thefe oracles: at leaft the inconfiderable merit of their commentaries, ftrongly favours this fuppofition.

34. A Commentary on the whole of Homer. Suidas. A fpecimen of the great value of this work may be feen in our philofopher's commentaries on Plato's republic. The works of Homer are not only the great fountain of poetry, but likewife of philofophy; and are no Tefs admirable for infpiring the fury of the Mufes than for containing the myfteries of the most recondite theology.

35. Concerning the Gods, according to Homer. Had this work been preserved, we should doubtless have been furnished with a defence of the heathen religion, which would have filenced the ignorant clamours of its opponents.

36. The Symphony or Concord of Orpheus, Pythagoras, and Plato. Suidas. Froclus, in his published writings, is every where ftudious of reconciling the doctrines of these great men, and is always fuccefsful in this undertaking. Indeed, the fame divine genius feems to have irradiated and inspired these wonderful heroes, but in different ways: in Orpheus it was accompanied with the fire of the Mufes; in Pythagoras it fhone through the myftericus veil of numbers; and in Plato, combining the preceding modes, it was feen enshrined in awful majesty of thought, clothed with the graces of poetical diction, and resplendent with ineffable light,

37. Two Books on the Theurgic Difcipline. Suidas. How much Proclus excelled in this art, may be feen in the preceding Life.

38. Concerning the Oppofitions of Aristotle to Plato's Timaus. This work is mentioned by Proclus in the 3d book of his commentary on the Timæus, p. 226. and feems to have escaped the notice of the accurate Fabricius. Ariftotle may, no doubt, in many particulars be reconciled with Flato; but it is alfo certain, that in fome he is perfealy diffonant. And thus much for the Life and Writings of Proclus.

IT

CH HA P. I.

On the Middle Nature of the Mathematical Effence.

T is neceffary that the mathematical effence should neither be separated from the first nor laft genera of things, nor from that which obtains a fimplicity of effence; but that it fhould obtain a middle fituation between substances deftitute of parts, fimple, incomposite and indivisible, and such as are fubject to partition, and are: terminated in manifold compofitions and various divifions. For fince that which fubfifts in its inherent reafons remains perpetually the fame, is firm and durable, and cannot be confuted, it evidently declares it is fuperior to the forms exifting in matter. But that power of progreffion which apprehends, and which befides ufes the dimenfions of fubjects, and prepares different conclufions from different principles, gives it an order inferior to that nature which is allotted an indivisible effence, perfectly constituted in itself. Hence (as it appears to me) * Plato

alfo

All the ancient theologifts, among whom Plato holds a diftinguished rank, affirmed that the foul was of a certain middle nature and condition between intelligibles and fenfibles: agreeable to which doctrine, Plotinus divinely afferts that he is placed in the horizon, or in the boundary and ifthmus, as it were, of eternal and mortal natures; and hence, according to the Magi, fhe is fimilar to the moon, one of whofe parts is lucid, but the other dark. Now the foul, in

con

allo divides the knowledge of things which are, into firft, middle, and laft fubftances. And to indivisible natures, indeed, he attributes an

66

confequence of this middle condition, muft neceffarily be the receptacle of all middle energies, both vital and gnoftic: fo that her knowledge is inferior to the indivifible fimplicity of intellectual comprehenfion, but fuperior to the impulfive perceptions of fenfe. Hence the mathematical genera and fpecies refide in her effence, as in their proper and natural region; for they are entirely of a middle nature, as Proclus proves in this and the fixth following chapter. But this doctrine of Plato's, originally derived from Brontinus and Archytas, is thus elegantly explained by that philofopher, in the concluding part of the fixth book of his Republic. Socrates, know then, they are, as we say, two (the Good itself, and the Sun,) and that the one reigns over the intelligible world, but the other over the visible, not to fay the heavens, left I fhould deceive you by the name. You comprehend then, thefe two orders of things, I mean the visible and the intelligible?-Glauco. I do.-Socrates. Continue this divifion then, as if it were a line divided into two unequal fegments; and each part again, i. e. the fenfible and intelligible, divided after a fimilar manner, and you will have evidence and obfcurity placed by each other. In the vifible fegment, indeed, one part will contain images. But I call images, in the first place, fhadows; afterwards, the refemblances of things appearing in water, and in dense, smooth, and lucid bodies, and every thing of this kind, if you apprehend me ?-Glauco. I apprehend you. -Socrates. Now conceive that the other fection comprehends the things, of which these images are nothing more than fimilitudes, fuch as the animals around us, together with plants, and whatever is the work of nature and art.-Glauco. I conceive it.-Socrates. Do you confider this fection then, as divided into true and falfe? And that the hypothefis of opinion is to the knowledge. of science, as a refemblance to its original ?-Glauco. I do, very readily.-Socrates. Now then, confider how the section of the intelligible is to be divided.-Glauco. How?-Socrates. Thus: one fegment is that which the foul enquires after, ufing the former divifions as images, and compelled to proceed from hypothefes, not to the principle, but to the conclufion. The other is that which employs the cogitative power of the foul, as fhe proceeds from an hypothefis to a principle no longer fuppofed, and, neglecting images, advances through their obfcurity into the light of ideas themselves.-Glauco. I do not, in this, fufficiently understand you.-Socrates. But again, for you will more easily understand me from what has been already premifed. I think you are not ignorant, that those who are converfant in geometry, arithmetic, and the like, fuppofe even and odd, together with various figures, and the three fpecies of angles, and other things fimilar to thefe, according to each method of proceeding. Now, having eftablished thefe, as hypothefes fufficiently known, they conceive that no reafon is to be required for their pofition but beginning from thefe, they defcend through the reft, and arrive at laft, at the object of their investigation.-Glauco. This I know perfectly well.-Socrates. This alfo you know, that they ufe vifible forms, and make them the fubject of their difcourfe, at the fame time not directing their intellect to the perception of thefe, but to the originals they refemble; I mean the fquare itself, and the diameter itfelf; and not to the figures they delineate. And thus, other forms, which are reprefented by fhadows and images in water, are employed by them, merely as refemblances, while they ftrive to behold that which can be feen by cogitation alone.Glauco. You fpeak the truth.-Socrates. This is what I called above a species of the intelli gible, in the investigation of which, the foul was compelled to ufe hypothefes; not afcending to the principle, as incapable of rifing above hypothefes, but ufing the images formed from inferior objects, to a fimilitude of fuch as are fuperior, and which are fo conceived and diftinguished by opinion, as if they perfpicuously contributed to the knowledge of things themselves.-Glauco. I understand indeed, that you are fpeaking of the circumstances which take place in geomemetry, and her kindred arts.-Socrates. Underfland now, that by the other fection of the intelligible, I mean that which reafon herfelf reaches, by her power of demonfirating, when no longer efteeming hypothefes for principles, but receiving them in reality for hypothefes, fle ufes them as fo many steps and handles in her afcent, until he arrives at that which is no longer

hypo

intelligence, which, in a collective manner, and by a certain fimple power, divides the objects of intellectual perception; fo that being divested of matter, and endued with the greatest purity, it apprehends things themselves, by a certain unifying perception, and excels the other kinds of knowledge. But to divifible effences, and fuch as are allotted the loweft nature, and to all fenfible beings, he attributes opinion, which obtains an obfcure and imperfect truth. But to middle effences (and fuch are mathematical forms), and to things inferior to an indivisible and fuperior to a divisible nature, he attributes cogitation. For this, indeed, is inferior to intellect, and the fupreme fcience dialectic; but is more perfect than opinion, and more certain and pure. For it advances by a difcurfive proceffion, expands the indivisibility of intellect, and unfolds that which was involved in the unity of intellectual apprehenfion: but it collects things which are divided, and brings them back to mind. Hence, as knowledges differ among themselves, fo the objects of knowledge are diftinguished by nature. So that intelligible effences having an uniform fubfiftence, hypothetical, the principle of the univerfe; and afterwards defcending, holding by ideas which adhere to the principle, the arrives at the conclufion, employing nothing fenfible in her progrefs, but proceeding through ideas, and in thefe at laft terminating her defcent.-Glauco. I underftand you, but not fo well as I defire: for you feem to me to propose a great undertaking. You -endeavour, indeed, to determine that the portion of true being and intelligible, which we fpeculate by the feience of demonftration, is more evident than the discoveries made by the sciences called arts; because in the fift hypothefes are principles, and their masters are compelled to employ the eye of eogitation, and not the perceptions of the fenfes. Yet, because they do not afcend to the principle, but investigate from hypothefes, they feem to you not to have intelligence concerning thefe, though they are intelligible, through the light of the principle. But you feem to me to call the habit of reafoning on geometrical and the like concerns, cogitation, rather than intelligence, as if cogitation held the middle fituation between opinion and intellect. -Socrates. You underfland me fufficiently well. And again: with thefe four proportions take thefe four correfponding affections of the foul: with the higheft intelligence; with the second cogitation; againft the third fet opinion; and against the fourth affimilation, er imagination. Befides this, eftablish them in the order of alternate proportion, fo that they may partake of evidence, in the fame manner as their correfponding objects participate of reality." I have taken the liberty of translating this fine paffage differently from both Petvin and Spers; because they have neglected to give the proper meaning of the word davía, or cogitation, the former tranflating it mind, and the eye of the mind, and by this means confounding it with intellect; and the latter calling it underftanding. But it is certain that Plato, in this place, ranks intellect as the first, on accourt of the fuperior evidence of its perceptions; in the next place, cogitation; in the third, opinion; and in the fourth, imagination. However, the reader will please to remember, that by dania, or cogitation, in the prefent work, is underflood that power of the foul which reafons from premifcs to conclufions, and whofe fyllogiftic energy, on active subjects, is called prudence; and on fuch as are fpeculative, fience. But for farther information Concerning its nature, fee the differtation prefixed to this work, and the following fifth chapter. evidently

evidently excel all others. But fenfibles are entirely excelled by primary effences and mathematical natures, and whatever falls under cogitation, are allotted a middle order: for they are excelled by the divifion of intelligibles; but becaufe deftitute of matter, they are fuperior to fenfible natures; and by a certain fimple power, they are excelled by the firft; but by a certain reason are more exalted than the laft. Hence they poffefs notions of an intellectual effence, which are more manifeft than fenfibles, but which are, at the fame time, only the images of an intellectual nature; and they: imitate divisibly the indivifible, and, in a multiform manner, the uniform exemplars of things. And, that I may fum up the whole in a few words, they are placed in the vestibules or entrances of primary forms, and difclofe their indivifible and prolific fubfiftence collected into one, but they do not yet excel the divifion and compofition of reafons, and an effence accommodated to the obfcurity of images; nor are they capable of paffing beyond the various notions of the foul, endued with a difcurfive power, and of adhering to intellections perfectly fimple, and purified from all material imperfection. After this manner then, is the middle nature of mathematical genera and forms to be underftood; as filling up the medium between effences entirely indivifible, and fuch as are divifible about matter.

CHIA P.