be faid to poffefs a previous conception of its truth; while,. on the contrary, it may happen that he who is in the capacity of a learner, has no antecedent knowledge of the fcience he is about to learn. Thus we attain to the diftinct. knowledge of a thing whieh we formerly knew in a general way; and frequently, things of which we were ignorant are learned and known in the fame inftant.

Of this kind are the things contained under fome general ilea, of which we poffefs a previous knowledge: thus, he: who already knows that the three interior angles of every triangle are equal to two right, and is as yet ignorant that fome particular figure delineated on paper is a triangle, is no fooner convinced from inspection of its being a triangle,. than he immediately learns and knows he learns it is a triangle; he knows the equality of its angles to two right ones. That it is now a triangle he both fees and learns; but the equality of its angles he previously knew in that general and comprehenfive idea, which embraces every particular triangle.

Indeed, a definite knowledge of this triangle requires two conditions: the one, that it is a triangle; and the other, that it has angles equal to two right. The first we receive from inspection; the fecond is the refult of a fyllogiftic procefs; an operation too refined for the energies of fenfe,, and alone the province of intellect and demonftration. But demonstration without the knowledge of that which is auniverfal, cannot fubfift; and fince the propofition is uni-verfal, that in every triangle the anglès are equal to two right, as foon as any figure is acknowledged to be a triangle,, it must neceffarily poffefs this general property.

Hence we infer, that of the triangle delineated on paper,, and concealed, we are partly ignorant of this general pro-perty, the equality of its angles (because we are ignorant

off

of its exiftence); and we partly understand it as included in that univerfal idea we previously poffeffed. Hence too, it is evident that actual science arifes from a medium between abfolute ignorance and perfect knowledge; and that he who poffeffes the principles of demonftration, poffeffes in capacity the conclufions alfo, however complicated and remote; and that by an evocation of these principles from dormant power into energy, we advance from general and abstracted knowledge to that which is fenfible and particular.

4. Two acceptations of knowledge may be admitted; the one common and without any restriction; the other limited and peculiar. Since all knowledge, whether arising from accidents, or fupported by neceffary principles, is called science. Knowledge, properly fo called, arises from a poffeffion of that cause from which a thing derives its existence, and by which we infer the neceffity of its exiftence; and this conftitutes fimple and abfolute fcience. Thus too, the definitions of those general conceptions and fuppofitions, which from their primary nature are incapable of demonstration, are called science. But the science which treats of the method of arriving at knowledge, is called demonstration; for every demonstration is a fyllogifm producing science. Hence, if in every fyllogifm it is necessary that the propofitions should be the cause of the conclufion; and to know any thing properly, a knowledge of its cause is requifite; in the propofitions of demonftration, both thefe conditions are required: that they should be effective of the conclufion; and the causes of the thing demonftrated.

Thus, from the ruins of a ftately edifice, we may juftly infer, that the building was beautiful when entire; and from the fmoke we may collect the existence of the fire,

though

one.

though concealed: but the ruins of the edifice are not the cause of its beauty; nor does fire originate from smoke, but, on the contrary, smoke is the natural result of fire: the inference, therefore, is in neither case à demonstrative Again, fince every cause is both prior to, and more excellent than its effect, it is neceffary that the propofitions should be more peculiar, primary, and excellent than the conclufions. And because we then know a thing properly when we believe it to have a neceffary existence, hence it is requifite that the propofitions fhould be true; for if falfe, a false conclufion may enfue, fuch as, that the diameter of a fquare is commenfurable with its fide. But if every science arifes from antecedent knowledge, demonAtration must be founded on fomething previous; and on this account it is requifite that the propofitions should be more known than the conclufions. The neceffary properties, then, of all demonstrative propofitions, are these; that they exift as caufes, are primary, more excellent, peculiar, true, and known, than the conclufions. Indeed, every demonstration not only confifts of principles prior to others, but of fuch as are eminently firft; for if the affumed propofitions may be demonftrated by other affumptions, fuch propofitions may, indeed, appear prior to the conclufions, but are by no means entitled to the appellation of first. But others, on the contrary, which require no demonstration, but are of themfelves probable or manifeft, are deservedly esteemed the first, the trueft, and the best. Such indemonftrable truths were called by the ancients,>, axioms, from their majesty and authority; as the affumptions which constitute the beft fyllogifms derive all their force and efficacy from these.

And on this account, above all others, they merit' the title of the principles of demonftration. But here it is

worth

worth obferving, that thefe primary propofitions are not the first in the order of our conceptions; but first to na→ ture, or in the nature of things. To us, that which is firft is particular, and fubject to fenfible infpection; to nature, that which is univerfal, and far remote from the apprehenfion of fenfe. Demonftration does not submit itfelf to the measure of our ingenuity, but, with invariable rectitude, tends to truth as its ultimate aim; and without stopping to consider what our limited powers can attain, it alone explores and traces out the nature of a thing, though to us unperceived and unknown.

This demonftrative fyllogifm differs not a little from others, by the above property; the reft can as well educe a true conclufion from falfe premises, which is frequent among the rhetoricians, as that which is prior from that which is pofterior; fuch as, Is every fyllogifm derived from conjecture?

With respect to the reft, as we have already confeffed, they may be formed from principles that are true, but not from fuch as are proper and peculiar; as if a phyfician fhould endeavour to prove an orbicular wound the most difficult to coalefce and heal, because its figure.is of all others, the most capacious; fince the demonstration of this is not the province of the phyfician, but of the geometrician alone.

5. That propofition is called immediate, which has none fuperior to itself, and which no demonstration whatever can confirm: fuch as thefe are held together by the embraces of univerfals. There are fome, indeed, united from that which is fenfible and particular: thus, that the garment is white, is an immediate propofition, but not of that kind whose principles require to be demonftrative ones; the cause of which we fhall hereafter investigate.

Of immediate

mediate propofitions fubfervient to the purposes of demonstration, some are of fuch a fuperior nature, that all men poffefs a knowledge of them without any previous inftruction; and thefe are called axioms, or general notions; for without thefe all knowledge and enquiry is vain, Another species of immediate propofitions is pofition; incapable of being ftrengthened by demonftration, yet not neceffarily foreknown by the learner, but received from the teacher. With respect to the genus of pofition, one of its species is definition, and another hypothefis. Definition is an oration, in which we neither speak of the existence, nor non-existence of a thing; but alone determine its nature and effence. It is common to every hy-`` pothefis, not to be derived from nature, but to be the entire refult of the art of the preceptor.

It likewife always affirms the existence or non-existence of its subject; such as, that motion is, and that from nothing nothing is produced. Those which are not so perfo fpicuous are called poftulates, or petitions; as that a circle may be described from any centre, and with any radius ; and fuch as these are properly hypothefes and poftulates.

6. We have now feen the privilege affigned to the principles of demonstration :—whether or no our decision. haş been juft, the enfuing confiderations will evince. We faid that the affumptions in demonstration were more known than the conclusions,—not indeed without reason, fince through these our knowledge and belief of the conclufion arifes. For univerfally, that quality which is attributed to many different things fo as to be affigned to one through the medium of another, abounds moft in that medium by which it is tranfmitted to the reft.

Thus the fun, through the medium of the moon, illu minates the earth by night; thus the father loves the VOL. I.

f

preceptor