[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 simply _philosophical_, 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, or _to 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 [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 [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 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.”
Illustration: 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.
[71] All the ancient theologists, among whom Plato holds a distinguished rank, affirmed that the soul was of a certain middle nature and condition between intelligibles and sensibles: agreeable to which doctrine, Plotinus divinely asserts that she is placed in the horizon, or in the boundary and isthmus, as it were, of eternal and mortal natures; and hence, according to the Magi, she is similar to the moon, one of whose parts is lucid, but the other dark. Now the soul, in consequence of this middle condition, must necessarily be the receptacle of all middle energies, both vital and gnostic; so that her knowledge is inferior to the indivisible simplicity of intellectual comprehension, but superior to the impulsive perceptions of sense.
Hence the mathematical genera and species reside in her essence, as in their proper and natural region; for they are entirely of a middle nature, as Proclus proves in this and the sixth following chapter.
But this doctrine of Plato’s, originally derived from Brontinus and Archytas, is thus elegantly explained by that philosopher, in the concluding part of the sixth 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 say the heavens, lest I should deceive you by the name. You comprehend then, these two orders of things, I mean the visible and the intelligible?--Glauco. I do.--Socrates. Continue this division then, as if it were a line divided into two unequal segments; and each part again, i. e. the sensible and intelligible, divided after a similar manner, and you will have evidence and obscurity placed by each other. In the visible segment, indeed, one part will contain images. But I call images, in the first place, shadows; afterwards, the resemblances 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 section comprehends the things, of which these images are nothing more than similitudes, such as the animals around us, together with plants, and whatever is the work of nature and art.--Glauco. I conceive it.--Socrates. Do you consider this section then, as divided into true and false? And that the hypothesis of opinion is to the knowledge of science, as a resemblance to its original?--Glauco. I do, very readily.--Socrates. Now then, consider how the section of the intelligible is to be divided.--Glauco. How?--Socrates. Thus: one segment is that which the soul enquires after, using the former divisions as images, and compelled to proceed from hypotheses, not to the principle, but to the conclusion. The other is that which employs the cogitative power of the soul, as she proceeds from an hypothesis to a principle no longer supposed, and, neglecting images, advances through their _obscurity_ into _the light of_ ideas themselves.--Glauco. I do not, in this, sufficiently understand you.--Socrates. But again, for you will more easily understand me from what has been already premised. I think you are not ignorant, that those who are conversant in geometry, arithmetic, and the like, suppose even and odd, together with various figures, and the three species of angles, and other things similar to these, according to each method of proceeding. Now, having established these, as hypotheses sufficiently known, they conceive that no reason is to be required for their position: but beginning from these, they descend through the rest, and arrive at last, at the object of their investigation.--Glauco. This I know perfectly well.--Socrates. This also you know, that they use visible forms, and make them the subject of their discourse, at the same time not directing their intellect to the perception of these, but to the _originals_ they resemble; I mean the square itself, and the diameter itself; and not to the figures they delineate. And thus, other forms, which are represented by shadows and images in water, are employed by them, merely as resemblances, while they strive to behold that which can be seen by cogitation alone.--Glauco. You speak the truth.--Socrates. This is what I called above a species of the intelligible, in the investigation of which, the soul was compelled to use hypotheses; not ascending to the principle, as incapable of rising above hypotheses, but using the images formed from inferior objects, to a similitude of such as are superior, and which are so conceived and distinguished by opinion, as if they perspicuously contributed to the knowledge of things themselves.--Glauco. I understand indeed, that you are speaking of the circumstances which take place in geometry, and her kindred arts.--Socrates. Understand now, that by the other section of the intelligible, I mean that which reason herself reaches, by her power of demonstrating, when no longer esteeming hypotheses for principles, but receiving them in reality for hypotheses, she uses them as so many steps and handles in her ascent, until she arrives at that which is no longer hypothetical, the principle of the universe; and afterwards descending, holding by ideas which adhere to the principle, she arrives at the conclusion, employing nothing sensible in her progress, but proceeding through ideas, and in these at last terminating her descent.--Glauco. I understand you, but not so well as I desire: for you seem to me to propose a great undertaking. You endeavour, indeed, to determine that the portion of true being and intelligible, which we speculate by the science of demonstration, is more evident than the discoveries made by the sciences called arts; because in the first hypotheses are principles, and their masters are compelled to employ the eye of cogitation, and not the perceptions of the senses. Yet, because they do not ascend to the principle, but investigate from hypotheses, they seem to you not to have intelligence concerning these, though they are intelligible, through the light of the principle. But you seem to me to call the habit of reasoning on geometrical and the like concerns, cogitation, rather than intelligence, as if cogitation held the middle situation between opinion and intellect.--Socrates. You understand me sufficiently well.
And again: with these four proportions take these four corresponding affections of the soul: with the highest intelligence; with the second cogitation; against the third set opinion; and against the fourth assimilation, or imagination. Besides this, establish them in the order of alternate proportion, so that they may partake of evidence, in the same manner as their corresponding objects participate of reality.” I have taken the liberty of translating this fine passage differently from both Petvin and Spens; because they have neglected to give the proper meaning of the word διάνοια, or cogitation, the former translating it _mind_, and the _eye of the mind_, and by this means confounding it with intellect; and the latter calling it _understanding_. But it is certain that Plato, in this place, ranks intellect as the first, on account of the superior 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 διάνοια, or cogitation, in the present work, is understood that power of the soul which reasons from premises to conclusions, and whose syllogistic energy, on active subjects, is called prudence; and on such as are speculative, science. But for farther information concerning its nature, see the dissertation prefixed to this work, and the following fifth chapter.
[72] These two principles, _bound_ and _infinite_, will doubtless be considered by the unthinking part of mankind, as nothing more than general terms, and not as the most real of beings.
However, an accurate contemplation of the universe, will convince every _truly_ philosophic mind of their reality. For the heavens themselves, by the coherence and order of their parts, evince their participation of bound. But by their prolific powers, and the unceasing revolutions of the orbs they contain, they demonstrate their participation of _infinity_. And the finite and perpetually abiding forms with which the world is replete, bear a similitude _to bound_: while, on the contrary, the variety of particulars, their never-ceasing mutation, and the connection of more and less in the communion of forms, represents an image of _infinity_. Add too, that every natural species, by its form is similar to _bound_; but by its matter, to _infinity_. For these two, form and matter, depend on _bound_ and _infinity_, and are their ultimate progressions. And each of these, indeed, participates of unity; but form is the measure and bound of matter, and is more _one_. But matter is in capacity all things, because it subsists by an emanation from the first capacity, or the _infinite itself_.
[73] Of human disciplines, those alone deserve to be called sciences which use no hypotheses, which resolve things into their principles, which are conversant with true being, and elevate us to ideas themselves. Dialectic is wholly of this kind (I mean the dialectic of Plato); for this alone uses no suppositions, but, neglecting shadows and images, raises us, by a sublime investigation, to the principle of the universe; and on this account, deserves to be called the very apex of disciplines. But we must not imagine, that by the word dialectic here, is meant logic, or any part of logic, or that method of disputation, by which we fabricate probable reasons; but we must conceive it as signifying a discipline, endued with the greatest acuteness; neglecting all hypotheses, truly soaring to primary causes, and ultimately reposing in their contemplation. Plotinus has given us most happy specimens of this method, in his books _on the genera of being_.
[74] See note to the first chapter.
[75] I would particularly recommend this chapter to modern mathematicians, most of whom, I am afraid, have never considered whether or not the subjects of their speculation have any real subsistence: though it is surely an enquiry worthy the earnest attention of every liberal mind. For if the objects of mathematical investigation are merely imaginary, I mean the point without parts, the line without breadth, &c. the science, founded on these false principles, must of course be entirely delusive. Indeed, an absolutely true conclusion, can never flow from an erroneous principle, as from its cause: as the stream must always participate of its source. I mean such a conclusion as is demonstrated by the proper cause, πλὴν οὐ διότι, ἀλλ’ ὅτι, says Aristotle, in his first Analytics; that is, a syllogism from false principles will not prove the _why_, but only simply _that it is_: indeed it can only simply prove _that it is_, to him who admits the false propositions; because he who allows the premises, cannot deny the conclusion, when the syllogism is properly constructed. Thus we way syllogize in the first figure, Every thing white, is an animal: Every bird is white: Therefore, Every bird is an animal.
And the conclusion will be true, though the major and minor terms are false; but then these terms are not the causes of the conclusion, and we have an inference without a proof. In like manner, if mathematical species are delusive and fictitious, the conclusions deduced from them as principles, are merely hypothetical, and not demonstrative.
[76] Aristotle, in his last Analytics. The reader will please to observe, that the whole force of this nervous, accurate, and elegant reasoning, is directed against Aristotle; who seems unfortunately to have considered, with the moderns, that mathematical species subsist in the soul, by an abstraction from sensibles. See the preceding Dissertation.
Proclus’s excellent Commentary on the Timæus.
[78] Plato frequently, both in the Meno and elsewhere, shews that science is Reminiscence; and I think not without the strongest reason. For since the soul is immaterial, as we have demonstrated in the dissertation to this work, she must be truly immortal, i. e.
both _a parte ante_, & _a parte post_. That she must be eternal, indeed, with respect to futurity, if immaterial, is admitted by all; and we may prove, with Aristotle, in his first book de Cœlo, that she is immortal, likewise _a parte ante_, as follows.
Every thing without generation, is incorruptible, and every thing incorruptible, is without generation: for that which is without generation, has a necessity of existing infinitely _a parte ante_ (from the hypothesis); and therefore, if it possesses a capacity of being destroyed, since there is no greater reason why it should be corrupted now, rather than in some former period, it is endued with a capacity of being destroyed and ceasing to be, in every instant of infinite time, in which it necessarily is. In like manner, that which is incorruptible, has a necessity of existing infinitely _a parte post_; therefore, if it possesses a capacity of being generated, since there is no greater reason why it should be generated now rather than afterwards, it possesses a capacity of being generated, in every instant of time, in which it necessarily is. If then the soul is essentially immortal, with respect to the past and future circulations of time; and if she is replete with forms or ideas of every kind, as we have proved in the dissertation, she must, from her circulating nature, have been for ever conversant in alternately possessing and losing the knowledge of these. Now, the recovery of this knowledge by science, is called by Plato, reminiscence; and is nothing more than a renewed contemplation of those divine forms, so familiar to the soul, before she became involved in the dark vestment of an earthly body. So that we may say, with the elegant Maximus Tyrus, (Disser.
28.) “Reminiscence is similar to that which happens to the corporeal eye, which, though always endued with a power of vision, yet darkness sometimes obstructs its passage, and averts it from the perception of things. Art therefore, approaches, which though it does not give to the eye the power of vision, yet removes its impediments, and affords a free egress to its rays. Conceive now, that our rational soul is such a power of perceiving, which sees and knows the nature of beings. To this the common calamity of bodies happens, that darkness spreading round it, hurries away its aspect, blunts its sharpness, and extinguishes its proper light. Afterwards, the art of reason approaches, which, like a physician, does not bring or afford it a new science, but rouses that which it possesses, though very slender, confused, and unsteady.”
Hence, since the soul, by her immersion in body, is in a dormant state, until she is roused by science to an exertion of her latent energies; and yet even previous to this awakening, since she contains the vivid sparks, as it were, of all knowledge, which only require to be ventilated by the wings of learning, in order to rekindle the light of ideas, she may be said in this case to know all things as in a dream, and to be ignorant of them with respect to vigilant perceptions. Hence too, we may infer that time does not antecede our essential knowledge of forms, because we possess it from eternity: but it precedes our knowledge with respect to a production of these reasons into perfect energy. I only add, that I would recommend the liberal English reader, to Mr. Sydenham’s excellent translation of Plato’s Meno, where he will find a familiar and elegant demonstration of the doctrine of Reminiscence.
[79] Concerning this valuable work, entitled ΙΕΡΟ‘Σ ΛΟΓΟ’Σ, see the Bibliotheca Græca of Fabricius, vol. i. p. 118 and 462, and in the commentary of Syrianus on Aristotle’s metaphysics, p. 7, 71, 83, and 108, the reader will find some curious extracts from this celebrated discourse; particularly in p. 83. Syrianus informs us, “that he who consults this work will find all the orders both of Monads and Numbers, without neglecting one, fully celebrated (ὐμνουμένας.)” There is no doubt, but that Pythagoras and his disciples concealed the sublimest truths, under the symbols of numbers; of which he who reads and understands the writings of the Platonists will be fully convinced.
Hence Proclus, in the third book of his excellent commentary on the Timæus, observes, “that Plato employed mathematical terms for the sake of mystery and concealment, as certain veils, by which the penetralia of truth might be secluded from vulgar inspection, just as the theologists made fables, but the Pythagoreans symbols, subservient to the same purpose: for in images we may speculate their exemplars, and the former afford us the means of access to the latter.”
[80] Concerning this Geometric Number, in the 8th book of Plato’s Republic, than which Cicero affirms there is nothing more obscure, see the notes of Bullialdus to Theo. p. 292.
[81] I am sorry to say, that this part of the enemies to pure geometry and arithmetic, are at the present time very numerous; conceptions of utility in these sciences, extending no farther than the sordid purposes of a mere animal life. But surely, if intellect is a part of our composition, and the noblest part too, there must be an object of its contemplation; and this, which is no other than truth in the most exalted sense, must be the most noble and useful subject of speculation to every rational being.
[82] In the 13th book of his Metaphysics, cap. iii.
[83] In. I. De Partib. Animalium, et in primo Ethic. cap. iii.
[84] See more concerning this in the Dissertation.
[85] Since number is prior to magnitude, the demonstrations of arithmetic must be more intellectual, but those of geometry more accommodated to the rational power. And when either arithmetic or geometry is applied to sensible concerns, the demonstrations, from the nature of the subjects, must participate of the obscurity of opinion.
If this is the case, a true mathematician will value those parts of his science most, which participate most of evidence; and will consider them as degraded, when applied to the common purposes of life.
[86] This division of the mathematical science, according to the Pythagoreans, which is nearly coincident with that of Plato, is blamed by Dr. Barrow in his Mathematical Lectures, p. 15. as being confined within too narrow limits: and the reason he assigns for so partial a division, is, “because, in Plato’s time, others were either not yet invented, or not sufficiently cultivated, or at least were not yet received into the number of the mathematical sciences.” But I must beg leave to differ from this most illustrious mathematician in this affair; and to assert that the reason of so confined a distribution (as it is conceived by the moderns) arose from the exalted conceptions these wise men entertained of the mathematical sciences, which they considered as so many preludes to the knowledge of divinity, when properly pursued; but they reckoned them degraded and perverted, when they became mixed with sensible objects, and were applied to the common purposes of life.
[87] That is, a right and circular line.
[88] I am afraid there are few in the present day, who do not consider tactics as one of the most principal parts of mathematics; and who would not fail to cite, in defence of their opinions, that great reformer of philosophy, _as he is called_, Lord Bacon, commending pursuits which come home to men’s businesses and bosoms. Indeed, if what is lowest in the true order of things, and best administers to the vilest part of human nature, is to have the preference, their opinion is right, and Lord Bacon is a _philosopher_!
[89] By this is to be understood the art new called Perspective: from whence it is evident that this art was not unknown to the ancients, though it is questioned by the moderns.
[90] From hence it appears, that it is doubtful whether Plato is the author of the dialogue called Epinomis; and I think it may with great propriety be questioned. For though it bears evident marks of high antiquity, and is replete with genuine wisdom, it does not seem to be perfectly after Plato’s manner; nor to contain that great depth of thought with which the writings of this philosopher abound. Fabricius (in his Bibliotheca Græca, lib. i. p. 27.) wonders that Suidas should ascribe this work to a philosopher who distributed Plato’s laws into twelve books, because it was an usual opinion; from whence it seems, that accurate critic had not attended to the present passage.
[91] This proximate conjunction of the mathematical sciences, which Proclus considers as subordinate to dialectic, seems to differ from that vertex of science in this, that the former merely embraces the principles of all science, but the latter comprehends the universal genera of being, and speculates the principle of all.
[92] In the Meno.
[93] This is certainly the true or philosophical employment of the mathematical science; for by this means we shall be enabled to ascend from sense to intellect, and rekindle in the soul that divine light of truth, which, previous to such an energy, was buried in the obscurity of a corporeal nature. But by a contrary process, I mean, by applying mathematical speculations, to experimental purposes, we shall blind the liberal eye of the soul, and leave nothing in its stead but the darkness of corporeal vision, and the phantoms of a degraded imagination.
[94] The design of the present chapter is to prove that the figures which are the subjects of geometric speculation, do not subsist in external and sensible matter, but in the receptacle of imagination, or the matter of the phantasy. And this our philosopher proves with his usual elegance, subtilty, and depth. Indeed, it must be evident to every attentive observer, that sensible figures fall far short of that accuracy and perfection which are required in geometrical definitions: for there is no sensible circle perfectly round, since the point from which it is described is not without parts; and, as Vossius well observes, (de Mathem. p. 4.) there is not any sphere in the nature of things, that only touches in a point, for with some part of its superficies it always touches the subjected plane in a line, as Aristotle shews Protagoras to have objected against the geometricians. Nor must we say, with that great mathematician Dr.
Barrow, in his Mathematical Lectures, page 76, “that all imaginable geometrical figures, are really inherent in every particle of matter, in the utmost perfection, though not apparent to sense; just as the effigies of Cæsar lies hid in the unhewn marble, and is no new thing made by the statuary, but only is discovered and brought to sight by his workmanship, i. e. by removing the parts of matter by which it is overshadowed and involved. Which made Michael Angelus, the most famous carver, say, _that sculpture was nothing but a purgation from things superfluous. For take all that is superfluous_, (says he) _from the wood or stone, and the rest will be the figure you intend_. So, if the hand of an angel (at least the power of God) should think fit to polish any particle of matter, without vacuity, a spherical superficies would appear to the eyes, of a figure exactly round; not as created anew, but as unveiled and laid open from the disguises and covers of its circumjacent matter.” For this would be giving a perfection to sensible matter, which it is naturally incapable of receiving: since external body is essentially full of pores and irregularities, which must eternally prevent its receiving the accuracy of geometrical body, though polished by the hand of an angel. Besides, what polishing would ever produce a point without parts, and a line without breadth?
For though body may be reduced to the greatest exility, it will not by this means ever pass into an incorporeal nature, and desert its triple dimension. Since external matter, therefore, is by no means the receptacle of geometrical figures, they must necessarily reside in the catoptric matter of the phantasy, where they subsist with an accuracy sufficient for the energies of this science. It is true, indeed, that even in the purer matter of imagination, the point does not appear