a motory force of a body in one direction, and an equal force of the same body in an opposite direction is not incompatible, and the result, namely, rest, is real and representable. For the purposes of mathematical calculus it is indifferent which force we term negative, and which positive, and consequently we appropriate the latter to that, which happens to be the principal object in our thoughts.