idea of it [present to the mind]. For we frequently, in some sort of way, understand the words taken singly, or remember that we formerly understood them; yet as we rest satisfied with this blind knowledge, and do not sufficiently pursue the resolution of the notions, it may happen that the contradiction, which, perchance, a composite notion involves, escapes us.-Leibnitz.

P. 489, n. N, 1. 27.-M. Turgot studied the doctrine of M. Gournay and M. Quesnay with advantage, and made it his own; and, combining it with the knowledge he had of the law of right, and the expansive views of civil and criminal legislation that had occupied his mind and interested his heart, he succeeded, in this way, in forming a body of principles concerning national government, which comprehended both systems, and was more complete.

He was reported as being connected with several sects or societies so called. His friends in those societies were incessant in their complaints that he did not agree with their views. He, in his turn, continually reproached them with being desirous to establish a community of opinions, and with becoming security for the views of each other. He even considered such a course calculated to retard the progress of their discoveries.-Dupont.

P. 491, Continuation of Note O in second edition, 1. 12.-Without an act of the will there is no effort of attention. Without some effort of attention there is no recollection. In sleep the action of the will is suspended. How, then, do we preserve any recollection of our dreams?

I see two or three answers to this difficulty. For the present, they reduce themselves to the statement, either that in a state of perfect sleep there is no recollection, and that, when we have recollection, our sleep was not perfect, or that the effort of will, which is sufficient for recollection, is not suspended in sleep; that the mind preserves this degree of activity; that it is, so to speak, only an elementary, and, as it were, unconscious volition.-Prévost.

P. 497, n. P, 1. 12.-There can be no doubt that the word colour does not denote any property of body, but simply a modification of our mind; that whiteness for example, redness, &c., only exist in us and not at all in the bodies to which we refer them. The tendency we have to ascribe to a material and divisible substance that which really belongs to a spiritual and simple substance, and which is a habit in operation from infancy, is a very singular one,

and worthy of the attention of metaphysicians; and there is nothing, perhaps, more extraordinary in the operations of our mind than to observe it transport its sensations beyond itself, and, so to speak, spread them over a substance to which they cannot belong.D'Alembert.

P. 497, 1. 28.-We might suppose a case in which smell would teach us to judge with perfect accuracy of size, figure, situation, and distance. On the one hand, it would only be necessary to subject the odoriferous particles to tl e laws of dioptrics, and, on the other, to construct the organ of smell nearly on the model of that of sight; so that the odoriferous rays, after crossing each other at the opening, might impress upon an interior membrane as many distinct points as there were on the surface from which they were reflected.

In such a case, we should very soon acquire the habit of spreading smells over objects, and philosophers would not fail to say that the sense of smell had no need of the information of touch in order to perceive size and figure.-Condillac.

P. 498, n. Q, l. 1.-It is indeed true, that musicians of the present day are accustomed so to express themselves, considering acute above and grave below, and that some of the later Greeks seem to have expressed themselves in the same way, though rarely, and that the habit gradually grew on them. But the more ancient Greeks employed a totally opposite mode of expression, considering the grave above and the acute below. This practice continued even to the times of Boethius, who, in his scales, uniformly places the grave in the highest place and the acute in the lowest.-David Gregory.

P. 498, 1. 12.-And, indeed, the grave takes place when from the lower part of the throat the breath is carried upwards, but the acute when it issues from the highest part.-Aristides Quintilianus.

P. 499, footnote 1, c. 1, 1. 5.-By the association of ideas is to be understood, not any natural and necessary conjunction of them, but one which is fortuitous, or produced by custom or superinduced disposition; in virtue of which ideas, that in themselves have no natural connexion, are so joined that, on the recurrence of one, the whole troop of them present themselves to the view of the mind. -Brucker.

P. 501, n. S, 1. 8.-What then? Are we to suppose that the mind is impressed like wax, and that memory is the trace in the mind of the objects stamped? What traces can there be of words?

what of things themselves? what magnitude, again, is there so vast, which can give rise to so many impressions ?-Cicero.

P. 501, 1. 14.-See above, vol. ii. p. 25, n. 2, 1. 1.

VOL. III.

(ELEMENTS, VOL. II.)

P. 9, n., c. 2, 1. 2.-Supposing the planets to be inhabited by reasoning beings, the question remains, as to whether what we call reason is the same with them as with us? It would seem that it is in every respect the same, and that it cannot be otherwise, whether we consider the use of reason in matters pertaining to morals and equity, or in those that relate to the principles and foundations of the sciences. For with us, reason is that which generates a sense of justice, honour, praise, clemency, gratitude, and, in general, teaches us to distinguish between good and evil; and, besides, renders the mind a proper subject of instruction, and fits it for making various discoveries.-Huygens.

P. 10, n. 1, c. 2, 1. 10.-There is indeed a true law, right reason, whose office it is to summon to duty by a command; to

deter from crime by a prohibition.-Cicero.

P. 12, n., c. 1, 1. 15.—

All my household are busy reasoning,

And from it reasoning has banished Reason.-Molière. P. 36, n., c. 2, 1. 4.—All mathematical propositions are identical, and represented by the formula a=a.-Berlin Dissertation.

P. 44, 1. 13.—That which most astonishes me here, is to see myself here. From D'Alembert.

-

P. 58, n. 1, c. 1, 1. 10.—I likewise applied myself to logic, which taught me to argue incessantly. So strong was my relish for debate, that I pounced on the passers by, whether I was acquainted with them or not, and set about a discussion with them. I sometimes addressed myself to Irish characters, who liked nothing better, and then you should have seen us disputing. Such gestures, such grimaces, such contortions! Our eyes spoke fury, and our mouths foamed. You

would have taken us for demoniacs rather than philosophers.-Le Sage.

P. 60, n. 1, c. 2, 1. 4.-The consent of all nations on one point is to be esteemed a law of nature.-Cicero.

P. 60, n. 1, c. 2, 1. 7.—We are accustomed to defer greatly to what all have concurred in presuming to be true; with us it is a proof of truth when all agree in one opinion, &c.—Seneca.

P. 65, n. 2, c. 2, 1. 9.-See above, vol. i. p. 450, n., 1. 5.

P. 66, n., c. 1, 1. 8.-See above, vol. i. p. 450, n., c. 2, 1. 4.

P. 66, n., c. 2, 1. 1.-I greatly regret that Condillac, in his profound and sagacious reflections on the human understanding, has not paid more attention to the views of Father Buffier.-Destutt-Tracy. P. 96, n. 1, c. 1, 1. 9.-See above, vol. ii. p. 483, n. I, 1. 1.

P. 97, 1.

above, vol. ii. p. 483, n. I, l. 1.

P. 99, n., c. 1, 1. 6.—Wherefore, this mode of deceiving is to be placed among those paralogisms which lie in the diction. In the first place, because we more readily fall into the error when considering along with others than by ourselves; for examination with others is carried on by speech, but by ourselves it is performed no less by the thing itself. And, in the next place, it happens, in examining by ourselves, that we fall into error when we employ speech in the consideration. Still farther, the deception is from resemblance, but resemblance arises from language.—Aristotle.

P. 124, 1. 4.—The geometrician proceeds from hypothesis to hypothesis ; and while the thought assumes a thousand forms, it is still but by an incessant repetition of the principle, the same is the same, that he performs all his prodigies.-Leibnitz.

P. 128, n., c. 1, 1. 1.-When Archimedes demonstrated that a circle is equal to a right-angled triangle, the base of which is equal to the radius, and the altitude to the circumference of the circle, he did nothing more than prove, if we examine the matter more closely, that the area of a circle, or of a regular polygon having an indefinite number of sides, could be divided into so many very small triangles as would be equal to just as many very small triangles of the given triangle; now the equality of those triangles is demonstrated in the elements from coincidence alone. Whence, accordingly, Archimedes demonstrated the coincidence of the circle with the triangle, howsoever dissimilar to it. . . Thus, the dissimilarity of figures is no barrier to their coincidence; but whether similar or dissimilar, provided they

be equal, they always can, they always must coincide. Wherefore, the eighth axiom either, when converted, does not at all hold good, or it can be universally converted; the former, if the coincidence specified in it denote actual coincidence, the latter, if it be understood of potential coincidence simply.-Barrow.

P. 128, 1. 9.—All mathematical propositions are identical, and represented by the formula a = a. They are identical truths, expressed under various forms, even that itself which is called the principle of Contradiction, enounced and involved in various ways; indeed, all propositions of this class are really contained in it. But, according to our faculty of understanding, the difference of propositions consists in this, that some by a longer, others by a shorter process of reasoning, are reducible to and capable of resolution into the first principle of all. Thus, for example, the proportion 2 + 2 = 4, is at once resolved into this, 1+1+1+1=1+1+1+1; that is, the same is the same; and properly speaking, it ought to be thus enounced. If it should happen that four entities are anywhere or exist, then four entities exist, for geometricians do not positively deal with existence, but only hypothetically assume it. Accordingly, he reaches the highest certainty who thus runs back propositions to their last grounds, for he observes the identity of ideas; and this is the evidence that immediately compels our assent, which we call mathematical or geometrical. It is not, however, peculiar and proper to the science of mathematics, for it springs from the apprehension of identity which can have place, although the ideas do not represent extension.-Berlin Dissertation.

P. 130, 1. 15.—The evidence of reason consists solely in identity, as we have demonstrated. This truth must needs be very simple to have escaped the observation of all the philosophers, who are so deeply interested in reaching the ground of evidence, a word which is ever in their mouths.-Condillac.

P. 130, n. 1, c. 2, 1. 2.-Interrogate honest mathematicians, and they will admit that their propositions are all identical, and that so many volumes on the circle, for example, amount merely to the repetion in a hundred thousand different ways of the truth, that it is a figure of which all the lines drawn from the centre to the circumference are equal. We know therefore next to nothing.—

Diderot.

P. 130, n. 2, c. 2, 1. 2.-The whole system of human knowledge