DEFINITION S. TH DEFINITION I. A POINT is that which has no PARTS. HAT geometry, according to the transition which takes place from things more composite to fuch as are more fimple, runs from body, which is diffused into distance by three dimenfions, to a fuperficies by which it is bounded; but from fuperficies to a line, the boundary of fuperficies; and from a line to a point deftitute of all dimension, has been often faid, and is perfectly manifeft.. But because these terms, in many places, on account of their fimplicity, appear to be more excellent than the nature of compofites; but in many, as when they fubfift in things which they terminate, they are fimilar to accidents, it is neceffary to determine in what genera of beings each of these may be beheld *. I fay then, that such things as are deftitute of matter, which subsist in separate reasons, and in those forms which are placed under themselves, are always allotted a subfiflence of more fimple effences, fuperior to the fubfiftence of such as are more compolite. On this account, both in intellect, and in the ornaments, as well of the middle kind as among those peculiar to the foul, and in natures themselves, the terms which proximately vivify bodies, excel according to effence the things which are terminated; and are more impartible, more uniform, and more primary than these. For in immaterial forms, unity is more perfect than multitude; that which *The prefent Comment, and indeed most of the following, eminently evinces the truth of Kepler's obfervation, in his excellent work, De Harmonia Mundi, p. 118. For, fpeaking of our author's compofition in the prefent work, which he every where admires and defends, he remarks as follows, "oratio fluit ipfi torrentis inftar, ripas inundans, et cæca dubitationum vada gurgitefque occultans, dum mens plena majeftatis tantarum rerum, luctatur in anguftiis linguæ, et conclufio nunquam fibi ipfi verborum copiâ fatisfaciens, propofitionum fimplicitatem excedit." But Kepler was killed in the Platonic philofophy, and appears to have been no lefs acquainted with the great depth of our author's mind than with the magnificence and fublimity of his language. Perhaps Kepler is the only infance among the moderns, of the philofophical and mathematical genius being united in the fame perfon. is And, in like manner, a point compofite natures deriving their For this alfo is again manifeft, is impartible, than that which is endued with unbounded progreffion; and that which terminates, than that which receives bound from another. But fuch things as are indigent of matter, and abide in others, and degenerate from the perfection of their effence, which are scattered about fubje&ts, and have an unnatural union, are allotted more compofite reafons, prior to fuch as are more fimple. Hence, things which appear in the phantafy invefted with form, and the matter of the figures which the phantafy contains, and whatever in fenfibles is generated by nature, have, in a preceding order, the reasons of the things terminated; but the reafons which terminate, in a following and adventitious rank *.] For left that which is diftributed into three dimensions, should be extended into infinite magnitude, either according to intelligence or fenfe, it was every way terminated by fuperficies. And left a plane superficies fhould conceal itself in an infinite progreffion, a line approaching oppofed its diffufion, and gave bound to its indefinite extenfion. limited the progreffions of a line; fubfiftence from fuch as are timple. that in separate forms the reafons of terms fubfift in themselves, but not in those which are terminated; and abiding fuch as they are in reality, poffefs a power of conftituting fecondary natures. But, in infeparable forms they give themfelves up to things which are terminated, refide in them, become, as it were, their parts, and are replenished with baser natures. On which account, that which is impartible is there endued with a partible effence, and that which is void of latitude is diffufed into breadth. And terms are no longer able to preferve their fimplicity and purity. For fince they abide in another, they neceffarily change their own nature into the matter of their containing fubject. Matter, indeed, difturbs the perfection of these, and causes the reafon of a plane to become a profound plane; but obfcuring the one dimenfion of a line, causes it to be every way partible; and gives corporeity to the indivifibility of a point, and feparates it together with the natures which it terminates. For all these reasons falling into matter, the one kind from cogitation into intelli * That is, the reafon of a triangular figure (for instance) in the phantafy, or triangle itself, is fuperior to the triangular nature participated in that figure. Q 2 gible gible matter, but the other from nature into that which is fenfible, are replenished with their containing fubjects; and depart from their own fimplicity, into foreign compofitions and intervals. But here a doubt arises how all these, exifting in intellect and foul in an impartible manner, and without any dimension, are diftributed into matter, some indeed, principally, but others on account of its nature? Shall we fay that there is a certain order in immaterial forms, fo that fome are allotted the firft, fome the middle, and others the laft place; and that of forms fome are more uniform, but that others are more multiplied; and that fome have their powers collected together, but others tending into interval; and that fome, again, border upon bound, but that others are proximate to infinity? For though all participate of these two principles, yet fome originate from bound, but others from infinity, of which they more largely participate. Hence, a point is entirely impartible, fince it fubfifts according to bound, yet it occultly contains an infinite power, by which it produces every interval, and the progreffion of all intervals, unfolds its infinite power. But body, and the reason of body, participates more of an infinite nature; on which account it is among the number of things terminated by another, and divifible in infinitum, according to all dimenfions. But the mediums between these, according to the distance of the extremes, are either among the number of things which have an abundance of bound; or among fuch as have an affluence of infinity: on which account they both terminate and are terminated. For, indeed, fo far as they confift from bound, they are able to terminate others; but so far as they participate of infinity, they are indigent of termination from others. Hence, fince a point is also a bound, it preferves its proper power in participation: but fince it likewife contains infinity occultly, and is compelled to be every where prefent with the natures which it terminates, it refides with them infinitely. And, because among immaterial forms there was a certain infinite power capable of producing things diftant from each other by intervals, a point is present with its participants in capacity. For infinity in intelligibles is the primary cause and prolific power of the univerfe; but in material natures it is imperfect, and is alone all things in dormant capacity. And in short, thofe forms which, on account of their fimplicity fimplicity and impartibility, hold a fuperior rank among principles, preferve, indeed, (in conformity to their nature,) their own property in their participations, but become worse than more compofite reafons. For matter is able to participate thefe more clearly, and to be prepared for their reception, rather than that of the moft fimple causes of beings. On which account, the veftigies of separate principles defcend into matter; but the participations of thofe in a fecond and third order, become more confpicuous. Hence, matter participates more of the cause of body, than of a plane; and of this more than the form of a line; and of this ftill more than that of a point, which contains all these, and is the boundary of them all. For the reason of a point prefides over this whole feries, unites and contains all partible natures, terminates their progreffions, produces them all by its infinite power, and comprehends them in its indivifible bound. On which account alfo, in the images of immaterial forms, fome, are the boundaries of others; but a point is the limit of them all. But that we must not think with the Stoics, that thefe boundaries of bodies alone fubfift from cogitation; but that there are certain natures of this kind among beings, which previously contain the demiurgical reasons of things, we shall be enabled to remember, if we regard the whole world, the convolutions of its parts, the centres of those convolutions, and the axes which penetrate through the whole of thefe revolving circles. For the centres fubfift in energy, fince they contain the Ipheres, preserve them in their proper ftate, unite their intervals, and bind and establish to themselves the powers which they poffefs. But the axes themselves being in an immoveable position, evolve the fpheres, give them a circular motion, and a revolution round their own abiding nature. And the poles of the spheres, which both terminate the axes, and bind in themselves the other convolutions, do they not perspicuously evince, that points are endued with demiurgical and capacious powers, that they are perfective of every thing distant by intervals, and are the fources of union, and an unceasing motion? From whence, indeed, Plato * also says, that they have an adamantine fubfiftence; fhewing by this, the immutable, eternal, and ftable power In the tenth book of his Republic. of of their effence, ever preferving itself in the fame uniform mode of existence. He adds too, that the whole spindle of the Fates, is turned about these, and leaps round their coercive union. But other more recondite and abftrufe difcourfes affirm, that the demiurgus prefides over the world, feated in the poles, and, by his divine love, converting the universe to himself. But the Pythagoreans thought that the pole fhould be called the Seal of Rhea *; because the zoogonic, or vivific goddefs, pours through thefe into the univerfe, an inexplicable and efficacious power. And the centre they called the prifon of Jupiter; because, fince Jupiter has placed a demiurgical guard in the bofom of the world, he has firmly eftablished it in the midft. For, indeed, the centre abiding, the universe poffeffes its immoveable ornament, and unceafing convolution: and the gods who prefide over the poles, obtain a power collective of divifible natures, and unific of fuch as are multiplied and those who are allotted the government of the axes, reftrain and eternally evolve their perpetual convolutions. And, if it is lawful to offer our own opinion on this subject, the centres and poles of all the spheres are the fymbols of the conciliating gods, fhadowing forth their imperceptible and unifying compofition. But the axes exprefs the coherencies of the univerfal ornaments; and are endued with a power of comprehending the mundane integrities and periods, in the fame manner as their prefiding deities, of such as are intellectual. But the spheres themselves are images of the gods, called perfectors of works, copulating the principle with the end, and excelling all figures in fimplicity, fimilitude, and perfection. But we have been thus prolix, that we might evince the power of impartibles, and of the terms which the world contains, and that so far as they bear an image of primary and most principal caufes, they are allotted the moft excellent order in the univerfe. For centres and poles are not of the fame kind with things which are terminated; but they fubfift in energy, and poffefs an effence, and perfect power, which pervades through all partible natures. But many beholding those terms which imperfectly fubfit in terminated effences, confider them as endued with a flender fubfiftence; and fome indeed fay, that See the Hymn to the Mother of the Gods, in my tranflation of the Orphic Initiations. they |