FOOTNOTES:

FOOTNOTES:[1]The Grecian literature of this writer will now prove of real utility; and the graces and the sublimities ofPlatowill soon be familiarised to the English reader, by a hand that I am persuaded will not appear inferior to his great original. Let me also be permitted to recommend his version ofPlotinusonthe Beautiful.[2]i.e. Capable of parts.[3]i.e. Not capable of parts.[4]Dr. Young, in his Night Thoughts.[5]See book the second, of Aristotle’s Metaphysics.[6]Ennead vi. lib. vii.[7]In his commentary on the 2d, 12th, and 13th books of Aristotle’s Metaphysics, page 60. A Latin translation only of this invaluable work is extant; but I have fortunately a copy in my possession, with the version every where corrected by the learned Thomas Gale, and with large extracts from the Greek.[8]See Proclus on Plato’s Theology, p. 226.[9]Ennead vi. lib. 6.[10]In giving monadic number a subsistence in opinion, I have followed the distribution of Proclus, in the conclusion of his comment on a point; and, I think, not without sufficient reason. For since monadic numbers are more immaterial than geometrical lines and figures, they must have a more immaterial subsistence. But as they are correspondent to matter, they cannot reside in the essential reasons of the soul; nor can they subsist in the phantasy, because they are superior to geometrical figures. It remains, therefore, that we must place them between διάνοια or cogitation, and the phantasy; and this middle situation is that of opinion. For cogitation, which Plato defines, in his Sophista, to be an inward discourse, without voice, is an energy of the rational soul, extending itself from propositions to conclusions. And, according to Plato, in the same place, opinion is the silent affirmation, or negation of διάνοια, or thought. Hence, says he, “opinion is the conclusion of cogitation; but imagination, the mutual mixture of sense and opinion.” So that opinion may, with great propriety, be said to contain monadic number, to which it bears the proportion of matter. And hence the reason is obvious, why the Pythagoreans called the duad opinion.[11]Ἄτροπον, ἀκαμάτον Δεκάδα κλείουσιν μιν ἁγιὴν,Ἀθάνατοί τε θεοὶ καὶ γηγενέεις ἃνθρωποι.Syrian. in Meta. Aristot. p. 113. Gr.i.e. (According to the Pythagoreans) “the immortal gods and earth-born men, call the venerable decad, immutable and unwearied.”[12]Αυτὸς μὲν Πυθαγόρας ἐν τῷ ἱερῷ λόγῳ διαῤῥηδην μορφῶν καὶ ἰδεῶν κράντορα τὸν ἀριθμόν ἔλεγεν εἶναι.Vid. Syrian. in Arist. Meta. p. 85. Gr.[13]Φιλόλαος δέ, τῆς τῶν κοσμικὼν αἰωνίας διαμονῆς τὴν κρατιστεύουσαν καὶ αὐτογειῆ συνοχὴν εἶναι ἀπεφήνατο τὸν ἀριθμόν.Syrian. in eodem loco.[14]Οἱ δὲ περὶ Ἴππασον ἀκουσματικοὶ, ἀριθμόν εἶπον παράδειγμα πρῶτον κοσμοποιίας. Καὶ πάλιν κριτικὸν κοσμουργοῦ θεοῦ ὄργανον.Jamb. in Nicomach. Arith. p. 11.[15]In his Mathematical Lectures, page 48.[16]In Arithmet. p. 23.[17]In Aristot. Meta. p. 113. Gr. vel 59. b. Lat.[18]For the tetrad contains all numbers within its nature, in the manner of an exemplar; and hence it is, that in monadic numbers, 1, 2, 3, 4, are equal to ten.[19]Notes to Letters on Mind, page 83.[20]This bright light is no other than that of ideas themselves; which, when it is once enkindled, or rather re-kindled in the soul, becomes the general standard, and criterion of truth. He who possesses this, is no longer the slave of opinion; puzzled with doubts, and lost in the uncertainties of conjecture. Here the fountain of evidence is alone to be found.—This is the true light, whose splendors can alone dispel the darkness of ignorance, and procure for the soul undecaying good, and substantial felicity. Of this I am certain, from my own experience; and happy is he who acquires this invaluable treasure. But let the reader beware of mixing the extravagancies of modern enthusiasm with this exalted illumination. For this light is alone brought into the mind by science, patient reflection, and unwearied meditation: it is not produced by any violent agitation of spirits, or extasy of imagination; for it is far superior to the energies of these: but it is tranquil and steady, intellectual and divine. Avicenna, the Arabian, was well acquainted with this light, as is evident from the beautiful description he gives of it, in the elegant introduction of Ebn Tophail, to the Life of Hai Ebn Yokdhan. “When a man’s desires (says he) are considerably elevated, and he is competently well exercised in these speculations, there will appear to him some small glimmerings of the truth, as it were flashes of lightning, very delightful, which just shine upon him, and then become extinct. Then the more he exercises himself, the oftener will he perceive them, till at last he will become so well acquainted with them, that they will occur to him spontaneously, without any exercise at all; and then as soon as he perceives any thing, he applies himself to the divine essence, so as to retain some impression of it; then something occurs to him on a sudden, whereby he begins to discern thetruthin every thing; till through frequent exercise he at last attains to a perfect tranquillity; and that which used to appear to him only by fits and starts, becomes habitual, and that which was only a glimmering before, a constant light; and he obtains a constant and steady knowledge.” He who desires to know more concerning this, and a still brighter light, that arising from an union with the supreme, must consult the eighth book of Plotinus’ fifth Ennead, and the 7th and 9th of the sixth, and his book on the Beautiful, of which I have published a translation.[21]Lest the superficial reader should think this is nothing more than declamation, let him attend to the following argument. If the soul possesses another eye different from that of sense (and that she does so, the sciences sufficiently evince), there must be, in the nature of things, species accommodated to her perception, different from feasible forms. For if our intellect speculates things which have no real subsistence, such as Mr. Locke’s ideas, its condition must be much more unhappy than that of the sensitive eye, since this is co-ordinated to beings; but intellect would speculate nothing but illusions. Now, if this be absurd, and if we possess an intellectual eye, which is endued with a visive power, there must be forms correspondent and conjoined with its vision; forms immoveable, indeed, by a corporeal motion, but moved by an intellectual energy.[22]The present section contains an illustration of almost all the first book of Aristotle’s last Analytics. I have for the most part followed the accurate and elegant paraphrase of Themistius, in the execution of this design, as the learned reader will perceive: but I have likewise everywhere added elucidations of my own, and endeavoured to render this valuable work intelligible to the thinking mathematical reader.[23]See the twenty-eighth proposition of the first book of Euclid’s Elements.[24]We are informed by Simplicius, in his Commentary on Aristotle’s third Category of Relation, “that though the quadrature of the circle seems to have been unknown to Aristotle, yet, according to Jamblichus, it was known to the Pythagoreans, as appears from the sayings and demonstrations of Sextus Pythagoricus, who received (says he) by succession, the art of demonstration; and after him Archimedes succeeded, who invented the quadrature by a line, which is called the line of Nicomedes. Likewise, Nicomedes attempted to square the circle by a line, which is properly called τεταρτημόριον, orthe quadrature. And Apollonius, by a certain line, which he calls the sister of the curve line, similar to a cockle, or tortoise, and which is the same with thequadratixof Nicomedes. Also Carpus wished to square the circle, by a certain line, which he calls simply formed from a twofold motion. And many others, according to Jamblichus, have accomplished this undertaking in various ways.” Thus far Simplicius. In like manner, Boethius, in his Commentary on the same part of Aristotle’s Categories (p. 166.) observes, that the quadrature of the circle was not discovered in Aristotle’s time, but was found out afterwards; the demonstration of which (says he) because it is long, must be omitted in this place. From hence it seems very probable, that the ancient mathematicians applied themselves solely to squaring the circle geometrically, without attempting to accomplish this by an arithmetical calculation. Indeed, nothing can be more ungeometrical than to expect, that if ever the circle be squared, the square to which it is equal must be commensurable with other known rectilineal spaces; for those who are skilled in geometry know that many lines and spaces may be exhibited with the greatest accuracy, geometrically, though they are incapable of being expressed arithmetically, without an infinite series. Agreeable to this, Tacquet well observes (in lib. ii. Geom. Pract. p. 87.) “Denique admonendi hic sunt, qui geometriæ, non satis periti, sibi persuadent ad quadraturam necessarium esse, ut ratio lineæ circularis ad rectam, aut circuli ad quadratum in numeris exhibeatur. Is sane error valde crassus est, et indignus geometrâ, quamvis enim irrationalis esset ea proportio, modo in rectis lineis exhibeatur, reperta erat quadratura.” And that this quadrature is possible geometrically, was not only the opinion of the above mentioned learned and acute geometrician, but likewise of Wallis and Barrow; as may be seen in the Mechanics of the former, p. 517 and in the Mathematical Lectures of the latter, p. 194. But the following discovery will, I hope, convince the liberal geometrical reader, that the quadrature of the circle may be obtained by means of a circle and right-line only, which we have no method of accomplishing by any invention of the ancients or moderns. At least this method, if known to the ancients, is now lost, and though it has been attempted by many of the moderns, it has not been attended with success.In the circleg o e f, letg obe the quadrantal arch, and the right-lineg xits tangent. Then conceive that the central pointaflows uniformly along the radiusa e, infinitely produced; and that it is endued with an uniform impulsive power. Let it likewise be supposed, that during its flux, radii emanate from it on all sides, which enlarge themselves in proportion to the distance of the pointafrom its first situation. This being admitted, conceive that the pointaby its impulsive power, through the radiia n,a m, &c. acting every where equally on the archg o, impells it into its equal tangent archg r. And when, by its uniform motion along the infinite lineaφ, it has at the same time arrived atb, the centre of the archg r, let it impel in a similar manner the archg r, into its equal tangent archg s, by acting every where equally through radii equal tob r. Now, if this be conceived to take place infinitely (since a circular line is capable of infinite remission) the archg owill at length be unbent into its equal, the tangent lineg x; and the extreme pointo, will describe by such a motion of unbending a circular lineo x. For since the same cause, acting every where similarly and equally, produces every where similar and equal effects; and the archg o, is every where equally remitted or unbent, it will describe a line similar in every part. Now, on account of the simplicity of the impulsive motion, such a line must either be straight or circular; for there are only three lines every where similar, i. e. the right and circular line, and the cylindric helix; but this last, as Proclus well observes in his following Commentary on the fourth definition, is not a simple line, because it is generated by two simple motions, the rectilineal and circular. But the line which bounds more than two equal tangent arches cannot be a right line, as is well known to all geometricians; it is therefore a circular line. It is likewise evident, that this archo xis concave towards the pointg: for if not, it would pass beyond the chordo x, which is absurd. And again, no arch greater than the quadrant can be unbent by this motion: for any one of the radii, asa pbeyondg o, has a tendency from, and not to the tangentg x, which last is necessary to our hypothesis. Now if we conceive another quadrantal arch of the circleg o e f, that isg y, touching the former ingto be unbent in the same manner, the archx yshall be a continuation of the archx o; for ifγ x κbe drawn perpendicular tox g, as in the figure, it shall be a tangent inxto the equal archesy x,x o; because it cannot fall within either, without making the sine of some one of the equal arches, equal to the right-linex g, which would be absurd. And hence we may easily infer, that the centre of the archy x o, is in the tangent linex g. Hence too, we have an easy method of finding a tangent right-line equal to a quadrantal arch: for having the pointsy,ogiven, it is easy to find a third point, ass; and then the circle passing through the three pointso,s,y, shall cut off the tangentx g, equal to the quadrantal archg o. And the pointsmay be speedily obtained, by describing the archg swith a radius, having to the radiusa gthe proportion of 6 to 4; for theng sis the sixth part of its whole circle, and is equal to the archg o. And thus, from this hypothesis, which, I presume, may be as readily admitted as the increments and decrements of lines in fluxions, the quadrature of the circle may be geometrically obtained; for this is easily found, when a right-line is discovered equal to the periphery of a circle. I am well aware the algebraists will consider it as useless, because it cannot be accommodated to the farrago of an arithmetical calculation; but I hope the lovers of the ancient geometry will deem it deserving an accurate investigation; and if they can find no paralogism in the reasoning, will consider it as a legitimate demonstration.[25]Axioms have a subsistence prior to that of magnitudes and mathematical numbers, but subordinate to that of ideas; or, in other words, they have a middle situation between essential and mathematical magnitude. For of the reasons subsisting in soul, some are more simple and universal, and have a greater ambit than others, and on this account approach nearer to intellect, and are more manifest and known than such as are more particular. But others are destitute of all these, and receive their completion from more ancient reasons. Hence it is necessary (since conceptions are then true, when they are consonant with things themselves) that there should be some reason, in which the axiom asserting,if from equals you take away equals,&c.is primarily inherent; and which is neither the reason of magnitude, nor number, nor time, but contains all these, and every thing in which this axiom is naturally inherent. Vide Syrian. in Arith. Meta. p. 48.[26]Geometry, indeed, wishes to speculate the impartible reasons of the soul, but since she cannot use intellections destitute of imagination, she extends her discourses to imaginative forms, and to figures endued with dimension, and by this means speculates immaterial reasons in these; and when imagination is not sufficient for this purpose, she proceeds even to external matter, in which she describes the fair variety of her propositions. But, indeed, even then the principal design of geometry is not to apprehend sensible and external form, but that interior vital one, resident in the mirror of imagination, which the exterior inanimate form imitates, as far as its imperfect nature will admit. Nor yet is it her principal design to be conversant with the imaginative form; but when, on account of the imbecility of her intellection, she cannot receive a form destitute of imagination, she speculates the immaterial reason in the purer form of the phantasy; so that her principal employment is about universal and immaterial forms. Syrian. in Arist. Meta. p. 49.[27]Syrianus, in his excellent Commentary on Aristotle’s Metaphysics, (which does not so much explain Aristotle, as defend the doctrine of ideas, according to Plato, from the apparent if not real opposition of Aristotle to their existence), informs us that it is the business of wisdom, properly so called, to consider immaterial forms or essences, and their essential accidents. By the method of resolution receiving the principles of being; by a divisive and and definitive method, considering the essences of all things; but by a demonstrative process, concluding concerning the essential properties which substances contain. Hence (says he) because intelligible essences are of the most simple nature, they are neither capable of definition nor demonstration, but are perceived by a simple vision and energy of intellect alone. But middle essences, which are demonstrable, exist according to their inherent properties: since, in the most simple beings, nothing is inherent besides their being. On which account we cannot say thatthisis their essence, andthatsomething else; and hence they are better than definition and demonstration. But in universal reasons, considered by themselves, and adorning a sensible nature, essential accidents supervene; and hence demonstration is conversant with these. But in material species, individuals, and sensibles, such things as are properly accidents are perceived by the imagination, and are present and absent without the corruption of their subjects. And these again being worse than demonstrable accidents, are apprehended by signs, not indeed by a wise man, considered as wise, but perhaps by physicians, natural philosophers, and all of this kind.[28]See Note to Chap. i. Book i. of the ensuing Commentaries.[29]Page 227.[30]Page 250.[31]Methodus hæc cum algebrâ speciosâ facilitate contendit, evidentiâ vero et demonstrationum elegantiâ eam longe superare videtur: ut abunde constabit, si quis conferat hanc Apollonii doctrinamde Sectione Rationiscum ejusdem Problematis Analysi Algebraicâ, quam exhibuit clarissimus Wallisius, tom. ii. Operum Math. cap. liv. p. 220.[32]Verum perpendendum est, aliud esse problema aliqualiter resolutum dare, quod modis variis, plerumque fieri potest, aliud methodo elegantissimâ ipsum efficere; Analysi brevissimâ et simul perspicuâ, Synthesi concinnâ et minime operosâ.[33]In his Mathematical Lectures, p. 44.[34]Lib. iv.[35]Lib. i. p. 30.[36]In Theæteto.[37]In his most excellent work on Abstinence, lib. i. p. 22, &c.[38]See the Excerpta of Ficinus from Proclus, on the first Alcibiades of Plato; his Latin version only of which is extant. Ficini Opera, tom. ii.[39]Marinus, the author of the ensuing life, was the disciple of Proclus; and his successor in the Athenian school. His philosophical writings were not very numerous, and have not been preserved. A commentary ascribed to him, on Euclid’s data, is still extant; but his most celebrated work, appears to have been, the present life of his master. It is indeed in the original elegant and concise; and may be considered as a very happy specimen of philosophical biography. Every liberal mind must be charmed and elevated with the grandeur and sublimity of character, with which Proclus is presented to our view. If compared with modern philosophical heroes, he appears to be a being of a superior order; and we look back with regret on the glorious period, so well calculated for the growth of the philosophical genius, and the encouragement of exalted merit. We find in his life, no traces of the common frailties of depraved humanity; no instances of meanness, or instability of conduct: but he is uniformly magnificent, and constantly good. I am well aware that this account of him will be considered by many as highly exaggerated; as the result of weak enthusiasm, blind superstition, or gross deception: but this will never be the persuasion of those, who know by experience what elevation of mind and purity of life the Platonic philosophy is capable of procuring; and who truly understand the divine truths contained in his works. And the testimony of the multitude, who measure the merit of other men’s characters by the baseness of their own, is surely not to be regarded. I only add, that our Philosopher flourished 412 years after Christ, according to the accurate chronology of Fabricius; and I would recommend those who desire a variety of critical information concerning Proclus, to the Prolegomena prefixed by that most learned man to his excellent Greek and Latin edition of this work, printed at London in 1703.[40]Plato in Phædro. Meminit et Plutarch. VIII. Sympos. Suidas in μήτοι. Fabricius.[41]For a full account of the distribution of the virtues according to the Platonists, consult the sentences of Porphyry, and the Prolegomena of Fabricius to this work.[42]See the sixth book of his Republic, and the Epinomis.[43]We are informed by Fabricius, that the Platonic Olympiodorus in his MS. Commentary on the Alcibiades of Plato, divides the orders of the Gods, into ὑπερκόσμιοι, or super-mundane, which are separate from all connection with body; and into ἐγκόσμιοι, or mundane. And that of these, some are οὐράνιοι, or celestial, others αἰθέριοι, or, or etherial, or πύριοι, fiery, others ἀέριοι, or aerial, others ἔνυδροι, or watry, others χθόνιοι, or earthly; and others ὑποταρτάριοι, or subterranean. But among the terrestrial, some are κλιματάρχαι, or governors of climates, others πολιοῦχοι, or rulers over cities, and others lastly κατοικίδιοι, or governors of houses.[44]This epithet is likewise ascribed by Onomacritus to the Moon, as may be seen in his hymn to that deity; and the reason of which we have given in our notes to that hymn.[45]Divine visions, and extraordinary circumstances, may be fairly allowed to happen to such exalted geniuses as Proclus; but deserve ridicule when ascribed to the vulgar.[46]What glorious times! when it was considered as an extraordinary circumstance for a teacher of rhetoric to treat a noble and wealthy pupil as his domestic. When we compare them with the present, we can only exclaim,O tempora! O mores!Philosophy sunk in the ruins of ancient Greece and Rome.[47]Fabricius rightly observes, that this Olympiodorus is not the same with the Philosopher of that name, whose learned commentaries, on certain books of Plato, are extant in manuscript, in various libraries. As in these, not only Proclus himself, but Damascius, who flourished long after Proclus, is celebrated.[48]Concerning the various mathematicians of this name, see Fabricius in Bibliotheca Græca.[49]The word in the original is λογικὰ, which Fabricius rightly conjectures has in this place a more extensive signification than either Logic, or Rhetoric: but I must beg leave to differ from that great critic, in not translating it simplyphilosophical, as I should rather imagine, Marinus intended to confine it to that part of Aristotle’s works, which comprehends only logic, rhetoric, and poetry. For the verb ἐξεμάνθανω, orto learn, which Marinus uses on this occasion, cannot with propriety be applied to the more abstruse writings of Aristotle.[50]Hence Proclus was called, by way of eminence, διάδοχος Πλατωνικός, or the Platonic Successor.[51]Concerning Polletes, see Suidas; and for Melampodes, consult Fabricius in Bibliotheca Græca.[52]This Syrianus was indeed a most excellent philosopher, as we may be convinced from his commentary on the metaphysics of Aristotle, a Latin translation only of which, by one Hieronimus Bagolinus, was published at Venice in 1558. The Greek is extant, according to Fabricius, in many of the Italian libraries, and in the Johannean library at Hamburg. According to Suidas, he writ a commentary on the whole of Homer in six books; on Plato’s politics, in four books; and on the consent of Orpheus, Pythagoras, and Plato, with the Chaldean Oracles, in ten books. All these are unfortunately lost; and the liberal few, are by this means deprived of treasures of wisdom, which another philosophical age, in some distant revolution, is alone likely to produce.[53]Socrates, in the 6th book of Plato’s Republic, says, that from great geniuses nothing of a middle kind must be expected; but either great good, or great evil.[54]The reader will please to take notice, that this great man is not the same with Plutarch the biographer, whose works are so well known; but an Athenian philosopher of a much later period.[55]Aristotle’s philosophy, when compared with the discipline of Plato is, I think, deservedly considered in this place as bearing the relation of the proteleia to the epopteia in sacred mysteries. Now the proteleia, or things previous to perfection, belong to the initiated, and the mystics; the former of whom were introduced into some lighter ceremonies only: but the mystics, were permitted to be present with certain preliminary and lesser sacred concerns. On the other hand, the epoptæ were admitted into the sanctuary of the greater sacred rites; and became spectators of the symbols, and more interior ceremonies. Aristotle indeed appears to be every where an enemy to the doctrine of ideas, as understood by Plato; though they are doubtless the leading stars of all true philosophy. However, the great excellence of his works, considered as an introduction to the divine theology of Plato, deserves the most unbounded commendation. Agreeable to this, Damascius informs us that Isidorus the philosopher, “when he applied himself to the more holy philosophy of Aristotle, and saw that he trusted more to necessary reasons than to his own proper sense, yet did not entirely employ a divine intellection, was but little solicitous about his doctrine: but that when he had tasted of Plato’s conceptions, he no longer deigned to behold him in the language of Pindar. But hoping he should obtain his desired end, if he could penetrate into the sanctuary of Plato’s mind, he directed to this purpose the whole course of his application.” Photii Bibliotheca. p. 1034.[56]according to the oracle.[57]Nothing is more celebrated by the ancients than that strict friendship which subsisted among the Pythagoreans; to the exercise of which they were accustomed to admonish each other,not to divide the god which they contained, as Jamblichus relates, lib. i. c. 33. De Vita Pythagoræ. Indeed, true friendship can alone subsist in souls, properly enlightened with genuine wisdom and virtue; for it then becomes an union of intellects, and must consequently be immortal and divine.[58]Pythagoras, according to Damascius, said, that friendship was the mother of all the political virtues.[59]A genuine modern will doubtless consider the whole of Proclus’ religious conduct as ridiculously superstitious. And so, indeed, at first sight, it appears; but he who has penetrated the depths of ancient wisdom, will find in it more than meets the vulgar ear. The religion of the Heathens, has indeed, for many centuries, been the object of ridicule and contempt: yet the author of the present work is not ashamed to own, that he is a perfect convert to it in every particular, so far as it was understood and illustrated by the Pythagoric and Platonic philosophers. Indeed the theology of the ancient, as well as of the modern vulgar, was no doubt full of absurdity; but that of the ancient philosophers, appears to be worthy of the highest commendations, and the most assiduous cultivation. However, the present prevailing opinions, forbid the defence of such a system; for this must be the business of a more enlightened and philosophic age. Besides, the author is not forgetful of Porphyry’s destiny, whose polemical writings were suppressed by the decrees of emperors; and whose arguments in defence of his religion were so very futile and easy of solution, that, as St. Hierom informs us, in his preface on Daniel, Eusebius answered him in twenty-five, and Apollinaris in thirty volumes![60]See Proclus on Plato’s Politics, p. 399. Instit. Theolog. num. 196; and the extracts of Ficinus from Proclus’s commentary on the first Alcibiades, p. 246. &c.[61]Alluding to the beautiful description given of Ulysses, in the 3d book of the Iliad, v. 222.Καί ἔπεα νιφάδεσιν ἐοικότα χειμερίησιν.Which is thus elegantly paraphrased by Mr. Pope.But when he speaks, what elocution flows!Soft as the fleeces of descending snowsThe copious accents fall, with easy art;Melting they fall, and sink into the heart! &c.[62]Concerning Domninus, see Photius and Suidas from Damascius in his Life of Isidorus.[63]Nicephorus, in his commentary on Synesius de Insomniis, p. 562. informs us, that the hecatic orb, is a golden sphere, which has a sapphire stone included in its middle part, and through its whole extremity, characters and various figures. He adds, that turning this sphere round, they perform invocations, which they call Jyngæ. Thus too, according to Suidas, the magician Julian of Chaldea, and Arnuphis the Egyptian, brought down showers of rain, by a magical power. And by an artifice of this kind, Empedocles was accustomed to restrain the fury of the winds; on which account he was called ἀλεξάνεμος, or a chaser of winds.[64]No opinion is more celebrated, than that of the metempsychosis of Pythagoras: but perhaps, no doctrine is more generally mistaken. By most of the present day it is exploded as ridiculous; and the few who retain some veneration for its founder, endeavour to destroy the literal, and to confine it to an allegorical meaning. By some of the ancients this mutation was limited to similar bodies: so that they conceived the human soul might transmigrate into various human bodies, but not into those of brutes; and this was the opinion of Hierocles, as may be seen in his comment on the Golden Verses. But why may not the human soul become connected with subordinate as well as with superior lives, by a tendency of inclination? Do not similars love to be united; and is there not in all kinds of life, something similar and common? Hence, when the affections of the soul verge to a baser nature, while connected with a human body, these affections, on the dissolution of such a body, become enveloped as it were, in a brutal nature, and the rational eye, in this case, clouded with perturbations, is oppressed by the irrational energies of the brute, and surveys nothing but the dark phantasms of a degraded imagination. But this doctrine is vindicated by Proclus with his usual subtilty, in his admirable commentary on the Timæus, lib. v. p. 329, as follows, “It is usual, says he, to enquire how souls can descend into brute animals. And some, indeed, think that there are certain similitudes of men to brutes, which they call savage lives: for they by no means think it possible that the rational essence can become the soul of a savage animal. On the contrary, others allow it may be sent into brutes, because all souls are of one and the same kind; so that they may become wolves and panthers, and ichneumons. But true reason, indeed, asserts that the human soul way be lodged in brutes, yet in such a manner, as that it may obtain its own proper life, and that the degraded soul may, as it were, be carried above it, and be bound to the baser nature, by a propensity and similitude of affection. And that this is the only mode of insinuation, we have proved by a multitude of reasons, in our commentaries on the Phædrus. But if it is requisite to take notice, that this is the opinion of Plato, we add, that in his politics, he says, that the soul of Thersites assumed an ape, but not the body of an ape: and in the Phædrus, that the soul descends into a savage life, but not into a savage body; for life is conjoined with its proper soul. And in this place he says it is changed into a brutal nature: for a brutal nature is not a brutal body, but a brutal life.”[65]Pericles Lydus, a Stoic philosopher.[66]Vide Pausan. lib. i. Atticorum, cap. 21. et 20.[67]He means the Christians.[68]Proclus was born in the year of Christ 412, on the 6th of the Ides of February. But, for the sake of the astrologers, I have subjoined the following figure from the Prolegomena of Fabricius to this life: and though I am not skilled in the art myself, I am persuaded, from the arguments of Plotinus, that it contains many general truths; but when made subservient to particulars, is liable to great inaccuracy and error. In short, its evidence is wholly of a physiognomic nature; for such is the admirable order and connection of things, that throughout the universe, one thing is signified by another, and wholes are after a manner contained in their parts. So that the language of the obscure and profound Heraclitus is perfectly just, when he says, “You must connect the perfect and the imperfect, the agreeing and the disagreeing, the consonant and the dissonant, and out of one all things, and out of all things one.”A Scheme of the situation of the Stars, such as it was at Byzantium, when the philosopher Proclus was born.[69]It was formerly the custom of almost all nations, to have their burial places in the suburbs, and not in the city itself.[70]This eclipse happened, according to Fabricius, in A. C. 484. 19 Cal. Feb. at sun-rise.

[1]The Grecian literature of this writer will now prove of real utility; and the graces and the sublimities ofPlatowill soon be familiarised to the English reader, by a hand that I am persuaded will not appear inferior to his great original. Let me also be permitted to recommend his version ofPlotinusonthe Beautiful.

[2]i.e. Capable of parts.

[3]i.e. Not capable of parts.

[4]Dr. Young, in his Night Thoughts.

[5]See book the second, of Aristotle’s Metaphysics.

[6]Ennead vi. lib. vii.

[7]In his commentary on the 2d, 12th, and 13th books of Aristotle’s Metaphysics, page 60. A Latin translation only of this invaluable work is extant; but I have fortunately a copy in my possession, with the version every where corrected by the learned Thomas Gale, and with large extracts from the Greek.

[8]See Proclus on Plato’s Theology, p. 226.

[9]Ennead vi. lib. 6.

[10]In giving monadic number a subsistence in opinion, I have followed the distribution of Proclus, in the conclusion of his comment on a point; and, I think, not without sufficient reason. For since monadic numbers are more immaterial than geometrical lines and figures, they must have a more immaterial subsistence. But as they are correspondent to matter, they cannot reside in the essential reasons of the soul; nor can they subsist in the phantasy, because they are superior to geometrical figures. It remains, therefore, that we must place them between διάνοια or cogitation, and the phantasy; and this middle situation is that of opinion. For cogitation, which Plato defines, in his Sophista, to be an inward discourse, without voice, is an energy of the rational soul, extending itself from propositions to conclusions. And, according to Plato, in the same place, opinion is the silent affirmation, or negation of διάνοια, or thought. Hence, says he, “opinion is the conclusion of cogitation; but imagination, the mutual mixture of sense and opinion.” So that opinion may, with great propriety, be said to contain monadic number, to which it bears the proportion of matter. And hence the reason is obvious, why the Pythagoreans called the duad opinion.

[11]Ἄτροπον, ἀκαμάτον Δεκάδα κλείουσιν μιν ἁγιὴν,Ἀθάνατοί τε θεοὶ καὶ γηγενέεις ἃνθρωποι.Syrian. in Meta. Aristot. p. 113. Gr.i.e. (According to the Pythagoreans) “the immortal gods and earth-born men, call the venerable decad, immutable and unwearied.”

[11]

Ἄτροπον, ἀκαμάτον Δεκάδα κλείουσιν μιν ἁγιὴν,Ἀθάνατοί τε θεοὶ καὶ γηγενέεις ἃνθρωποι.Syrian. in Meta. Aristot. p. 113. Gr.

Ἄτροπον, ἀκαμάτον Δεκάδα κλείουσιν μιν ἁγιὴν,

Ἀθάνατοί τε θεοὶ καὶ γηγενέεις ἃνθρωποι.

Syrian. in Meta. Aristot. p. 113. Gr.

i.e. (According to the Pythagoreans) “the immortal gods and earth-born men, call the venerable decad, immutable and unwearied.”

[12]Αυτὸς μὲν Πυθαγόρας ἐν τῷ ἱερῷ λόγῳ διαῤῥηδην μορφῶν καὶ ἰδεῶν κράντορα τὸν ἀριθμόν ἔλεγεν εἶναι.Vid. Syrian. in Arist. Meta. p. 85. Gr.

[12]

Αυτὸς μὲν Πυθαγόρας ἐν τῷ ἱερῷ λόγῳ διαῤῥηδην μορφῶν καὶ ἰδεῶν κράντορα τὸν ἀριθμόν ἔλεγεν εἶναι.Vid. Syrian. in Arist. Meta. p. 85. Gr.

Αυτὸς μὲν Πυθαγόρας ἐν τῷ ἱερῷ λόγῳ διαῤῥηδην μορφῶν καὶ ἰδεῶν κράντορα τὸν ἀριθμόν ἔλεγεν εἶναι.

Vid. Syrian. in Arist. Meta. p. 85. Gr.

[13]Φιλόλαος δέ, τῆς τῶν κοσμικὼν αἰωνίας διαμονῆς τὴν κρατιστεύουσαν καὶ αὐτογειῆ συνοχὴν εἶναι ἀπεφήνατο τὸν ἀριθμόν.Syrian. in eodem loco.

[13]

Φιλόλαος δέ, τῆς τῶν κοσμικὼν αἰωνίας διαμονῆς τὴν κρατιστεύουσαν καὶ αὐτογειῆ συνοχὴν εἶναι ἀπεφήνατο τὸν ἀριθμόν.Syrian. in eodem loco.

Φιλόλαος δέ, τῆς τῶν κοσμικὼν αἰωνίας διαμονῆς τὴν κρατιστεύουσαν καὶ αὐτογειῆ συνοχὴν εἶναι ἀπεφήνατο τὸν ἀριθμόν.

Syrian. in eodem loco.

[14]Οἱ δὲ περὶ Ἴππασον ἀκουσματικοὶ, ἀριθμόν εἶπον παράδειγμα πρῶτον κοσμοποιίας. Καὶ πάλιν κριτικὸν κοσμουργοῦ θεοῦ ὄργανον.Jamb. in Nicomach. Arith. p. 11.

[14]

Οἱ δὲ περὶ Ἴππασον ἀκουσματικοὶ, ἀριθμόν εἶπον παράδειγμα πρῶτον κοσμοποιίας. Καὶ πάλιν κριτικὸν κοσμουργοῦ θεοῦ ὄργανον.Jamb. in Nicomach. Arith. p. 11.

Οἱ δὲ περὶ Ἴππασον ἀκουσματικοὶ, ἀριθμόν εἶπον παράδειγμα πρῶτον κοσμοποιίας. Καὶ πάλιν κριτικὸν κοσμουργοῦ θεοῦ ὄργανον.

Jamb. in Nicomach. Arith. p. 11.

[15]In his Mathematical Lectures, page 48.

[16]In Arithmet. p. 23.

[17]In Aristot. Meta. p. 113. Gr. vel 59. b. Lat.

[18]For the tetrad contains all numbers within its nature, in the manner of an exemplar; and hence it is, that in monadic numbers, 1, 2, 3, 4, are equal to ten.

[19]Notes to Letters on Mind, page 83.

[20]This bright light is no other than that of ideas themselves; which, when it is once enkindled, or rather re-kindled in the soul, becomes the general standard, and criterion of truth. He who possesses this, is no longer the slave of opinion; puzzled with doubts, and lost in the uncertainties of conjecture. Here the fountain of evidence is alone to be found.—This is the true light, whose splendors can alone dispel the darkness of ignorance, and procure for the soul undecaying good, and substantial felicity. Of this I am certain, from my own experience; and happy is he who acquires this invaluable treasure. But let the reader beware of mixing the extravagancies of modern enthusiasm with this exalted illumination. For this light is alone brought into the mind by science, patient reflection, and unwearied meditation: it is not produced by any violent agitation of spirits, or extasy of imagination; for it is far superior to the energies of these: but it is tranquil and steady, intellectual and divine. Avicenna, the Arabian, was well acquainted with this light, as is evident from the beautiful description he gives of it, in the elegant introduction of Ebn Tophail, to the Life of Hai Ebn Yokdhan. “When a man’s desires (says he) are considerably elevated, and he is competently well exercised in these speculations, there will appear to him some small glimmerings of the truth, as it were flashes of lightning, very delightful, which just shine upon him, and then become extinct. Then the more he exercises himself, the oftener will he perceive them, till at last he will become so well acquainted with them, that they will occur to him spontaneously, without any exercise at all; and then as soon as he perceives any thing, he applies himself to the divine essence, so as to retain some impression of it; then something occurs to him on a sudden, whereby he begins to discern thetruthin every thing; till through frequent exercise he at last attains to a perfect tranquillity; and that which used to appear to him only by fits and starts, becomes habitual, and that which was only a glimmering before, a constant light; and he obtains a constant and steady knowledge.” He who desires to know more concerning this, and a still brighter light, that arising from an union with the supreme, must consult the eighth book of Plotinus’ fifth Ennead, and the 7th and 9th of the sixth, and his book on the Beautiful, of which I have published a translation.

[21]Lest the superficial reader should think this is nothing more than declamation, let him attend to the following argument. If the soul possesses another eye different from that of sense (and that she does so, the sciences sufficiently evince), there must be, in the nature of things, species accommodated to her perception, different from feasible forms. For if our intellect speculates things which have no real subsistence, such as Mr. Locke’s ideas, its condition must be much more unhappy than that of the sensitive eye, since this is co-ordinated to beings; but intellect would speculate nothing but illusions. Now, if this be absurd, and if we possess an intellectual eye, which is endued with a visive power, there must be forms correspondent and conjoined with its vision; forms immoveable, indeed, by a corporeal motion, but moved by an intellectual energy.

[22]The present section contains an illustration of almost all the first book of Aristotle’s last Analytics. I have for the most part followed the accurate and elegant paraphrase of Themistius, in the execution of this design, as the learned reader will perceive: but I have likewise everywhere added elucidations of my own, and endeavoured to render this valuable work intelligible to the thinking mathematical reader.

[23]See the twenty-eighth proposition of the first book of Euclid’s Elements.

[24]We are informed by Simplicius, in his Commentary on Aristotle’s third Category of Relation, “that though the quadrature of the circle seems to have been unknown to Aristotle, yet, according to Jamblichus, it was known to the Pythagoreans, as appears from the sayings and demonstrations of Sextus Pythagoricus, who received (says he) by succession, the art of demonstration; and after him Archimedes succeeded, who invented the quadrature by a line, which is called the line of Nicomedes. Likewise, Nicomedes attempted to square the circle by a line, which is properly called τεταρτημόριον, orthe quadrature. And Apollonius, by a certain line, which he calls the sister of the curve line, similar to a cockle, or tortoise, and which is the same with thequadratixof Nicomedes. Also Carpus wished to square the circle, by a certain line, which he calls simply formed from a twofold motion. And many others, according to Jamblichus, have accomplished this undertaking in various ways.” Thus far Simplicius. In like manner, Boethius, in his Commentary on the same part of Aristotle’s Categories (p. 166.) observes, that the quadrature of the circle was not discovered in Aristotle’s time, but was found out afterwards; the demonstration of which (says he) because it is long, must be omitted in this place. From hence it seems very probable, that the ancient mathematicians applied themselves solely to squaring the circle geometrically, without attempting to accomplish this by an arithmetical calculation. Indeed, nothing can be more ungeometrical than to expect, that if ever the circle be squared, the square to which it is equal must be commensurable with other known rectilineal spaces; for those who are skilled in geometry know that many lines and spaces may be exhibited with the greatest accuracy, geometrically, though they are incapable of being expressed arithmetically, without an infinite series. Agreeable to this, Tacquet well observes (in lib. ii. Geom. Pract. p. 87.) “Denique admonendi hic sunt, qui geometriæ, non satis periti, sibi persuadent ad quadraturam necessarium esse, ut ratio lineæ circularis ad rectam, aut circuli ad quadratum in numeris exhibeatur. Is sane error valde crassus est, et indignus geometrâ, quamvis enim irrationalis esset ea proportio, modo in rectis lineis exhibeatur, reperta erat quadratura.” And that this quadrature is possible geometrically, was not only the opinion of the above mentioned learned and acute geometrician, but likewise of Wallis and Barrow; as may be seen in the Mechanics of the former, p. 517 and in the Mathematical Lectures of the latter, p. 194. But the following discovery will, I hope, convince the liberal geometrical reader, that the quadrature of the circle may be obtained by means of a circle and right-line only, which we have no method of accomplishing by any invention of the ancients or moderns. At least this method, if known to the ancients, is now lost, and though it has been attempted by many of the moderns, it has not been attended with success.In the circleg o e f, letg obe the quadrantal arch, and the right-lineg xits tangent. Then conceive that the central pointaflows uniformly along the radiusa e, infinitely produced; and that it is endued with an uniform impulsive power. Let it likewise be supposed, that during its flux, radii emanate from it on all sides, which enlarge themselves in proportion to the distance of the pointafrom its first situation. This being admitted, conceive that the pointaby its impulsive power, through the radiia n,a m, &c. acting every where equally on the archg o, impells it into its equal tangent archg r. And when, by its uniform motion along the infinite lineaφ, it has at the same time arrived atb, the centre of the archg r, let it impel in a similar manner the archg r, into its equal tangent archg s, by acting every where equally through radii equal tob r. Now, if this be conceived to take place infinitely (since a circular line is capable of infinite remission) the archg owill at length be unbent into its equal, the tangent lineg x; and the extreme pointo, will describe by such a motion of unbending a circular lineo x. For since the same cause, acting every where similarly and equally, produces every where similar and equal effects; and the archg o, is every where equally remitted or unbent, it will describe a line similar in every part. Now, on account of the simplicity of the impulsive motion, such a line must either be straight or circular; for there are only three lines every where similar, i. e. the right and circular line, and the cylindric helix; but this last, as Proclus well observes in his following Commentary on the fourth definition, is not a simple line, because it is generated by two simple motions, the rectilineal and circular. But the line which bounds more than two equal tangent arches cannot be a right line, as is well known to all geometricians; it is therefore a circular line. It is likewise evident, that this archo xis concave towards the pointg: for if not, it would pass beyond the chordo x, which is absurd. And again, no arch greater than the quadrant can be unbent by this motion: for any one of the radii, asa pbeyondg o, has a tendency from, and not to the tangentg x, which last is necessary to our hypothesis. Now if we conceive another quadrantal arch of the circleg o e f, that isg y, touching the former ingto be unbent in the same manner, the archx yshall be a continuation of the archx o; for ifγ x κbe drawn perpendicular tox g, as in the figure, it shall be a tangent inxto the equal archesy x,x o; because it cannot fall within either, without making the sine of some one of the equal arches, equal to the right-linex g, which would be absurd. And hence we may easily infer, that the centre of the archy x o, is in the tangent linex g. Hence too, we have an easy method of finding a tangent right-line equal to a quadrantal arch: for having the pointsy,ogiven, it is easy to find a third point, ass; and then the circle passing through the three pointso,s,y, shall cut off the tangentx g, equal to the quadrantal archg o. And the pointsmay be speedily obtained, by describing the archg swith a radius, having to the radiusa gthe proportion of 6 to 4; for theng sis the sixth part of its whole circle, and is equal to the archg o. And thus, from this hypothesis, which, I presume, may be as readily admitted as the increments and decrements of lines in fluxions, the quadrature of the circle may be geometrically obtained; for this is easily found, when a right-line is discovered equal to the periphery of a circle. I am well aware the algebraists will consider it as useless, because it cannot be accommodated to the farrago of an arithmetical calculation; but I hope the lovers of the ancient geometry will deem it deserving an accurate investigation; and if they can find no paralogism in the reasoning, will consider it as a legitimate demonstration.

In the circleg o e f, letg obe the quadrantal arch, and the right-lineg xits tangent. Then conceive that the central pointaflows uniformly along the radiusa e, infinitely produced; and that it is endued with an uniform impulsive power. Let it likewise be supposed, that during its flux, radii emanate from it on all sides, which enlarge themselves in proportion to the distance of the pointafrom its first situation. This being admitted, conceive that the pointaby its impulsive power, through the radiia n,a m, &c. acting every where equally on the archg o, impells it into its equal tangent archg r. And when, by its uniform motion along the infinite lineaφ, it has at the same time arrived atb, the centre of the archg r, let it impel in a similar manner the archg r, into its equal tangent archg s, by acting every where equally through radii equal tob r. Now, if this be conceived to take place infinitely (since a circular line is capable of infinite remission) the archg owill at length be unbent into its equal, the tangent lineg x; and the extreme pointo, will describe by such a motion of unbending a circular lineo x. For since the same cause, acting every where similarly and equally, produces every where similar and equal effects; and the archg o, is every where equally remitted or unbent, it will describe a line similar in every part. Now, on account of the simplicity of the impulsive motion, such a line must either be straight or circular; for there are only three lines every where similar, i. e. the right and circular line, and the cylindric helix; but this last, as Proclus well observes in his following Commentary on the fourth definition, is not a simple line, because it is generated by two simple motions, the rectilineal and circular. But the line which bounds more than two equal tangent arches cannot be a right line, as is well known to all geometricians; it is therefore a circular line. It is likewise evident, that this archo xis concave towards the pointg: for if not, it would pass beyond the chordo x, which is absurd. And again, no arch greater than the quadrant can be unbent by this motion: for any one of the radii, asa pbeyondg o, has a tendency from, and not to the tangentg x, which last is necessary to our hypothesis. Now if we conceive another quadrantal arch of the circleg o e f, that isg y, touching the former ingto be unbent in the same manner, the archx yshall be a continuation of the archx o; for ifγ x κbe drawn perpendicular tox g, as in the figure, it shall be a tangent inxto the equal archesy x,x o; because it cannot fall within either, without making the sine of some one of the equal arches, equal to the right-linex g, which would be absurd. And hence we may easily infer, that the centre of the archy x o, is in the tangent linex g. Hence too, we have an easy method of finding a tangent right-line equal to a quadrantal arch: for having the pointsy,ogiven, it is easy to find a third point, ass; and then the circle passing through the three pointso,s,y, shall cut off the tangentx g, equal to the quadrantal archg o. And the pointsmay be speedily obtained, by describing the archg swith a radius, having to the radiusa gthe proportion of 6 to 4; for theng sis the sixth part of its whole circle, and is equal to the archg o. And thus, from this hypothesis, which, I presume, may be as readily admitted as the increments and decrements of lines in fluxions, the quadrature of the circle may be geometrically obtained; for this is easily found, when a right-line is discovered equal to the periphery of a circle. I am well aware the algebraists will consider it as useless, because it cannot be accommodated to the farrago of an arithmetical calculation; but I hope the lovers of the ancient geometry will deem it deserving an accurate investigation; and if they can find no paralogism in the reasoning, will consider it as a legitimate demonstration.

[25]Axioms have a subsistence prior to that of magnitudes and mathematical numbers, but subordinate to that of ideas; or, in other words, they have a middle situation between essential and mathematical magnitude. For of the reasons subsisting in soul, some are more simple and universal, and have a greater ambit than others, and on this account approach nearer to intellect, and are more manifest and known than such as are more particular. But others are destitute of all these, and receive their completion from more ancient reasons. Hence it is necessary (since conceptions are then true, when they are consonant with things themselves) that there should be some reason, in which the axiom asserting,if from equals you take away equals,&c.is primarily inherent; and which is neither the reason of magnitude, nor number, nor time, but contains all these, and every thing in which this axiom is naturally inherent. Vide Syrian. in Arith. Meta. p. 48.

[26]Geometry, indeed, wishes to speculate the impartible reasons of the soul, but since she cannot use intellections destitute of imagination, she extends her discourses to imaginative forms, and to figures endued with dimension, and by this means speculates immaterial reasons in these; and when imagination is not sufficient for this purpose, she proceeds even to external matter, in which she describes the fair variety of her propositions. But, indeed, even then the principal design of geometry is not to apprehend sensible and external form, but that interior vital one, resident in the mirror of imagination, which the exterior inanimate form imitates, as far as its imperfect nature will admit. Nor yet is it her principal design to be conversant with the imaginative form; but when, on account of the imbecility of her intellection, she cannot receive a form destitute of imagination, she speculates the immaterial reason in the purer form of the phantasy; so that her principal employment is about universal and immaterial forms. Syrian. in Arist. Meta. p. 49.

[27]Syrianus, in his excellent Commentary on Aristotle’s Metaphysics, (which does not so much explain Aristotle, as defend the doctrine of ideas, according to Plato, from the apparent if not real opposition of Aristotle to their existence), informs us that it is the business of wisdom, properly so called, to consider immaterial forms or essences, and their essential accidents. By the method of resolution receiving the principles of being; by a divisive and and definitive method, considering the essences of all things; but by a demonstrative process, concluding concerning the essential properties which substances contain. Hence (says he) because intelligible essences are of the most simple nature, they are neither capable of definition nor demonstration, but are perceived by a simple vision and energy of intellect alone. But middle essences, which are demonstrable, exist according to their inherent properties: since, in the most simple beings, nothing is inherent besides their being. On which account we cannot say thatthisis their essence, andthatsomething else; and hence they are better than definition and demonstration. But in universal reasons, considered by themselves, and adorning a sensible nature, essential accidents supervene; and hence demonstration is conversant with these. But in material species, individuals, and sensibles, such things as are properly accidents are perceived by the imagination, and are present and absent without the corruption of their subjects. And these again being worse than demonstrable accidents, are apprehended by signs, not indeed by a wise man, considered as wise, but perhaps by physicians, natural philosophers, and all of this kind.

[28]See Note to Chap. i. Book i. of the ensuing Commentaries.

[29]Page 227.

[30]Page 250.

[31]Methodus hæc cum algebrâ speciosâ facilitate contendit, evidentiâ vero et demonstrationum elegantiâ eam longe superare videtur: ut abunde constabit, si quis conferat hanc Apollonii doctrinamde Sectione Rationiscum ejusdem Problematis Analysi Algebraicâ, quam exhibuit clarissimus Wallisius, tom. ii. Operum Math. cap. liv. p. 220.

[32]Verum perpendendum est, aliud esse problema aliqualiter resolutum dare, quod modis variis, plerumque fieri potest, aliud methodo elegantissimâ ipsum efficere; Analysi brevissimâ et simul perspicuâ, Synthesi concinnâ et minime operosâ.

[33]In his Mathematical Lectures, p. 44.

[34]Lib. iv.

[35]Lib. i. p. 30.

[36]In Theæteto.

[37]In his most excellent work on Abstinence, lib. i. p. 22, &c.

[38]See the Excerpta of Ficinus from Proclus, on the first Alcibiades of Plato; his Latin version only of which is extant. Ficini Opera, tom. ii.

[39]Marinus, the author of the ensuing life, was the disciple of Proclus; and his successor in the Athenian school. His philosophical writings were not very numerous, and have not been preserved. A commentary ascribed to him, on Euclid’s data, is still extant; but his most celebrated work, appears to have been, the present life of his master. It is indeed in the original elegant and concise; and may be considered as a very happy specimen of philosophical biography. Every liberal mind must be charmed and elevated with the grandeur and sublimity of character, with which Proclus is presented to our view. If compared with modern philosophical heroes, he appears to be a being of a superior order; and we look back with regret on the glorious period, so well calculated for the growth of the philosophical genius, and the encouragement of exalted merit. We find in his life, no traces of the common frailties of depraved humanity; no instances of meanness, or instability of conduct: but he is uniformly magnificent, and constantly good. I am well aware that this account of him will be considered by many as highly exaggerated; as the result of weak enthusiasm, blind superstition, or gross deception: but this will never be the persuasion of those, who know by experience what elevation of mind and purity of life the Platonic philosophy is capable of procuring; and who truly understand the divine truths contained in his works. And the testimony of the multitude, who measure the merit of other men’s characters by the baseness of their own, is surely not to be regarded. I only add, that our Philosopher flourished 412 years after Christ, according to the accurate chronology of Fabricius; and I would recommend those who desire a variety of critical information concerning Proclus, to the Prolegomena prefixed by that most learned man to his excellent Greek and Latin edition of this work, printed at London in 1703.

[40]Plato in Phædro. Meminit et Plutarch. VIII. Sympos. Suidas in μήτοι. Fabricius.

[41]For a full account of the distribution of the virtues according to the Platonists, consult the sentences of Porphyry, and the Prolegomena of Fabricius to this work.

[42]See the sixth book of his Republic, and the Epinomis.

[43]We are informed by Fabricius, that the Platonic Olympiodorus in his MS. Commentary on the Alcibiades of Plato, divides the orders of the Gods, into ὑπερκόσμιοι, or super-mundane, which are separate from all connection with body; and into ἐγκόσμιοι, or mundane. And that of these, some are οὐράνιοι, or celestial, others αἰθέριοι, or, or etherial, or πύριοι, fiery, others ἀέριοι, or aerial, others ἔνυδροι, or watry, others χθόνιοι, or earthly; and others ὑποταρτάριοι, or subterranean. But among the terrestrial, some are κλιματάρχαι, or governors of climates, others πολιοῦχοι, or rulers over cities, and others lastly κατοικίδιοι, or governors of houses.

[44]This epithet is likewise ascribed by Onomacritus to the Moon, as may be seen in his hymn to that deity; and the reason of which we have given in our notes to that hymn.

[45]Divine visions, and extraordinary circumstances, may be fairly allowed to happen to such exalted geniuses as Proclus; but deserve ridicule when ascribed to the vulgar.

[46]What glorious times! when it was considered as an extraordinary circumstance for a teacher of rhetoric to treat a noble and wealthy pupil as his domestic. When we compare them with the present, we can only exclaim,O tempora! O mores!Philosophy sunk in the ruins of ancient Greece and Rome.

[47]Fabricius rightly observes, that this Olympiodorus is not the same with the Philosopher of that name, whose learned commentaries, on certain books of Plato, are extant in manuscript, in various libraries. As in these, not only Proclus himself, but Damascius, who flourished long after Proclus, is celebrated.

[48]Concerning the various mathematicians of this name, see Fabricius in Bibliotheca Græca.

[49]The word in the original is λογικὰ, which Fabricius rightly conjectures has in this place a more extensive signification than either Logic, or Rhetoric: but I must beg leave to differ from that great critic, in not translating it simplyphilosophical, as I should rather imagine, Marinus intended to confine it to that part of Aristotle’s works, which comprehends only logic, rhetoric, and poetry. For the verb ἐξεμάνθανω, orto learn, which Marinus uses on this occasion, cannot with propriety be applied to the more abstruse writings of Aristotle.

[50]Hence Proclus was called, by way of eminence, διάδοχος Πλατωνικός, or the Platonic Successor.

[51]Concerning Polletes, see Suidas; and for Melampodes, consult Fabricius in Bibliotheca Græca.

[52]This Syrianus was indeed a most excellent philosopher, as we may be convinced from his commentary on the metaphysics of Aristotle, a Latin translation only of which, by one Hieronimus Bagolinus, was published at Venice in 1558. The Greek is extant, according to Fabricius, in many of the Italian libraries, and in the Johannean library at Hamburg. According to Suidas, he writ a commentary on the whole of Homer in six books; on Plato’s politics, in four books; and on the consent of Orpheus, Pythagoras, and Plato, with the Chaldean Oracles, in ten books. All these are unfortunately lost; and the liberal few, are by this means deprived of treasures of wisdom, which another philosophical age, in some distant revolution, is alone likely to produce.

[53]Socrates, in the 6th book of Plato’s Republic, says, that from great geniuses nothing of a middle kind must be expected; but either great good, or great evil.

[54]The reader will please to take notice, that this great man is not the same with Plutarch the biographer, whose works are so well known; but an Athenian philosopher of a much later period.

[55]Aristotle’s philosophy, when compared with the discipline of Plato is, I think, deservedly considered in this place as bearing the relation of the proteleia to the epopteia in sacred mysteries. Now the proteleia, or things previous to perfection, belong to the initiated, and the mystics; the former of whom were introduced into some lighter ceremonies only: but the mystics, were permitted to be present with certain preliminary and lesser sacred concerns. On the other hand, the epoptæ were admitted into the sanctuary of the greater sacred rites; and became spectators of the symbols, and more interior ceremonies. Aristotle indeed appears to be every where an enemy to the doctrine of ideas, as understood by Plato; though they are doubtless the leading stars of all true philosophy. However, the great excellence of his works, considered as an introduction to the divine theology of Plato, deserves the most unbounded commendation. Agreeable to this, Damascius informs us that Isidorus the philosopher, “when he applied himself to the more holy philosophy of Aristotle, and saw that he trusted more to necessary reasons than to his own proper sense, yet did not entirely employ a divine intellection, was but little solicitous about his doctrine: but that when he had tasted of Plato’s conceptions, he no longer deigned to behold him in the language of Pindar. But hoping he should obtain his desired end, if he could penetrate into the sanctuary of Plato’s mind, he directed to this purpose the whole course of his application.” Photii Bibliotheca. p. 1034.

[56]according to the oracle.

[57]Nothing is more celebrated by the ancients than that strict friendship which subsisted among the Pythagoreans; to the exercise of which they were accustomed to admonish each other,not to divide the god which they contained, as Jamblichus relates, lib. i. c. 33. De Vita Pythagoræ. Indeed, true friendship can alone subsist in souls, properly enlightened with genuine wisdom and virtue; for it then becomes an union of intellects, and must consequently be immortal and divine.

[58]Pythagoras, according to Damascius, said, that friendship was the mother of all the political virtues.

[59]A genuine modern will doubtless consider the whole of Proclus’ religious conduct as ridiculously superstitious. And so, indeed, at first sight, it appears; but he who has penetrated the depths of ancient wisdom, will find in it more than meets the vulgar ear. The religion of the Heathens, has indeed, for many centuries, been the object of ridicule and contempt: yet the author of the present work is not ashamed to own, that he is a perfect convert to it in every particular, so far as it was understood and illustrated by the Pythagoric and Platonic philosophers. Indeed the theology of the ancient, as well as of the modern vulgar, was no doubt full of absurdity; but that of the ancient philosophers, appears to be worthy of the highest commendations, and the most assiduous cultivation. However, the present prevailing opinions, forbid the defence of such a system; for this must be the business of a more enlightened and philosophic age. Besides, the author is not forgetful of Porphyry’s destiny, whose polemical writings were suppressed by the decrees of emperors; and whose arguments in defence of his religion were so very futile and easy of solution, that, as St. Hierom informs us, in his preface on Daniel, Eusebius answered him in twenty-five, and Apollinaris in thirty volumes!

[60]See Proclus on Plato’s Politics, p. 399. Instit. Theolog. num. 196; and the extracts of Ficinus from Proclus’s commentary on the first Alcibiades, p. 246. &c.

[61]Alluding to the beautiful description given of Ulysses, in the 3d book of the Iliad, v. 222.Καί ἔπεα νιφάδεσιν ἐοικότα χειμερίησιν.Which is thus elegantly paraphrased by Mr. Pope.But when he speaks, what elocution flows!Soft as the fleeces of descending snowsThe copious accents fall, with easy art;Melting they fall, and sink into the heart! &c.

[61]Alluding to the beautiful description given of Ulysses, in the 3d book of the Iliad, v. 222.

Καί ἔπεα νιφάδεσιν ἐοικότα χειμερίησιν.

Which is thus elegantly paraphrased by Mr. Pope.

But when he speaks, what elocution flows!Soft as the fleeces of descending snowsThe copious accents fall, with easy art;Melting they fall, and sink into the heart! &c.

But when he speaks, what elocution flows!

Soft as the fleeces of descending snows

The copious accents fall, with easy art;

Melting they fall, and sink into the heart! &c.

[62]Concerning Domninus, see Photius and Suidas from Damascius in his Life of Isidorus.

[63]Nicephorus, in his commentary on Synesius de Insomniis, p. 562. informs us, that the hecatic orb, is a golden sphere, which has a sapphire stone included in its middle part, and through its whole extremity, characters and various figures. He adds, that turning this sphere round, they perform invocations, which they call Jyngæ. Thus too, according to Suidas, the magician Julian of Chaldea, and Arnuphis the Egyptian, brought down showers of rain, by a magical power. And by an artifice of this kind, Empedocles was accustomed to restrain the fury of the winds; on which account he was called ἀλεξάνεμος, or a chaser of winds.

[64]No opinion is more celebrated, than that of the metempsychosis of Pythagoras: but perhaps, no doctrine is more generally mistaken. By most of the present day it is exploded as ridiculous; and the few who retain some veneration for its founder, endeavour to destroy the literal, and to confine it to an allegorical meaning. By some of the ancients this mutation was limited to similar bodies: so that they conceived the human soul might transmigrate into various human bodies, but not into those of brutes; and this was the opinion of Hierocles, as may be seen in his comment on the Golden Verses. But why may not the human soul become connected with subordinate as well as with superior lives, by a tendency of inclination? Do not similars love to be united; and is there not in all kinds of life, something similar and common? Hence, when the affections of the soul verge to a baser nature, while connected with a human body, these affections, on the dissolution of such a body, become enveloped as it were, in a brutal nature, and the rational eye, in this case, clouded with perturbations, is oppressed by the irrational energies of the brute, and surveys nothing but the dark phantasms of a degraded imagination. But this doctrine is vindicated by Proclus with his usual subtilty, in his admirable commentary on the Timæus, lib. v. p. 329, as follows, “It is usual, says he, to enquire how souls can descend into brute animals. And some, indeed, think that there are certain similitudes of men to brutes, which they call savage lives: for they by no means think it possible that the rational essence can become the soul of a savage animal. On the contrary, others allow it may be sent into brutes, because all souls are of one and the same kind; so that they may become wolves and panthers, and ichneumons. But true reason, indeed, asserts that the human soul way be lodged in brutes, yet in such a manner, as that it may obtain its own proper life, and that the degraded soul may, as it were, be carried above it, and be bound to the baser nature, by a propensity and similitude of affection. And that this is the only mode of insinuation, we have proved by a multitude of reasons, in our commentaries on the Phædrus. But if it is requisite to take notice, that this is the opinion of Plato, we add, that in his politics, he says, that the soul of Thersites assumed an ape, but not the body of an ape: and in the Phædrus, that the soul descends into a savage life, but not into a savage body; for life is conjoined with its proper soul. And in this place he says it is changed into a brutal nature: for a brutal nature is not a brutal body, but a brutal life.”

[65]Pericles Lydus, a Stoic philosopher.

[66]Vide Pausan. lib. i. Atticorum, cap. 21. et 20.

[67]He means the Christians.

[68]Proclus was born in the year of Christ 412, on the 6th of the Ides of February. But, for the sake of the astrologers, I have subjoined the following figure from the Prolegomena of Fabricius to this life: and though I am not skilled in the art myself, I am persuaded, from the arguments of Plotinus, that it contains many general truths; but when made subservient to particulars, is liable to great inaccuracy and error. In short, its evidence is wholly of a physiognomic nature; for such is the admirable order and connection of things, that throughout the universe, one thing is signified by another, and wholes are after a manner contained in their parts. So that the language of the obscure and profound Heraclitus is perfectly just, when he says, “You must connect the perfect and the imperfect, the agreeing and the disagreeing, the consonant and the dissonant, and out of one all things, and out of all things one.”A Scheme of the situation of the Stars, such as it was at Byzantium, when the philosopher Proclus was born.

A Scheme of the situation of the Stars, such as it was at Byzantium, when the philosopher Proclus was born.

[69]It was formerly the custom of almost all nations, to have their burial places in the suburbs, and not in the city itself.

[70]This eclipse happened, according to Fabricius, in A. C. 484. 19 Cal. Feb. at sun-rise.

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