Chapter XXI: Appendix (1)

When I first determined to give my labours to the public, in hopes of contributing to the restoration of the Platonic philosophy, I embraced the resolution of Dr. Johnson and Goldsmith, _to set the Reviewers at defiance_. For I was fully convinced that neither able criticism, nor candid attention could be expected, where composition is dictated by the spirit of malevolence, and influenced by the views of pecuniary reward. However, though contempt is the most philosophical mode of revenge, yet as a certain author well observes severe retaliation is sometimes requisite, in order to convince the subjects of our revenge, that we do not stoop to the meanness of abject submission. This mode of retaliation the defamation of the _Monthly Reviewers_ in their _bundle of criticism_ for August last obliges me to adopt: and they have afforded me in this review the most favourable opportunity I could desire, of exposing their _malevolence_, _ignorance_, and _pride_. I shall begin, therefore, with instancing their _malevolence_, as it is the first in our list of their bad qualities, and is the general characteristic of these assuming critics. In my preface to the translation of Orpheus, after representing the difficulty of well translating the compound epithets of the Greek, into English, and the necessity of possessing the philosophic genius for this purpose. I add: “_If some sparks of this celestial fire, shall appear to have animated the bosom of the translator, he will consider himself as well rewarded for his laborious undertaking_.” Upon which these _candid_ reviewers observe, (p. 138.) “Mr. Taylor was aware of this difficulty, though he seems to claim the merit of subduing it.” In the second place they assert, (p. 138.) that after lamenting, that the Commentary of Proclus on Plato’s Cratylus is not likely to be published, “I comfort myself with the hope that my own labours will in some measure supply its place, by opening the pure sources of genuine wisdom. And that to this end I promise copious and truly philosophic notes.” Now the passage which furnished this malevolent assertion is the following: “What farther light we have been able to throw on these mysterious remains of antiquity, will appear in our following notes. If the valuable Commentary of Proclus on the Cratylus of Plato, was once published, I am persuaded we should find them full of the most recondite theology: but as this is not to be expected in the present age, the lovers of wisdom will I doubt not gratefully accept the preceding and subsequent elucidations. _For on a subject so full of obscurity as the present, a glimmering light, is as conspicuous, and as agreeable to the eye of the mind, as a small spark in profound darkness, is to the corporeal sight._” Dissertation, p. 106. The infamy of such misrepresentation is too glaring to require any illustration, too shameful to admit of any excuse, and in any other cause than that of verbal criticism, too contemptible either to rouse resentment, or deserve the most trifling attention. Let us now examine the specimens of _ignorance_ which these Reviewers afford in great abundance; and which as I presume will appear much to the credit of my translation. In the first place I am charged with “universally translating the epithets φιλένθεος, φίλοιϛτρος, and μανικός, by the word _fanatic_, which I have employed in the sense of the Latin word, from which it is derived.” To which I reply, that the former part of this charge is false. For in the hymn to Minerva φιλοιϛρος is translated _rage_; in the hymn to Diana, _fierce_; and in the hymn to Dionysius Bassareus, μανικὸς is translated _furious_. [The latter part of this assertion is true. For as the word _fanatic_ is immediately derived from the Latin word _fanaticus_, which according to their own confession means _numine afflatus_, or _one inspired by a divine power_; and as the great Scaliger, whose authority is always decisive, constantly translates φιλένθεος, _fanaticus_, I made no scruple of adopting it in my translation. That, _fanatic_ is never used in a good sense by any author of repute may perhaps be true: but I see no reason why it should not be employed according to the meaning of its original, especially as there is no other word in our language so expressive of the words to which it corresponds in the Greek. The example of Aristotle, and the greatest men of antiquity sufficiently justifies both the invention of new terms when the poverty of a language requires a supply, and the adoption of old ones in a different sense, when the difficulty of the subject demands verbal innovation. After this I am accused of _totally mistaking_ the meaning of various passages, the greater part of which I shall expose to the view of the reader with a literal translation, and comment; that the ignorance of the _Reviewers_ may appear without that veil which at present screens it from the eyes of the unlearned in Greek. In the hymn to Pluto then, I have translated the following line:

Μοῦνος ἔφυς ἀφανῶν ἔργων φανερῶν τε βραβευτής·
Of unapparent works thou art alone
The dispensator visible and known.

That is, literally, “Thou art alone the dispensator of apparent and unapparent works.” Now there is nothing in my version can be objected to, but the omission of the word _apparent_, which the measure of the verse obliged me to neglect; and which the addition of _visible_ and _known_ in the second line renders superfluous, as the following observations will evince. According to the Orphic theology, _Pluto_ belongs to the same order as the _sun_, and from his subsisting in occult union with this deity, he is celebrated as one and the same: a custom frequent with the Orphic theologists, as is well known to those who are skilled in their writings. Hence considered as the _sun_, he is the dispensator of _apparent_, and as _Pluto_, of _unapparent works_: and thus I presume, I have not _totally mistaken_ the meaning of this line, in celebrating Pluto as a deity _visible and known_. But that the reader may be fully convinced of the truth of this assertion, concerning the occult union between Pluto and the sun, let him attend to the following Orphic verse, preserved by Justin Martyr, (in Cohortat. ad Gentes).

Εἷς ζεὺς, εἷς ᾄδης, εἷς ἥλιος, εἷς διόνυσος·----
i.e. “Jupiter, Pluto, the Sun, and Bacchus are one.”

Again, in the epithet ἀγλαότιμε, it seems I have _totally mistaken_ the meaning of my author, by translating it _honor’d light_. This word means literally _exceedingly honoured_: and the preceding exposition sufficiently proves the propriety of calling _Pluto_, _lucid_. Every reader knows the necessity there is in poetical translations of adding something to the original: and this is always allowed, when the addition is not contrary to the sense of the text, but either expands it, if condensed, or enlightens it, if obscure. I am likewise charged with mistaking the meaning of λόγου θνητοῖσι, προφῆτα, or, _prophet of discourse to mortals_, which I have rendered,

----‘Prophet of discourse.’

Now as this is literal, the mistake must consist in not substituting another word for _prophet_, which might express what the author meant; the _Reviewers_ never dreaming that this word, when properly understood, is perfectly sufficient for the purpose. As they appear, therefore, to be _totally_ ignorant of the original signification of a prophet, I shall subjoin its definition from Festus. “_Prophetas_ dicebant veteres antistites fanorum, oraculorumque interpretes:” i.e. “the ancients called prophets the priests of fanes, and the _interpreters_ of oracles.” _Prophet of discourse_, therefore, means _interpreter of discourse_: and as this epithet is applied to Mercury, it is doubtless highly proper; if we consider that he first reduced the infinity of voice into bound, by dividing letters into species; and thus truly became the interpreter of speech to mankind. In the hymn to Venus, I have translated,

Εἴτ’ ἐν Κύπρῳ, ἄνασσα τροφῷ σέο----
“Or if in Cyprus with thy mother fair.”

And it is literally “_Or if in Cyprus O queen, with thy nurse_”. Fortunately for me, the metaphrase of Scaliger agrees with my version, “_Sive in Cupro, matre tua_”. Perhaps the Reviewers forgot, or perhaps they are ignorant, that a mother and a nurse are frequently synonymous terms! I shall not trouble the reader with any more instances of my _mistakes_, as I can faithfully assure him, that the remaining passages adduced by the _Reviewers_, betray _if possible_, more malevolence and ignorance than the present. I shall, therefore, proceed to a defence of some epithets, and expressions which I have employed; and in which these _exquisite critics_, can neither discover _beauty_, nor even _propriety_.

In the first place then, they confess that they have too little _taste_, or too little _knowledge_ to discover either _beauty_, or propriety, in my translation of the following line:

Νύμφαι θυγατέρες μεγαλήτορς Ὠκεανοῖο----
‘Nymphs, who from _ocean’s stream_ derive your birth.’

i.e. literally, ‘Nymphs, daughters of the mighty ocean.’ Now as the exceptionable part of this line, is _ocean’s stream_, as appears by its being printed in _italics_; I can only assure the reader that I can plead no less authority than that of both _Homer_, _Hesiod_, _Plato_, and _Milton_ for its _propriety_ and _beauty_. Thus Homer, (Iliad xviii. l. 606.) speaking of the fabrication of Achilles’ shield by Vulcan, says:

Ἐν δ’ ἐτίθει ποταμοῖο μέγα σθένος ὠκεανοῖο.
i.e. ‘But he placed in it the mighty strength of the _ocean’s
stream_.’

So likewise: (Iliad xx. l. 7.)

Οὔτε τις οὗν ποταμῶν ἀπέην νόσφ’ ὠκεανοῖο.
i.e. ‘No _stream_ was absent, except the _stream of the ocean_.’

Thus again, in the Odyssey: (lib. xi. l. 637.)

Τὴν δὲ κατ’ Ὠκεανὸν ποταμὸν φέρε κῦμα ῥόοιο.

i.e. ‘But the waves of the current bore it (the vessel) through the _ocean stream_.’ And Milton had doubtless an eye to this last passage, when, speaking of the Leviathan, (Paradise Lost, book I.) he says:

----or that sea beast
Leviathan, whom god of all his works
Created hugest, that swim th’ _ocean stream_.

For here, as the reader must observe, he uses the very same expression with Homer. But Milton was not only a great poet, but a man of great learning; and was doubtless much better acquainted with Homer than the Reviewers.

Thus too Hesiod: (in Theog. l. 241. &c.):

----καὶ Δωρίδος ἠϋκόμοιο,
Κούρης Ὠκεανοῖο τελήεντος ποταμοῖο.

i.e. ‘and from the fair haired Doris, the daughter of the perfect _stream_ of the _ocean_.’ And the same epithet is used in l. 959. of the same work. And lastly, Plato in the Phædo, thus speaks of the _ocean_, as one of the four great _rivers_, of which Tartarus is the source: τὰ μὲν οὖν δὴ ἄλλα πολλά τε καὶ μεγάλα καὶ παντοδαπὰ ῥεύματά ἐϛι. τυγχάνει δ’ ἄρα ὄντα ἐν τούτοις τοῖς πολλοῖς τέτταρ’ ἄττα ῥεύματα, ὦν τὸ μὲν μέγιϛον και ἐξωτάτω ῥέον περί κύκλῳ, ὁ καλούμενος Ὠκεανός ἐϛι. i.e. ‘There are many other both great and all-various _rivers_, but principally four; the greatest and last of which, flowing round the earth in a circle, is called the _ocean_.’

I only add that this expression is perfectly philosophical, as will be evident from considering the ever-_flowing_ condition of the ocean, by means of which it admirably corresponds with the nature of a _stream_. Homer indeed was so sensible of this truth, that he generally (if not always) speaks of the ocean in this manner; and there is no doubt, but he derived his conviction from the first and most profound philosophy in the world. After this the expression, a _blameless tide_ of abundance is objected to. But if the epithet _blameless_ may be applied to _abundance_, which it is in the original; (ἠδ’ ὄλβον ἀμεμφῆ) and if a _tide_ of wealth, is an usual expression, I see no reason why abundance, when conferred with moderation, may not be said to be poured in a _blameless tide_. The objections to the translations of (θνητῶν ϛήριγμα) ‘basis of mankind,’ and the first part of the hymn to Protogonus, are too contemptible to deserve any reply. This too would be the case with the epithet ‘_Bacchic King_,’ which is literally translated from the Greek; (Βακχεῖον ἄνακτα) but very fortunately these _sagacious critics_ have employed a correspondent expression, in their Review of Wharton’s Milton: for in page 1. they speak of the _Miltonic muse_, which I presume must fall under the same imputation of _impropriety_, and want of _beauty_ with _Bacchic king_. I shall only adduce one instance more, and then proceed to take notice of the pride of these uncandid and _ignorant_ censors. In the hymn to Boreas, that deity is requested to dissolve the all-_misty station_ of the air:

Λῦέ τε παννέφελον ϛάσιν ἠέρος----

Which I have accordingly translated,

‘The _misty station_ of the air dissolve.’

And I must confess, that as I cannot find the least impropriety in speaking of the air as being in a _misty station_, I must conclude that this was exactly the _station_ of the Reviewers, at the time when they composed the present criticism; the whole of which appears to have been the result of _misty_ visions, _clouded_ conceptions, and _uncertain_ conjectures.

Let us now proceed to a _review_ of their _pride_. In the first place then, they very pompously inform us of their natural gravity as follows: ‘Grave though we be, _our own_ risibility has been provoked,’ &c. As if it was of any consequence to the public, whether they are _grave_ or _facetious_, solemn or _ludicrous_, sanguine or _bilious_: whether they possess the qualities of the _owl_, or the ape; and whether they laugh like the tickled Hyæna, or like Milton’s _death_ ‘grin horribly a ghastly smile.’ In the next place, after having praised my paraphrase of Plotinus on the Beautiful, they add: ‘this praise ought to convince Mr. Taylor, that we are neither insensible to the real value of his author’s work, nor blind to the merits of the translation’. As if the praise of a Reviewer could be of any importance to a man, whose writings, are not calculated for the multitude: or as if the censure of ignorant judges, was not preferable to their most unbounded approbation! I only add that from men who are critics by profession on the writings of others, the most perfect composition may be justly expected: and yet the _Monthly Reviewers_ have grosly failed in this respect, as the following instances will evince: Polybius makes use of the expression, νεύειν πρὸς ἔνα καὶ τὸν αὐτόν σκοπόν, i.e. ‘to verge to one and the same end:’ and this our admirable critics _translate_ (p. 122.) ‘to verge to one _point_, and conspire to one _end_:’ which is obviously a most ridiculous tautology. For it is impossible that any thing can verge to one _point_, and at the same time conspire to an _end_, different from that _point_. Again, in their review of Bell’s Shakespeare, (p. 156.) they make use of the following simile: ‘Shakespeare, now stands (among the French) as a _Colossus_, while the most that can be done by Voltaire, and indeed the very best of our modern writers at home, is to _creep_ under his _feet_.’ But here we may very justly enquire, what similitude there is between _modern wits_ endeavouring to imitate Shakespeare, considered as a _dramatic writer_, and _men_ crawling under his feet, considered as a _Colossus_? If Shakespeare indeed had been a quadruped, men by creeping under his feet might be considered as his _groveling_ imitators: but I cannot conceive any similitude between a _creeping_, and an _upright_ figure. I only add, that the Analytical Reviewers, are not more fortunate in their review of my translation of Proclus. For after asserting that the original is not remarkable for its elegance (though the contrary is the opinion of the best ancient and modern writers) and that I have too faithfully copied my author in this respect, they inform us, among other _interesting_ particulars, ‘that the employment of an ancient philosopher did not consist in relieving the _distresses_ of the _wretched_, and the _wants_ of the _miserable_!’ After such a specimen of tautology, we cannot wonder that Proclus is considered as an inelegant writer: for though his language is always overflowing and majestic, it never degenerates into weak and needless repetition. While on the other hand, there is such a _perfect_ sameness, in the above sentence, that, ‘to relieve the _distresses_ of the _wretched_, and the _wants_ of the _miserable_,’ is indeed no other, than ‘to verge to one _point_, and conspire to one _end_!’

And thus much for the Reviewers, whom in any other cause than that of verbal criticism, I should consider as too mean for censure, and even too insignificant for _contempt_. For what attention can those writers deserve, who decide dogmatically on subjects they have never studied; who endeavour by malevolent aspersions to ruin the reputation of men they have never seen; and who abuse the credulity of the ignorant, by a monthly compilation of criticisms, which originate from vanity, and ultimately tend to illiberal gain?

THE END.

FOOTNOTES:

[1] In the two preceding books of this work our author has displayed an uncommon degree of philosophic elegance and depth; and in the present two, he no less manifests the greatest geometrical accuracy and skill. In the former he elevates us from participated truth to truth itself; and from the glimmering light of universals reflected in the catoptric bosom of the phantasy, to the bright refulgence of ideas. In the latter he combines geometry and philosophy, occasionally cloathes the rigid accuracy of demonstration with the enchanting imagery of divine imaginations, and unites the graces of diction with the precision and sanctity of truth. Yet his genius, though rapid as a torrent, never passes beyond the bounds of propriety; and though his thoughts are vehement and vast, they are at the same time orderly and majestic. For my own part I confess myself enamoured with the grandeur of his diction, astonished with the magnificence of his conceptions, and enlightened by the irradiations of his powerful genius. And I desire nothing so much as that others may experience similar effects from this admirable work. I only add, that the study of this second part is absolutely necessary to a perfect comprehension of Euclid’s method and meaning; and to the understanding geometry completely and philosophically. It is easy indeed to learn a science in a manner sufficient for mechanical purposes; for this is accomplished by the _many_: but it is arduous to learn it with a view to the perception of truth; for this is alone the province of a _few_. It is easy to be knowing in effects, for these are obvious and common; but it is difficult to investigate causes, for these are occult and rare. In short, a general and confused apprehension of a science may be readily obtained, without much labour and toil; but a particular and accurate knowledge requires liberal application, and patient endurance. For the one is like the distant prospect of a country, in which the larger parts are alone conspicuous to the observer’s eye; but the other resembles a near and distinct view, in which every thing is recognized essential to the perfection of the whole.

[2] See the second section of the Dissertation, Vol. I.

[3] The nature of place has been a subject of much curious and deep speculation to the Peripatetic and Platonic philosophers, as may be seen in the very valuable Commentaries of Simplicius on Aristotle’s Physics; so that Proclus does not affirm without reason, that place is more obscure than the natures it contains. But as the opinion of our philosopher, concerning place, is so admirably profound, subtle, and remarkable, I persuade myself the following translation from the fourth book of Simplicius on the Physics, containing his sentiments at large on this subject, will not be unacceptable to the liberal English reader. “Proclus (says Simplicius) having proved from the arguments of Aristotle, that place is neither matter nor form, concludes, that it is a certain interval:” after which, he reasons as follows. “This interval then, is either, nothing or something; and if nothing, local motion will consist in a transition from nothing to nothing; but all motion subsists according to something. But if it ought to be called something, it is either corporeal or incorporeal; and if incorporeal, an absurdity will ensue; for it is necessary that place should be equal to the thing placed. But how can body, and that which is incorporeal be equal? For equal is found in quantities, and especially in those of a similar kind, as lines are equal to lines, superficies to superficies, and bodies to bodies: place, therefore, is body, if it be a certain interval; but if body, it is either moveable or immoveable; and if moveable, in whatever manner it may be moved, it must necessarily be moved according to place, so that place again will require another place, which is impossible, as was also evident to Aristotle and Theophrastus; for Aristotle says, that a vessel is a moveable place, but place an immoveable vessel, because place is naturally immoveable. But if it be immoveable, it is either indivisible, which cannot be divided by the bodies entering its receptacle, since one body cannot penetrate another; or it is divisible, as air and water are divided by the bodies entering into their yielding natures; but if it be divisible, the whole being dissected or divided, the divided parts will be moved on each side, and place will be the first mutable, since its parts are moved; but we have demonstrated that it is immoveable. Again, the parts being separated, we ask where that which is divided betakes itself; for there must be again given or investigated another interval, intervening between the divided parts, which may receive and be placed together with that which is divided; and this will be the case, in infinitum. Place, therefore, is an indivisible body; and if an indivisible body, either material, or destitute of matter: but if material it will not be indivisible, for it is requisite that all material bodies, when permeated by other material bodies, should be divided by them, as is the case with our bodies when they fall into water. But immaterials alone resist all division and this from a necessity of nature; for every body destitute of matter is void of passion; but every thing which is divided likewise suffers. Since division is a certain affection of bodies, which extirpates and destroys their unity and connection; for that which is continuous, so far as continuous suffers no other affection or molestation than section, which destroys and takes away its continuity. That we may therefore collect together what we have separately demonstrated, place is an immoveable indivisible body, destitute of matter. And if this be admitted, it is evident that it is a body by far less material than the rest, and indeed less than the matter contained in things which are moved. Hence, if light is the most simple of these (for fire is more incorporeal than the other elements, and fire is lucid) it will be manifest, that since light is the purest among the rest, light will be place. Conceive, therefore, two spheres, of which one is composed from many bodies, and the other of light alone, and let both be of equal bulk; then, by establishing the sphere of light, together with the centre, and giving the composite sphere a revolution in the circumscribing sphere of light, you will perceive the world moved in immoveable light, and according to its whole extension, immoveable, similar to place, but moved according to its parts, because these are less than place.” Now, from this demonstration of Proclus, it follows by a necessary consequence, since contraries are contained under the same genus that darkness, if it be any thing positive, is the most material of all bodies; and hence, the most material natures will participate the most of darkness, as indeed, is evident in the elements of earth and water. It likewise follows that whatever exists in perfect darkness, exists out of corporeal place, which, however paradoxical, is perhaps, no less true than wonderful to conceive.

[4] See Section second, of the Dissertation, in Vol. I. of this work.

[5] See the third figure of this problem.

[6] This is easily proved from the mensuration of a triangular space, which it is well known is obtained by multiplying the base into half the altitude; and this in the first triangle will be equal to 3 multiplied by 2; and in the second, to 2 multiplied by 2½ = 5.

[7] The quantity of this perpendicular in each triangle may be easily obtained from the 47th proposition of this book; for in the first triangle it will be three units; and in the second four. Hence, the area of each will be 12 units; but the ambit of the one will be 18, and of the other 16 units, as is evident in the following figures.

[8] That is angles formed from the circumferences of circles cutting or touching each other, when they are on both sides concave.

[9] Most probably Zeno, the Epicurean.

[10] Mr. Simpson, in his note on the 7th proposition of this book, positively asserts, that it contains two cases, though there is but one in the Greek text; and ridicules Proclus for asserting that the second part of the present proposition was added, in order to solve objections which might be urged against the seventh. But that Euclid never added any more than one case, is, I think, evident, not only from no such case being found in the Greek copies so early as the age of Proclus; but from his not converting it in the 6th proposition. Besides, it is employed with advantage in the solution of objections against the 9th proposition, as the reader will perceive in its commentary; and the objection there started merits the appellation of a case, as much as the 7th. But Mr. Simpson seems to have been ignorant of Euclid’s design in these elements;--the tradition of that only which is accommodated to an elementary institution. Hence, Euclid every where avoids a multiplicity of cases; and anticipates objections where he foresees they may be urged. Mr. Simpson adds in support of his dogmatical assertion, “that the translation from the Arabic has this case explicitly demonstrated.” As if an Arabic translation was of greater authority than the Greek text which Proclus consulted! And lastly, he concludes, with observing, that “whoever is curious, may read what Proclus says of this in his commentary on the 5th and 7th propositions; for it is not worth while to relate his trifles at full length.” If an accurate knowledge of the nature, beauty, and tendency of a science, or a collection of scientific propositions, is trifling, Proclus, indeed, deserves this accusation; as I doubt not the liberal reader, is, by this time, fully convinced. But Mr. Simpson was no philosopher; and therefore the greatest part of these Commentaries must be considered by him as trifles, from the want of a philosophic genius to comprehend their meaning, and a taste superior to that of a _mere mathematician_, to discover their beauty and elegance. It is common, indeed, to hear geometricians of the present day exclaiming, _What need of a comment on Euclid! Is he not perspicuous to every one?_ I will readily admit that such gentlemen know enough of geometry for all mechanical and sensible purposes: but I fear they are totally ignorant of its end; and have never dreamt that when properly studied it is the handmaid of true philosophy, the purifier of the rational soul, and the bridge by which we may pass from the obscurity and delusion of a material nature, to the splendor and reality of intellectual vision. I add farther, that I am greatly inclined to doubt, whether such geometricians ever considered what kind of subsistence geometrical forms possess Whether they have any certainty, or are only imaginary? Where these forms, if real, reside? And a multitude of other questions which are discussed in these Commentaries. And lastly, what is most material of all, if geometry be a science, what science itself is? This last question, indeed, they would doubtless consider so _trifling_ and easy of solution, that they would readily and confidently answer with young Theætetus in Plato, “that sciences are such things as may be learned from Mathematicians, geometry, and the like; shoe-making, and other mechanical arts; and that all, and each of them are no other than sciences!” To which admirable definition we may justly reply in the words of Socrates, “Generously and magnificently O my friends, when interrogated concerning _one thing_, have you given instead of something simple, things _many_ and _various_.”

[11] Triangular numbers, are 1, 3, 6, 10, &c.; and sexangular numbers, 1, 6, 15, 28, &c. But concerning their formation, see note to page 95, Vol. I. of this work; by means of which, the truth of this assertion will be evident.

[12] Concerning the meaning of total predication, see page 45 of the Dissertation, Vol. I. of this work.

[13] Mr. Simson in his note to this proposition observes, that he thought proper to change its enunciation, so as to preserve the same meaning; “because (says he) the literal translation from the Greek, is extremely harsh, and difficult to be understood by beginners.” Whatever difficulty learners may find in conceiving this proposition abstractedly, is easily removed by its exposition in the figure; and therefore, I conceive, that Mr. Simson acted very injudiciously in altering its enunciation. Besides, the following comment of Proclus shews, that there is great beauty in Euclid’s statement of this proposition; the greatest part of which is lost in Mr. Simson’s indiscreet alteration. It would appear strange that such liberties should be taken by one, who professes in his preface, _to remove blemishes, and restore the principal books of the Elements to their original accuracy_, if Mr. Simson had not informed us in his note, that the present Commentary of Proclus unfolding the beauty and _accuracy_ of this proposition, is too _trifling_ to merit a relation! See more concerning this proposition in the note to Prop. 5.

[14] See the Comment of Clavius on this proposition.

[15] And from hence, also appears the emptiness and arrogance of Mr. Simson’s note to this proposition, which we have already exploded.

[16]

This too may be easily effected by means of the first problem, and the present. Thus let _a b c_ be a right angle, which it is required to trisect; then, upon the side _a b_, describe an equilateral triangle _c d b_, and bisect the angle _d b c_, and the angles _a b d_, _d b e_, _e b c_, shall be equal. For the angle _d b c_, is one third of two right angles, or two thirds of one right, and consequently the angle _d b a_, is one third of a right angle; and this is equal to _d b e_, the half of _d b c_. Therefore they are all equal.

[17]

The method of dividing an angle in any given ratio, by means of a right line and circle only, seems to have been entirely unknown to the ancients, as well as to the moderns. However, the author of this translation presumes he has discovered the means of solving this arduous problem; and that such as admit the truth of his demonstration respecting the quadrature of the circle in page 56 of his Dissertation, vol. I. of this work, must necessarily subscribe to the following method of dividing an angle in any required proportion. Let there be an acute angle given _g a k_, which it is required to divide in the ratio of the right line _a c_ to _c g_. Bisect _a c_ in _b_, and from the centre _a_, with the radius _a b_, describe the arch _b e_, and with a radius equal to _a c_, describe an arch touching _b e_, in the point _b_. Likewise with a radius double to _a c_, describe another tangent arch at the point _b_, and with a radius equal to _a g_, a tangent arch at the same point, according to the figure; and lastly, let the arches _c d_, _g k_, from the centre _a_ be drawn. Then ½ of the arch _b e_, shall be equal to ¼ of _c d_, and to ⅛ of the arch similarly placed, described with a radius the double of _a c_, as is well known. Bisect then _b e_ in _f_, and make each of its two next tangent arches at _b_, equal to _b f_, which is easily done, from what has been already observed; and through the points of equality describe a circle, this (by the theorem in page 56, of our Dissertation), shall cut off some part of the tangent arch described with the radius _a g_, equal to _b f_, or the fourth part of _c d_. Hence, a part in the arch _g k_, may be easily taken equal to _c d_, which let be _g l_, and drawing the right line _a l_, the angle _g a l_, shall be to _l a k_, as _a c_ to _e g_, which was required to be done.

The same construction will serve for the division of a right angle in any given ratio, as is evident; and if the given angle be obtuse, the problem may be solved by a two-fold operation, that is, by bisecting the obtuse angle, and dividing either of the equal sections in the given ratio; for when this is effected, the whole angle may be easily divided in the same proportion. Hence, too, a right line may be speedily obtained equal to a given arch of a circle.

[18] In the 30th Prop.

[19] See Chap. 8. Book 2d.

[20] Mr. Simson having a great objection to the word infinite, though it is adopted by Euclid, substitutes in its place the word _unlimited_; but not in my opinion with any success. For if by _unlimited_, he means infinite, the alteration is ridiculous: but if he means only _indefinite_, or a line which has boundaries, though they are not ascertained, the problem will not succeed, as the ensuing commentary most beautifully evinces. I only add, that the reader, if he be a man of taste, and possesses any spark of the philosophic genius, must be greatly delighted with the digression of Proclus in this comment, concerning the nature of infinite, as it is perfectly philosophical and truly sublime.

[21] That no other figure besides these can fill place, will be evident, if its angle, when found, is multiplied by any number: for, as Tacquet well observes, it will always either exceed, or be deficient from four right angles. For a more particular demonstration of this admirable theorem, see Tacquet Elementa Geometriæ, p. 88.

[22] Pappus in Mathem. Collect. shews that any two sides, whose ratio to the external sides is less than two to one, may be inscribed after this manner in a triangle.

[23] See likewise concerning these triangles, ol. I. p. 173 of these Commentaries.

[24] In the second comment of this book.

[25] This will be manifest from the following figure. Let the circles _a c_, _b d_, be drawn passing through their respective centres _a_, _b_; and from the centre _c_, with the radius _c b_, equal to _a b_, describe the arch _a b d_, and draw the lines _c b_, _c d_, _c a_. Then because _a c b_ is an equilateral triangle, as also _c b d_, each of the angles _a c b_, _b c d_, shall be equal to ⅔ of one right angle; and because the biline _c d_, is equal to the biline _c b_, hence, the angle formed by the arch _c b_, and the arch _c d_, viz. the angle _a c f_, shall be equal to the angle formed by the right line _c b_, and the right line _c d_, i.e. to ⅔ of one right angle. Q. E. D.

[26] See more concerning these universal genera in the third section of the Dissertation, Vol I. of this work.

[27] In Book II. Comment 2. of this work.

[28] In the Comment on the 32d proposition.

[29] In book III. chap. I. and in Com. 3.

[30] In lib. i. de Cælo, tex. 35.

[31] Clavius and Simson have employed a multitude of propositions in the demonstration of this petition, but their demonstrations fall far short in my opinion of the elegance of the present.

[32] In Lib. III. Com. 2.

[33] i.e. In his last analytics. See the second section of the Dissertation, Vol. I, of this work.

[34] In the definitions which are with great propriety called by the Platonists hypotheses, because their evidence is admitted without proof, which at the same time they are capable of receiving from the first philosophy.

[35] In his last Analytics. See page 49, of the Dissertation, Vol. I. of this work.

[36] See the last preceding figure.

[37] This is a well known property of the hyperbola, and its asymptotes; and is thus expressed by Mr. Simson, in his Conic Sections, Lib. 3. Prop. 16. “If from a point in the hyperbola, any two lines are drawn to the asymptotes, and if from any point, in the same or opposite hyperbolas, there are drawn to the asymptotes other right lines parallel to the former; then the rectangle contained by the lines first drawn, shall be equal to the rectangle contained by the other drawn lines.”

[38] Thus let there be a square, whose side is equal to three, and a parallelogram whose longest side is equal to four, and its shortest to two; the ambit of each figure will indeed be equal to twelve, but the area of the square will be equal to nine, and of the parallelogram to eight.

[39] This will be evident by conceiving a rectangular parallelogram equal to that which is non-rectangular, described on the same base: for the ambit of the former will be less than that of the latter, and consequently less than the parallelogram, with an ambit equal to the non-rectangular parallelogram.

[40] From hence it is evident that it was the intention of Proclus to comment on the whole of Euclid: but it does not appear that he ever carried this design into execution.

[41] The present Commentary is imperfect, both in the Greek, and the translation of Barocius; who observes that the conclusion is wanting in all the copies which he had an opportunity of perusing. Those who are curious may consult his scholium, in which he has endeavoured to complete it.

[42] See Comment 8, of the third book, with its note.

[43] Barocius is of opinion, that this Commentary was originally mutilated; and that the part which follows the word _drawn_, was added by some skilful geometrician, as necessary to the perfection of the demonstration. See his Scholium to this Commentary.

[44] The Commentary of Proclus, on this proposition is wanting in the Greek, and, as we are informed by Barocius in all the MS. copies which he had an opportunity of consulting. Barocius has endeavoured to supply this deficiency, after the manner of Proclus; but he appears to have fallen into prolixity, by a too minute division of the problem.

[45] See Sims. Sect. Con. Lib. I. Prop. 13. and Lib. II. Prop. 23, and Lib. III. Prop. 48.

[46] In the sixth Commentary of this book.

[47] In the 31st proposition.

[48] Ἅπασα γὰρ ἡ παρ’ Ἕλλησι θεολογία τῆς Ὀρφικῆς ἐϛὶ μυϛαγωγίας ἔκγονος·: πρώτου μὲν Πυθαγόρου παρὰ Ἀγλαοφήμου τὰ περὶ Θεῶν ὄργια διδαχθέντος. Procl. in Plat. Theol. p. 13.

[49] In Lib. ii. Florid.

[50] Euseb. Prepar. Evang. lib. xiv.

[51] This pestilence was in the time of the emperor Gallienus, and raged so vehemently, according to Trebellius Pollio, that five thousand men perished with an equal disease in one day. This happened in the year of Christ 262, and of Gallienus, 9, 10; and not long after Porphyry applied himself to Plotinus. Fabricius.

[52] This is the Firmus Castricius to whom Porphyry inscribes his books on Abstinence.

[53] This was probably nothing more than a small serpent resembling the form of a dragon.

[54] It is strange that Fabricius should think it ought to be entitled περὶ τῆς ἀπαθείας τῶν σωμάτων: for he who reads this book must see that such a title would be ridiculous. Vide Bibl. Grec. tom. iv. p. 143.

[55] This Rogatianus is the person Porphyry alludes to in his Treatise on Abstinence, lib. i. p. 106, when he speaks as follows. “There was once an instance, where a negligence of terrene concerns and a contemplation and intuition of such as are divine, expelled an articular disease, which had infested a certain person for the space of eight years. So that at the very same time, that his soul was divested of a solicitous concern for riches, and material affairs, his body was freed from a troublesome disease.”

[56] I have, however, the happiness of being intimate with a lady, who is a noble exception to this remark; and is both an excellent Greek scholar, and skilled in the Platonic philosophy.

[57] For this is alone the virtue of traffic; and is the chief support of its professors.

[58] Concerning the Ἱεροὶ Γάμοι, or holy marriages, which were first celebrated by the Orphic Theologers, see the note to the hymn to Proserpine, in my translation of the Orphic Initiations.

[59] A line somewhat altered from Homer. The original is βάλλ’ οὕτως αἴ κέν τι φόως Δαναοῖσι γένηαι. Iliad. 8. l. 282.

[60] In the original.

Οἶδα δ’ ἐγὼ ψάμμου τ’ ἀριθμόν, καὶ μέτρα θαλάσσης,
Καὶ κωφοῦ ξυνίημι, καὶ οὐ λαλέοντος ἀκούω.

[61] Lib. 6.

[62] Vide Procl. in Plat. Theol. p. 89, et 90.

[63] This passage is cited by Ficinus, in the second volume of his works, p. 1186. and is, I doubt not, taken from the manuscript Commentary of Proclus on the Parmenides.

[64] οὗτος γὰρ (i.e. Moderatus) κατὰ τοὺς Πυθαγορείους τὸ μὲν πρῶτον ἓν ὑπὲρ τὸ ὄν καὶ πᾶσαν οὐσίαν ἀποφαίνεται. Simp. in Ar. Phys. fol. 50.

[65] In the note to page 14, of this volume, we have shewn from Proclus that light is place, and is an immaterial body. Indeed that light is something superior to sensible matter may, I think, be evinced by the following consideration. As the supreme principle of the universe, (who can be compared to nothing so properly as light,) is the light of the intelligible world, and is at the same time more exalted than every thing which it contains; so in this sensible, which is the image of the intelligible world, it is necessary that corporeal light, should be more excellent than any material nature. But as Proclus prosecutes this speculation on light, in the above mentioned passage, in a most admirable and uncommon manner; let us attend him in the abstruse investigation. In the first place speaking of that light which emanates from the fontane soul of the world, and which, according to the Zoroastrian oracle,

Ἄρδην ἐμψυχοῦσα φάος, πῦρ, αἰθέρα, κόσμους,

abundantly animates, light, fire, ether, and the world; he says that this light is one fire, above the three others, viz. the empyrean, etherial, and material fire; and that it first unfolds the eternal quiet of the gods, and illustrates essential spectacles to such as are worthy of their inspection. For by the assistance of this light, things destitute of figure and impression, are impressed according to reason and intelligence. And perhaps (says Simplicius) he calls light place, because it is a certain description and type of the universe, and gives distance to things, which without the presence of light would not appear to be distant. But here Proclus very philosophically doubts against his own position. In the first place, how body can be received and penetrated by body. In the second place, whether place, i.e. light, is inanimate, or participates of soul. But (says he) it cannot be inanimate, because it is better than the animated natures which it contains, and because rational beings are said to be animated. Hence this body, will be animated the first of all others. But if it is animated, how can it be immoveable? And he dissolves the first doubt, because there are some immaterial bodies void of affection and passion. For (says he) a body void of matter neither resists nor is resisted; since that which is impelled and repelled, is eminently passive in such operations. But neither can such a body be divided, since it is void of passivity. Hence neither can the absurdity be adduced, that the universe is received by a minimum, or penetrates a minimum. For if it cannot be divided, neither can it be equally divided with the smallest; and if this is impossible, neither can it be permeated by the universe.

But he removes the second objection, by asserting, that this body, i.e. light, is animated by that soul, which is the fountain of others; and that it possesses a divine life, and an essence self-motive, but not in energy. For if we assert that soul is self-motive, in a two-fold manner, in one respect according to essence, but in the other according to energy; we must likewise affirm that place, or light is partly moveable, and partly immoveable. For what should hinder our asserting, that place participates of such a life, and that it lives according to an immutable essence, and not according to a self-motive energy? But if you are desirous (says he) of considering the motion of place, according to energy, you will plainly perceive, that it is, as it were, the mover of the bodies which are moved, and which turn their parts according to a certain distance; since these cannot be every where, and are incapable of being present to all the parts of place, according to each of their parts. And this is that intervention and affinity, which it possesses with soul moving without dimension. For, life so far as life, appears to produce motion: and since place is that which first participates of life, motion to place, will confer a true motion on every part; and will produce a desire in every part of the moved body of arriving at its whole, and since it is not able to accomplish this, on account of the natural property of interval, of subsisting divisibly in the universe. For whatever desires any nature, which it is not able to reach, through its peculiar defect, is then more enflamed in the pursuit of that, which it cannot possess through the imbecility of its nature. For it is requisite (says he) that between an incorporeal and immutable life, such as that of soul, the fountain of the rest; and one corporeal and mutable, that one immutable and corporeal should intervene as a proper medium. And thus much from Proclus concerning place or light, whose reasonings appear to me equally elegant and philosophical, subtle and profound.

But the opinion of the Phœnicians respecting light, as preserved by the emperor Julian in his elegant oration to the sun, is no less admirable than that of Proclus; and at the same time asserts its immaterial nature. “According to the Phœnicians (says Julian) who are skilled in divine science and wisdom, the universally-diffused splendor of light, is the sincere energy of an intellect perfectly pure: i.e. of the solar intellect, which as Julian expresses it, scattering its light from the middle region of the heavens, fills all the celestial orbs with powerful vigour, and illuminates the universe with divine and incorruptible light.” With great reason, therefore, does Plotinus assert, that light is nothing else than that which is visible: for this must be the necessary property of a nature, possessing a triple dimension without sensible matter.

[66] En. 2. l. 9. c. i.

[67] Intellectual System, p. 562.

[68] In Timæum. p. 93. 94.

[69] In Plat. Theol. p. 158

[70] In Plat. Theol. p. 27.

[71] Ennead, 5. p. 492.

[72] Intellectual System, p. 568.

[73] Præpar. Evan. lib. iv. c. 6.

[74] Lib. x. cap. 29.

[75] It is necessary to inform the genuine Platonic reader, that Synesius was not a bishop, and had not embraced Christianity, when he composed the present excellent book. This is not only evident from the recondite wisdom of antiquity, which it every where displays, but from his expressly using in one place, p. 151, the epithet, _the mundane god_ (θεὸς ἐγκόσμιος) in the same manner as it is always employed by heathen Platonists. There are three Latin versions of this admirable work: the first and best by Ficinus, the next both in the order of time and excellence, by Cornarius, and the last and worst by Petavius. This industrious Jesuit, indeed, though sufficiently learned on other subjects, appears by his version to be very ignorant of the Greek philosophy. This will be evident by comparing his translation with the Greek, and, I hope, I may add, with the above version, which contains the greatest, and most important part of this inestimable work. With respect to Synesius, he was a native of Cyrene, in Africa; travelled into Egypt for improvement; and perfected his studies under the celebrated Hypatia: a woman no less eminent for her uncommon abilities, than remarkable for her tragical death, effected by the infernal revenge of the Alexandrian church, and the _orthodox_, _patriarchal_, _Christian_ malice of St. Cyril. Though Synesius was reluctantly consecrated bishop of Ptolemais about the year 410, yet we may collect from his tenets, that he was not a perfect convert to Christianity; and from his epistles, that he lamented his episcopal station. For with respect to the former, he denied the immediate creation of the world, its final destruction, and the resurrection of the dead: and with regard to the latter, he frequently and earnestly begs to be discharged from his office; and declares that as he was by education a heathen, and by profession a philosopher, he had met with no success since he presumed to serve at the altar. Particularly in a letter to his friend Olympius (Epist. 95.) he declares that if his duty as a bishop should be any hinderance to his philosophy, he would relinquish his diocese, abjure his orders, and remove into Greece. For farther conviction in this particular consult Epist. 11, 13, 57, 67, 80, 105: and the Clidophorus, and Hypatia of Toland, who largely and curiously descants on the life and writings of Synesius. I shall only add, that even Petavius, the editor of his works, affirms, that in some of the books composed after his profession of Christianity, Synesius appears as great a heathen as before: and this conduct may be reconciled, by what Synesius himself asserts in one of his letters: (Epist. 105.) “that it may be sometimes expedient to lye, in order to do good; since philosophical truth is not necessary for the vulgar, who may receive hurt from their knowledge. _Wherefore_ (says he) _if this method_, (that is of concealing the truth), _be consistent with the rights of episcopal dignity, I may be consecrated. I shall freely philosophize at home, and tell fables abroad; neither teaching, nor unteaching, but suffering people to live in the prejudices they have imbibed._” This must be allowed to be sound philosophy, excellent policy, and true _orthodoxy_!