The philosophie, commonlie called, the morals vvritten by the learned philosopher Plutarch of Chæronea. Translated out of Greeke into English, and conferred with the Latine translations and the French, by Philemon Holland of Coventrie, Doctor in Physicke. VVhereunto are annexed the summaries necessary to be read before every treatise

A COMMENTARIE OF THE CREATION OF THE SOULE, WHICH PLATO DE∣SCRIBETH [ 10] IN HIS BOOKE TIM AE US.

The Summarie.

AMong those discourses which may exercise the wittes, and busie the braines of most curious spirits, those of Plato may be raunged, which in divers places of his dialogues, but especially in his Timaeus he hath delivered, and namely, where he treateth of na∣ture metaphysically, intermingling with a certeine deepe and profound maner of [ 20] doctrine (as a man may perceive by his writings) his resolutions as I may say irresolute, proceeding all from the ignorance of the sacred story and the true sense of Moyses. As for example, that which he saith as touching the soule of the world: an absurd and fantasticall opinion, if it be not handled and expounded aright. Our authour being minded in this treatise to dispute philosophically upon the creation of the said soule, runneth thorow numbers, tones, tunes and harmonies, aswell terre∣striall as celestiall, for to declare the meaning of Plato: but with such brevitie in many places, that a man had need to reade with both his eies, and to have his minde wholly intentive and amused upon his words, for the under standing of him. Meanewhile, this would be considered, seeing that in such mat∣ters we have (God be thanked) sufficient to resolve us in the word of God, and the good books of the doctours of the church, all this present discourse should be read, as comming out of the hands of a man [ 30] walking in darknesse; and to speake in one word, of one blinde himselfe and following a blinde guide: to the end that in stead of highly admiring these subtilties of Plato, as some in these daies doe, whose heads are not staied and well setled, we might know that the higher that man in his wisdome mounteth with his pen, farre from Gods schoole, the lesse he is to be received and accepted of.

A COMMENTARIE OF THE creation of the soule, which Plato describeth in his booke Timaeus. [ 40]

The father to his two sonnes AUTOBULUS and PLUTARCH, Greeting.

FOrasmuch as ye are of this minde, that whatsoever I have heere and there said and written in divers places by way of exposition touch∣ing that which I supposed in mine opinion Plato held, thought and understood concerning the soule, ought to be reduced & brought together into one; and that I should doe well to declare the same at [ 50] large in a speciall 〈◊〉〈◊〉 apart by it selfe, because it is not a matter which otherwise is easie to be handled and managed; as also for that seeming as it doth, somewhat contrary to most of the Plato∣nique philosophers themselves: in which regard it had need to be well mollified. I will therefore in the first place set downe the very text of Plato in his owne proper tearmes, word for word, as I finde them written in his booke en∣tituled Timaeus.

Of that indivisible substance which alwaies continueth about the same things; as also of that which is divisible by many bodies, he composed a third kinde of substance in the mids of them both, holding partly of the nature of The same, and in part of The other: and this he ordeined and set in the mids betweene the indivisible substance conversant about the same things, and the other which is divisible by bodies. Then taking these three natures or substances, he mixed them altogether into one forme or idea, and fitted perforce the nature of The other, which was unto ward to be mixed, to that nature of The same. Having thus mingled them with Substance, and of three made one, he divided this whole againe into such portions, as were fit and conve∣nient: ech one of them being mingled with The same, with The other, and with Substance. And this division of his he began in this maner, &c. [ 10]

To begin withall if I should discourse unto you at this present what a number of disputations and contentious debates, these words have ministred unto those who tooke upon them to expound the same, it were for my selfe a peece of worke endlesse, and for you who have read the most part of them together with me, a labour needlesse. But seeing that of the most princi∣pall and excellent professours, Xenocrates hath drawen some unto his opinion, in defining the substance of the soule to be a number mooving it selfe: and others have ranged them selves to Crantor of Soli, who affirmed the 〈◊〉〈◊〉 to be tempered of the nature intellectuall & of the other which is opinionative about objects sensible; I suppose that these two sentences being well dis∣plaied and opened will make the way and give you an easie entrance to the understanding and finding of that which we seeke for and is in question. And verily there need not many words [ 20] for the exposition of them both. For * 1.1 the one sort of them thinke that Plato meaneth no∣thing else but the generation of number, by the said mixture of indivisible with divisible: for that unity is indivisible, and plurality divisible: of which twaine is engendred and produced number, whiles unity doth determine plurality, and limit out an end to that which is infinit, to wit, the binary or two indeterminate: which is the reason that Zaratas the master of 〈◊〉〈◊〉 called two the mother, and one the father of numbers: as also for that the better numbers be those which resembled unity: and yet for all that this number is not the soule, because that both the motor and the moovable is wanting: but when The same and the other were mingled toge∣ther, of which the one is the beginning of motion and mutation, the other of rest and station, then commeth the soule to have a being, which is as well the principall, to staie and to be staied, [ 30] as it is to moove and to be mooved.

But Crantor and his followers supposing that the proper and principall operation of the soule was to judge things intelligible and sensible, together with the similitudes and dissimili∣tudes which they have, as well them selves, as one in respect of another, affirme, that the soule is composed of All, to the end that she may judge of all. The which All aforesaid standeth upon fower principall kindes; the first is a nature intelligible, which is alwaies one and evermore after the same sort: the second a nature passible and mutable concerning bodies: the third the nature of the same: and the forth the nature of the other: for the two first, participate in some sort both of the same and also of the other. But all these doe jointly and equally holde, that the soule was never after a certaine time, nor ever engendred, but hath many powers and faculties, into [ 40] which Plato resolving for speculative disputation sake, the substance of her, supposeth in word onely, that she was engendred mixed and tempered, saying moreover that he thought as much of the world: for full well he knew, that eternal it was and ingenerable, but seeing it was not easie to comprehend how, and in what order it was found, composed, governed and administred, for those who at the first presupposed not the creation and generation neither of it selfe, or of such things as concurred thereto, he therefore tooke the course to speake in such sort.

This much you see in sum what they both doe say: which when Eudorus well considered, he thought there was good probability both in the one and the other of their opinions, but for mine owne part, perswaded verily I am, that neither of them twaine hath touched the point, or come neere unto the minde and meaning of Plato. [ 50]

If we wil use the rule of probability & verisimilitude indeed, not fully building our owne pro∣per opinions, but be willing for to say something agreeable & accordant thereto; for that mix∣ture of the substance intelligible and sensible which they speake of, giveth not us to understand thereby, that it is the generation of the soule, more than of any other thing whatsoever that a man may name. For the very world and every part thereof is compounded of a substance intel∣ligible or spirituall, and of a substance sensible or corporall: whereof the one hath furnished the thing that is made and engendred with forme and shape, the other with subject matter. And as

much of the matter as is forme by participation or resemblance of the intelligible, becommeth incontinently palpable and visible: but the soule is not perceptible by any sense. Neither was it ever found that Plato called the soule number, but alwaies a motion mooving of it selfe, yea the very fountain & beginning of motion. True it is, I confesse that embelished he hath & ador∣ned the substance therof with number, proportion, accord & harmony, which he hath bestowed therein as in a subject capable & susceptible of the most beautifull forme that can be imprinted therein, by those qualities before said. And I suppose it is not all one to say that the soule is composed by number, and that the substance thereof is number: for certaine it is that it hath the subsistence and composition by harmony, but harmonie it is none, according as himselfe hath shewed in his treatise of the soule. Moreover altogether ignorant they are, what Plato mea∣neth, [ 10] by the same and the other: for they say, that the same conferreth to the generation of the soule, the power or faculty of station and rest: the other, of motion: whereas Plato himselfe in his booke entituled, The Sophister, putteth downe, that which is, the same, the other, motion and station, as five distinct things differing the one from the other, severing them a part, as ha∣ving nothing to doe in common one with another; which they all with one accord, yea and many more even of those who lived and conversed with Plato, fearing and being mightily trou∣bled with, doe devise and immagin all that they can, bestir themselves wresting forcibly, heaving and shooving and turning every waie, as in case of some abominable thing and not to be na∣med, supposing that they ought either altogether, for his honour and credit to denie, or at least wise to cover and conceale that which he had delivered, as touching the generation or creation [ 20] of the world, and of the soule thereof, as if the same had not bene from all eternity, nor had time out of minde their essence: whereof we have particularly spoken a part else where; and for this present suffice it shall to say by the way, that the arguing and contestation, which Plato confes∣seth himselfe to have used with more vehemencie than his age would well beare, against Athe∣ists: the same I say they confound and shufflle up, or to speake more truely abolish altogether. For if it be so, that the world be eternall and was never created, the reason of Plato falleth to the ground, namely that the soule being more ancient than the bodie, and the cause and prin∣cipall author of all motion and mutation, the chiefe governour also and head Architect, as he himselfe hath said, is placed and bestowed therein. But what, and where of the soule is, and how it is said and to be understood, that it is more ancient than the body and before it in time, the [ 30] progresse of our discourse hereafter shall declare: for this point being either unknowen or not well understood, brings great difficulty as I thinke in the well conceiving, and hinderance in be∣leeving the opinion of the trueth?

In the first place therefore I will shew what mine owne conceit is, proving and fortifying my sentence, and withall, mollifying the same (because at the first sight it seemeth a strange para∣dox) with as probable reasons as I can devise: which done, both this interpretation and proofe also of mine, I will lay unto the words of the text out of Plato, and reconcile the one unto the o∣ther. For thus (in mine opinion) stands the case.

This world (quoth Heraclitus) there was never any god or man that made: as if in so saying he feared, that if we disavow God for creatour, we must of necessitie confesse that man was the [ 40] architect and maker thereof. But much better it were therefore, that we subscribe unto Plato, and both say and sing aloud, that the world was created by God: for as the one is the goodliest piece of worke that ever was made, so the other the most excellent workman and greatest cause that is. Now the substance and matter whereof it was created, was never made or engendred, but was for ever, time out of minde and from all eternitie, subject unto the workman for to dis∣pose and order it, yea and to make as like as possible was to himselfe. For of nothing and that which had no being, there could not possibly be made ought: but of that which was notwell made nor as it ought to bee, there may be made somewhat that is good; to wit, an house, a garment, or an image and statue. But before the creation of the world, there was nothing but a chaos, that is to say, all things in confusion and disorder: and yet was not the same without a bo∣die, [ 50] without motion, or without soule: howbeit, that bodie which it had, was without forme and consistence; and that mooving that it had, was altogether rash, without reason and under∣standing: which was no other but a disorder of the soule not guided by reason. For God crea∣ted not that bodie which was incorporall, nor a soule which was inanimate; like as we say that the musician maketh not a voice, nor the dancer motion; but the one maketh the voice sweet, accordant and harmonious; and the other, the motion to keepe measure, time, and compasse with a good grace. And even so, God created not that palpable soliditie of a bodie, nor that

moving and imaginative puissance of the soule; but finding these two principles, the one darke and obscure, the other turbulent, foolish and senselesse: both imperfect, disordered and indeter∣minate, he so digested and disposed them, that he composed of them the most goodly, beauti∣full and absolute living creature that is. The substance then of the bodie, which is a certeine na∣ture that he calleth susceptible of all things, the very seat, the nourse also of all things engendred, is no other thing than this. But as touching the substance of the soule, he tearmeth it in his booke entituled Philebus, Infinitie, that is to say, the privation of all number and proportion, having in it neither end, limit, nor measure, neither excesse nor defect, neither similitude nor dissimilitude. And that which hee delivereth in Timaeus, namely, that it is mingled with the indivisible nature, & is become divisible in bodies, we must not understand this to be either [ 10] multitude in unities, or length and breadth in points or pricks, which things agree unto bo∣dies, and belong rather to bodies than to soules: but that mooving principle, disordinate, indefinite, and mooving of it selfe, which hee calleth in manie places Necessitie, the same in his books of lawes hee tearmeth directly, a disorderly soule, wicked and evill doing. This is the soule simply, and of it selfe it is so called; which afterwards was made to participate un∣derstanding, and discourse of reason, yea, & wife proportion, to the end that it might become the soule of the world. Semblably, this materiall principle, capable of all, had in it a certeine magnitude, distance, and place: beauty, forme, proportionate figure, and measure it had none; but all these it gat afterwards, to the end that being thus digested and brought into decent or∣der, it might affoord the bodies and organs of the earth, the sea, the heavens, the starres, the [ 20] plants and living creatures, of all sorts. But as for them who attribute & give that which he cal∣leth in Timaeus, necessitie; and in his treatise Philebus, infinity and immensity of excesse & de∣fect of too much and too little; unto matter, and not unto the soule: how are they able to main∣taine that it is the cause of evill, considering that he supposeth alwaies that the said matter is without forme or figure whatsoever, destitute of all qualities and faculties proper unto it, com∣paring it unto those oiles, which having no smell of their owne, perfumers use in the composi∣tion of their odors and precious ointments: for impossible it is that Plato should suppose the thing which of it selfe is idle, without active qualitie, without mooving and inclination to any thing, to be the cause and beginning of evill, or name it an infinity, wicked & evill doing; not likewise a necessitie, which in many things repugneth against God, as being rebellious, and [ 30] refusing to obey him: for as touching that necessitie, which overthroweth heaven, as he saith in his Politiques, and turneth it cleane contrary; that inbred concupiscence and confusion of the first and auncient nature, wherein there was no order at all, before it was ranged to that beautifull disposition of the world as now it is; how came it among things, if the subject, which is matter, was without all qualities, and void of that efficacie which is in causes? and consi∣dering that the Creatour himselfe being of his owne nature all good, desired as much as might be, to make all things like unto himselfe? for a third, besides these two principles, there is none. And if we will bring evill into the world, without a precedent cause & principle to beget it, we shall run and fall into the difficult perplexities of the Stoicks; for of those two principles which are, it cannot be that either the good, or that which is altogether without forme and quality [ 40] whatsoever, should give being or beginning to that which is naught. Neither hath Plato done as some that came after him, who for want of seeing and understanding a third principle and cause, betweene God and matter, have runne on end, and tumbled into the most absurd and falsest reasons that is, devising forsooth I wot not how, that the nature of evill should come without forth casually and by accident, or rather of the owne accord: forasmuch as they will not graunt unto Epicurus that the least atome that is, should turne never so little or decline a side, saying, that he bringeth in a rash and inconsiderate motion, without any cause prece∣dent; whereas they themselves the meane-while affirme that sin, vice, wickednesse and ten thou∣sand other deformities and imperfections of the body, come by consequence without any cause efficient in the principles. But Plato saith not so, for he ridding matter from al different quality, [ 50] and remooving farre from God all cause of evill, thus hath hee written as touching the world in his Politiques: The world (quoth he) received al good things from the first author who crea∣ted it; but what evill thing soever there is, what wickednesse, what injustice in heaven, the same it selfe hath from the exterior habitude, which was before, and the same it doth transmit, & give to the creatures beneath. And a little after he proceedeth thus: In tract of time (quoth he) as oblivion tooke holde and set sure footing, the passion and imperfection of the old dis∣order

came in place and got the upper hand more and more; and great danger there is, least growing to dissolution, it be plunged againe into the vast gulfe, and bottomlesse pit of con∣fused dissimilitude.

But dissimilitude there can be none in matter, by reason that it is without qualitie, and void of all difference: whereof Eudemus among others being ignorant, mocked Plato for not put∣ting that to be the cause, source, and first originall of evill things, which in many places he cal∣leth mother and nurse: for Plato indeed tearmeth matter, mother and nurse: but he saith like∣wise: That the cause of evill is the motive puissance resiant in the said matter, which is in bo∣dies become divisible, to wit, a reasonlesse and disorderly motion; howbeit, for all that, not without soule, which plainly and expresly in his books of lawes, he tearmeth a soule, contrary [ 10] and repugnant to that which is the cause of all good; for that the soule may well be the cause and principle of motion; but understanding is the cause of order and harmony in motion: for God made not the matter idle, but hath kept it from being any any more 〈◊〉〈◊〉 & troubled with a foolish and rash cause: neither hath he given unto nature the beginnings and principles of mutations and passions, but being as it was enwrapped and enfolded with all sorts of passions and inordinate mutations, hee cleered it of all enormities, disorders, and errors whatsoever, using as proper instruments to bring about all this, numbers, measures, and proportions; the effect whereof, is not to give unto things, by mooving and mutation the passions and differen∣ces of the other and of diversitie, but rather to make them infallible, firme, and stable, yea, and like unto those things which are alwaies of one sort, and evermore resemble themselves. [ 20]

This is in my judgement the minde and sentence of Plato, whereof my principall proofe and argument is this: that by this interpretation is salved that contrariety which men say, and see∣meth indeed to be in his writings: for a man would not attribute unto a drunken sophister, much lesse than unto Plato, so great unconstance and repugnance of words, as to affirme one and the same nature to be created, and uncreated; and namely in his booke entituled Phaedrus, that the soule is eternall, and uncreated: but in Timaeus, that it was created and engendied. Now as tou∣ching those words of his in the treatise Phaedrus, they are well neere in every mans mouth verie rife; whereby he prooveth that the soule can not perish, because it was never engendred: and semblably he prooveth, that generation it had none, because it mooveth it selfe. Againe, in the booke entituled Timaeus, God (quoth he) hath not made the soule to be yoonger than the body, [ 30] according as now in this place we purpose to say, that it commeth after it, for never would he have permitted that the elder being coupled and linked with the yoonger should be commaun∣ded by it. But we standing much (I wot not how) upon inconsiderate rashnesse and vanity, use to speake in some sort accordingly: for certaine it is, that God hath with the bodie joined the soule, as precedent both in creation and also in power and vertue, like as the dame or mistresse with her subject, for to rule and commaund. Againe, when he had said that the soule being tur∣ned upon her selfe, began to live a wise and eternall life, The body of the heaven (quoth he) was made visible, but the soule invisible, participating the discourse of reason and of harmony, en∣gendred by the best of things intellectuall and eternall, being likewise it selfe the best of things engendred and temporall. Where it is to be noted that in this place expresly calling God the [ 40] best of all eternall things, and the soule the best of things created and temporall, by this most evident antithesis and contrariety, he taketh from the soule that eternity which is without begin∣ning and procreation.

And what other solution or reconciliation is there, of these contradictions, but that which himself giveth to those who are willing to receive it; for he pronounceth that soule to be inge∣nerable and not procreated, which mooved all things rashly and disorderly before the constitu∣tion of the world: but contrariwise he calleth that, procreated and engendred, which Godfra∣med and composed of the first, and of a parmanent, eternall, and perfect good substance, name∣ly by creating it wise and well ordered, and by putting and conferring even from himselfe unto sense, understanding; and order unto motion: which when he had thus made, he ordained and [ 50] appointed it to be the governor and regent of the whole world. And even after the same maner he pronounceth; that the body of the world is in one sort eternall, to wit, not created, nor en∣gendred; and after another sort both created and engendred. For when he saith that whatsoe∣ver is visible, was never at rest, but mooved rashly and without all order: and that God tooke the same, disposed and ranged it in good order: as also when he saith that the fowre generall ele∣ments, fire, water, earth, and aire, before the whole world was of them framed and ordered de∣cently

made a woonderfull trouble & trembling as it were in the matter, and were mightily sha∣ken by it, such was their deformity and inequality. It appeareth plainly that he maketh these bodies in some sort to have a being and subsistence before the creation of the world. Contrari∣wise when he saith that the body is yoonger than the soule, and that the world was made and created in as much as the same is visible and palpable, as having a body, and that all things ap∣peare so as they are, when they were once made and created, manifest it is, and every man may see, that he attributeth a kinde of nativity to the nature of the body; and vet for all that farre is he off, from being contradictory and repugnant to himselfe so notoriously, and that in the most maine points. For it is not the same body nor of the same sort, which he saith was created by God, and to have bene before it was; for that were directly the case of some mount-banke or [ 10] jugling enchanter; but himselfe sheweth unto us, what we are to understand by this, generation or creation: For before time (quoth he) all that is in the world, was without order, measure and proportion: but after that the universall world began to be fashioned, and brought into some decent forme, whereas he found the fire first, the water, the earth and the 〈◊〉〈◊〉 pell mell in the same places, and yet having some shew and token what they were, but confusedly hudled every where, (as a man may well thinke that every thing must needs be so, where God is absent) in this case as they were then, God I say finding them, first brought the same into frame and fashion, by the meanes of formes and numbers. Furthermore, having said before that it was the worke not of one onely proportion, but of twaine, to joine and frame together the fabricke of the world, a [ 20] solid masse as it was and carying a depth and thicknesse with it: and declared moreover, that God after he had bestowed water and aire, betweene fire and earth, conjoined withall and framed the heaven, together with them. Of these things (quoth he) such as they were, and fower in number, the body of the world was in engendred, agreeable in proportion and entertaining a∣mity by that meanes: Insomuch as being once thus united and compact, there is nothing that can make disunion or dissolution, but he alone who first limited and brought all together; teach∣ing us hereby most plainely that God was the father and author, not of the body simply, nor of the frame, fabricke and matter onely of the world, but also of that proportion, measure, beauty and similitude which is in the body thereof: semblably thus much we are to thinke of the soule, as if one were not created by God, nor the soule of the world, but a certaine power of motion, [ 30] fantasticall, turbulent, subject unto opinion, stirring and moving of it selfe, and alwaies, but with∣out any order, measure, or reason whatsoever. The other, when God had adorned it with num∣bers & proportions convenient, he ordained to be the regent & governesse of the world created like as it selfe was also created. Now that this is the true sentence & meaning of Plato, and not by a fantasticall manner of speculation and inquisition, as touching the creation or generation, as well of the world as of the soule: this besides many others, may be an argument, that of the soule, he saith it was created and not created; of the world alwaies, that it was engendred and cre∣ated, but never eternall and not created. To proove this, we need not for to cite testimonies out of the booke Timaeus, considering that the said booke throughout, from the one end to the o∣ther, treateth of nothing else, but of the generation or creation of the world. And of other bookes, in his Atlanticke Timaeus making his praiers, nameth him who beforetime was by his [ 40] worke, and now by his word, God. And in his Politique, his Parmenidian guest saith, that the world being framed and made by God, became partaker of many good things: and in case there be any evill thing in it, the same is a remnant mingled within the first habitude and estate where∣in it was at first, before the constitution thereof, all irregular and disorderly. And in his bookes of Common-wealth, speaking of that number, which some call the Mariage, Socrates began to discourse and say thus: The God (quoth he) who is created and engendred, hath his period and conversation, which the perfect number doth comptise. In which place, what can he call the God created and engendred, but the world. * * * * *

* * * * * * * * * * * * * * * * * * * [ 50]

The first copulation is of one and two, the second of three and foure, the third of five and six; of which there is not one that maketh a quadrate number either by it selfe or by others: the fourth is of seven and eight, which being joined to the first, make in all the square quadrat num∣ber six and thirtie.

[illustration]

[ 10]

But of those numbers which Plato hath set downe the quaternarie, hath a more perfect and absolute generation; namely, when even numbers are multiplied by even intervals, and un∣even numbers likewise by odde intervals: for first it conteineth unitie as the very common stocke of all numbers as well even as odde and of those under it; two and three be the first flat and plaine numbers, and after them foure and nine are the first squares, then follow eight and seven and twentie, the first cubique numbers, putting the unitie out of this account. By which it appeareth that his will was not, that these numbers should be all set one above another directly in a right line; but apart, one after another alternatively, the even of the one side and the odde of the other, according to the description above made. Thus shall the files or conjugations also [ 20] be of like with like, and make the notable numbers, aswel by composition or addition as by mul∣tiplication of one with another: by composition, thus, Two and three make five; foure & nine make thirteene; eight and seven and twentie arise to five and thirtie. For of these numbers the Pythagoreans call five, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, as much to say, as a sound, supposing that of the spaces and in∣tervals of Tone, the fift, was the first that spake or sounded: thirteene they tearmed 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, that is to say, the Remanent or Defect, like as Plato did; despairing to divide a Tone in two equall por∣tions: and five and thirtie they tearme Harmonie, for that it is composed of the first numbers cubique, proceeding from even and od of the foure numbers, to wit, six, eight, nine and twelve, conteining an Arithmeticall and Harmonicall proportion. But this will appeare more evident∣ly by this figure here described and represented to the eies. Suppose then there be a figure set [ 30] downe in forme of a tile, called Parallelogrammon, with right angles, A.B.C.D.

[illustration]

[ 40] where of the one side (to wit, the lesse) A.B. is of five; the other, and namely, the longer, A.D. is of seven parts: let the lesse side be divided into unequall sections, to wit, into three and three, unto E. and the greater into other two unequall sections, three and foure to F. Then draw lines from the sections, crossing directly one another, by E.G.H. and F.G.I. So A.E.G.F. shall be six, A.B.I.G. nine, G.H.D.F. eight, and G.I.C.H. twelve. This tile-forme figure cal∣led [ 50] Parallelogrammon, being more long than broad, composed of five and thirtie parts, contei∣neth in it all the proportions of the first accords and consonances of Musicke in the numbers of the spaces into which it is divided. For six and eight have the proportion Epitritos, to wit, the whole and one third part; wherein consisteth the symphonie Diatessaron, that is to say, a fourth. Six and nine cary the proportion Hemiolion, to wit, the whole and halfe; and therein

consisteth Diapente, that is to say, a fifth. Betweene six and twelve there is the double proporti∣on, & therin consisteth Diapason, that is to say, an eighth. There is also the proportion of Tone sesquioctave, in nine and eight, which is the reason that the number five and thirtie conteining the proportions of tones, the consonances also and accords, they call Harmonie, which being multiplied by six, ariseth to two hundred and tenne, the very just number of daies wherein seven moneth children have their perfection in the wombe, and are ready to be borne. Item, goe to worke another way, and begin by multiplication in this wise: Twice three make six, and foure times nine come to six and thirtie, and seven and twentie multiplied by eight, ariseth to two hundred and sixteene. Now the perfect number is six, for that it standeth of equall parts, and in regard of the copulation of even and odde it is called the Mariage. Againe, that which is [ 10] more, it consisteth of the beginning and foundation of number, to wit, Unitie or One, of the first even number which is two, and of the first and odde number that is three. Moreover, six and thirtie is the first number both foure-square and also triangular. Foure-square, if it arise from the basis, six, and triangular, from eight: for it ariseth by multiplication of two quadrate num∣bers, to wit, of foure, multiplying nine; and by addition of three 〈◊〉〈◊〉 , one, eight, and seven and twentie, which being put together, make up sixe and thirtie, the number before described. Furthermore, it may be drawen out in forme of a tile, more one way than another from the two sides, and ariseth by multiplying twelve by three, or nine by foure. Now if a man take the num∣bers of the sides in those figures before described, to wit, six of the foure-square, and eight of the [ 20] triangle; nine of one of Parallelograms, and twelve of the other; he shall sinde that they will make the proportions of all the symphonies or accords in Musicke. For twelve compared with nine, will be Diatessaron or the fourth, which is the proportion that Nete hath to Mese; but compared with eight, it is Diapente or a fifth, the proportion of Mese or the Meane to Hypate; with twelve, it will be Diapason or a just eighth, which is the proportion betweene Nete and Hypate. As for the number of two hundred and sixteene, it is a cubique, arising from six, as the basis, and is equall to the owne compasse or circuit. These numbers proposed, having such ver∣tues and properties, yet the last seven and twentie hath this peculiar qualitie by it selfe, that it is equall unto all the other before it, being put together; namely, one, two, three, 〈◊〉〈◊〉 , eight, and nine. Moreover, it conteineth the just number of the daies of the moones revolution. [ 30] The Pythagoreans also doe place the Tone of distances & intervals of sounds in this very nūber, which is the reason that they call 13 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, as one would say, the default, for that it wan∣teth one of being the halfe of twenty seven. Moreover, that these numbers conteine the propor∣tions of all the consonances & accords in musicke, it is easie to be understood; for there is the proportion double of two to one, & therein consisteth Diapason; the Hemiolion or one and halfe of three & two, wherein is Diapente: likewise Epitritos, of fower to three, and therein con∣sisteth Diatessaron: also the triple of nine and three, wherein you shall finde Diapason and Di∣apente, to wit, a fift above a duple. Item, the quadruple of eight and two wherein is Dis diapa∣son. There is besides, the sesquioctave, of eight to nine, wherein is Toniaeon. If then a man count the unitie which is common unto the numbers as well even as odde unto foure, the [ 40] whole yeeldeth ten: and the even numbers betweene it and ten, with the unity being put to∣gether make fifteene, a number triangular, arising from the basis five: as for the odde num∣bers, to wit, one, three, nine, and twenty seaven, arise to forty, if they be summed together, and this number of forty is composed of thirteene and twenty seven, by which the mathematicians doe precisely measure the intervals of musicke and melody in song, calling the one Diesis, and the other Tonos: and the said number of forty ariseth by way of multiplication, by the vertue of quaternity; for if you multiply foure times every one of the foure; first, whereas by them∣selves to wit, one, two, three, foure, there will arise foure, eight, twelve, and sixteene, which being all summed together, make forty; which number conteineth besides, all the proportions of consonances and accords: for compare sixteene with twelve, you shall have the proportion Epitritos, that is to say, one and the third part, with eight duple, with foure quadruple: also [ 50] twelve compared to eight, hath the proportion Hemiolion, that is to say, one and a halfe, to foure triple, which comprehend the proportions just of Diatessaron, Diapente, Diapason, and Dis-diapason: Over and besides, the foresaid number of forty, is equall to the first two qua∣drats, and the two first cubicke numbers taken together, for the two first squares or quadrats be one and foure, the cubicks eight and twenty seaven, which if they be put together, amount to forty: So that the quaternity of Plato is in the disposition thereof more ample, of greater 〈◊〉〈◊〉 and perfection than that quaternity of Pythagoras.

But forasmuch as the numbers proposed, affoord not places for the medieties which are infer∣red; necessary it was to extend the numbers to larger tearmes and bondes, reteining still the same proportions: in regard whereof, we must say somewhat what they be, and treat first of these medieties. The former then, is that which both surmounting, & being also surmounted in equall number, is called in these daies Arithmeticall: the other which surmounteth, and is sur∣mounted by the same part of their extremities, is named Hypenantia, that is to say, subcontrary; as for example: The two limits or extremities and the mids of the arithmetical, be six, nine and twelve: for nine which is in the middes, surmounteth sixe just as much in number as it is sur∣mounted of twelve, that is to say, by three: but of the subcontrary, these be the extremities and the mids, six, eight, and twelve, for eight which is the mids, surmounteth six by two, and is sur∣mounted [ 10] of twelve by foure, which foure is the third part of twelve, like as two is the third part of sixe. Thus it falleth out in the medietie Arithmaticall, the middes surmounteth the one of these extremities, and is surmounted of the other, equally by the same part of the owne, but in the subcontrary by the same part, not of the owne, but of the extremities out gone of the one, and outgoing the other: and heereupon it is called subcontrary, and the same they likewise call harmonicall, because it affourdeth to the extremities the first resonances, to wit, be∣tweene the greatest and the least Diapason, that is to say, an eight; betweene the greatest and the mids, Diapente, that is to say, a five; & betweene the mids and the least, Diatesseron, that is to say, a fourth: for the greatest tearme or extremity being set upon the note or string Nete, and the least upon Hypate, the middes will be found just upon Mese, that is to say, the meane, which [ 20] maketh in regard of the greatest Diapente, and of the least Diatessaron: so that by this reason, eight shall be upon the meane, twelve upon Nete, and six upon Hypate: but how to know easi∣ly and readily these medieties aforesaid, Eudorus hath shewed the maner plainly and simply: And first and formost in the Arithmeticall, consider thus much: for if you take the two ex∣tremities, and put them together, and then the moity of the entire sum, the same will fall out to be the medietie Arithmeticall: or take the moitie of ech one of the 〈◊〉〈◊〉 , & adde them one to the other, that which ariseth thereof shall be mediatie arithmeticall, in duples & triples alike: but in the subcontrary, or harmonicall, if the two extremities be one to the other in pro∣portion duple, take the halfe of the greater, and the third part of the lesse, and the number ari∣sing of those two shall be the medietie Harmonicall: but in case the two extremities be in pro∣portion [ 30] triple, then contrariwise a man ought to take the moitie of the lesse, and the third part of the greater, for then the summe will be the medietie that he looketh for: as for example, let the lesse extremity be in triple proportion six, and the greater eighteene, if you take the halfe of six which is three, and the third part of eighteene which is six, you shall come to nine, for the medietie which doth surmount, and is surmounted by the same part of the two extre∣mities, that is to say, the one halfe. Thus you see how the medieties are taken: now the same must be interjected and placed betweene, for to fill and make up the places or intervals double and triple; but of the number proposed, some have no place of the middle, others, not suffici∣ent; and therefore the maner is to augment and set them out, in reteining alwaies still the same proportions, and so by that meanes make places and receptacles sufficient for to receive the [ 40] said medieties or mediocrities: First therefore, for the lesse end or 〈◊〉〈◊〉 , in stead of one they put six, because of all numbers it is the first that hath a halfe and a third part, and multiply all the numbers under by six, as it is written underneath, for to receive both the medieties in duple intervals:

12. 2.	1.	3. 18.
24. 4.		9. 54.
48. 8.		27. 162.

〈◊〉〈◊〉 for that Plato hath said, the intervals being made sesquialterall, sesquitertia, and sesqui∣octaves, out of these links in the precedent distances, he filled all the epitrites, with the intervall of sesquioctave, leaving one part of ech, and this distance of this part being left number to [ 50] number, having for the tearmes & extremities, two hundred fifty six, and two hundred forty three, &c. Upon these words of the text, forced they were to reduce these numbers, and make them greater, forby order two ought to have sesquioctave proportion, seeing that six of it selfe could not have proportion sesquioctave, & if it were divided by cutting the units peece-meale, the intelligence and doctrine thereof would be very intricate and hard to be conceived, there∣fore he called this operation in some sort multiplication, like as in the harmonicall mutation, where if you extend and augment the first number, necessarily the discription of all the other

notes must be stretched out and enlarged likewise. And therefore Eudorus following herein Crantor, taketh for the first number three hundred fowre-score and fowre, which ariseth by mul∣tiplying three-score and fowre, by six: and these were induced so to doe by the number three∣score and fowre, having for the sesquioctave, eight, which is the proportion betweene three∣score and fowre and threescore and twelve. But it agreeth better with the text, and the wordes of Plato, to suppose a moity. For the default which they call 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, will have the sesquioctave pro∣portion in the numbers which Plato hath set downe, two hundred six and fiftie, and two hundred three and fortie, having put for the first one hundred fourescore and twelve: and if the double of it be supposed for the first, the 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 shall be of the same proportion, but in number double, which five hundred and twelve hath to foure hundred eighty foure: for two hundred fiftie & six [ 10] are in epitrite or sesquitertiall proportion to one hundred fourescore and twelve, and five hun∣dred and twelve to foure hundred fourescore and foure. And verily, the reduction to this num∣ber was not without reason and proportion, but yeelded a probable reason to Crantor: for the number of threescore and foure is a cube, proceeding from the first quadrate, and a quadrate likewise, arising from the first cube, and being multiplied by three, the first odde number: the first triangular number, the first perfect number and sesquialter, make one hundred fourescore and twelve, which number also (as we will shew) hath his sesquioctave. But first of all you shall understand better what is 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, as also what is the meaning of Plato, if you call to minde a little, that which is usually taught and delivered in the Pythagoreans schooles: for Diastema, that is to say, intervals or space in matter of song, is whatsoever is betweene two sounds different in Te∣nour [ 20] or Tension. Of these intervals, one is called Tonus, to wit, that whereof the harmonie Dia∣pente surmounteth Diatessaron. Of this entier Tone, as Musicians do holde, cut in twaine, by the moitie are made two intervals, and both of them, the one aswell as the other, goe under the name Haemitonium. But the Pythagoreans do not thinke that it can be equally divided: where∣as therefore the two sections be unequall, they call the lesse 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, that is to say, the default, be∣cause it is somewhat lesse than the one halfe. And therefore some masters of Musicke there be, who make the accord Diatesseron, of two Tones and a Demi-tone or Haemitonion: others a∣gaine of two Tones and a 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉. So as it seemeth that the testimonie of hearing accordeth with the harmonicall Musicians; and of demonstration with the Mathematicians: and their proofe of demonstration goeth in this maner. This is put downe by them for certeine, and approo∣ved [ 30] by their instruments, that Diapason hath a double proportion, Diapente a sesquialterall, Diatessaron a sesquitertiall, and a Tone a sesquioctave. And the trueth heereof, a man may trie presently by an experiment, namely, by hanging two weights double, unto two strings that be equall, or by making two concavities in pipes, the one twice as long as the other, otherwise e∣quall: for the shawme or hautboies, which is the longer, will sound more base and loud, as Hy∣pate in regard of Nete: and of the two strings, that which was stretched by the heavier weight will sound higher & smaller as Nete in comparison of Hypate: and this is the very consonance Diapason. Semblably, three compared unto twaine, be it in length or in weight, will make Dia∣pente; and foure to three, Diatessaron: for the one hath the proportion epitrite, and the other hemiolion. And if the unequalitie of the foresaid lengths or weights be in proportion hemio∣ctave, [ 40] that is to say, of seven to eight, it will make the intervall Toniaeon, not altogether an har∣monicall accord, howbeit (as one would say) somewhat musicall and melodious; for that these sounds, if one strike, touch or sound one after another, make a pleasant noise and delectable to the eares; but if altogether, the noise will be troublesome and offensive: whereas contrariwise, in consonances and accords, howsoever one touch them, either together, or one after another, the eare receiveth the consent and accord with great delight. And yet this may moreover be shewed by reason, for the harmonie Diapason is composed of Diapente and of Diatessa∣ron, like as in number the double is composed of Hemiolion and Epitritos; for twelve is in proportion of Epitritos to nine, and Hemiolion to eight, and double to six: so that the double proportion is compounded of the sesquialterall and the sesquitertion, like as Diapason of Dia∣pente [ 50] and Diatessaron: but as there Diapente is greater than Diatessaron by a Tone, so heere in numbers, Hemiolion is greater than Epitritos by a sesquioctave. This being thus prooved by demonstration, let us see now, whether our sesquioctave may be divided into two equall secti∣ons; for if it can not, no more then, can the Tone: and for that eight and nine make the first proportion sesquioctave, and have no intervall betweene; both the one and the other being doubled, the number falling out betweene, maketh two intervals; so that it appeareth, that if the two intervals be equall, the sesquioctave may bee equally divided in twaine. Now the double

of nine is eighteene, and of eight, sixteene, which admit betweene them, seventeene. So it fal∣leth out that one of the intervals is greater, and the other lesse; for the former is of eighteene to seventeene, and the other of seventeene to sixteene. Then the sesquioctave proportion is divi∣ded into portions and sections unequall, and so consequently the tone also: and therefore this division being made, none of the sections is properly a Demytone, but one of them by good right hath beene tearmed by the mathematicians 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉: and this is it that Plato said: God when he filled the epitrites with sesquioctaves, left a portion of ech: whereof there is the same reason and proportion, that two hundred fiftie six have unto two hundred forty three; for take a Dia∣tessaron in two numbers, which have betweene them a proportion Epitritos, as two hundred fifty and six, to one hundred nintie two; of which let, the lesse number, one hundred nintie two [ 10] beset upon the base note of a tetracord, and the greater, to wit, two hundred fiftie and six upon the highest note: It must be shewed, that if this be filled with two sesquioctaves, there remaineth an intervall as great as is betweene two hundred fiftie six and two hundred forty three. For if the baser sound be stretched one tone; which is the proportion sesquioctave it maketh two hundred and sixteene: and againe if it be stretched another tone, it becommeth two hundred forty three, which surmounteth two hundred & sixteene, by twenty & seven, and two hundred and sixteene surmounteth one hundred fourescore & twelve by foure and twenty, of which, the seven and twenty is the sesquioctave of two hundred and sixteene, and foure and twentie, of one hundred fourescore and twelve: and therefore of these three numbers, the greatest sesquioctave is of the middest, and the middle of the least; and the distance or intervall, from the least to the [ 20] greatest, to wit, from one hundred fourescore and twelve unto two hundred fortie and three, two tones filled with two sesquioctaves: which intervall being taken away, there remaineth the inter∣vall of the whole, which is betweene two hundred fortie and three, and two hundred fiftie and sixe, and that is thirteene: and that is the reason why they called that number 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, that is to say, a default or residue.

For mine owne part, I thinke verily, that the sense of Plato is most cleerely expounded and declared in these numbers. Others having put downe the ends and tearmes of Diatesseron, for the treble two hundred eighty eight, and for the base, two hundred sixteene; goe through with the rest proportionably, save onely that they take the two defaults or remnants, betweene the two extremities: for the base being set up one tone or note, maketh two hundred fortie three: [ 30] and the treble being let downe another note, becommeth two hundred fiftie six: for these be sesquioctaves, two hundred forty three, and two hundred sixteene; likewise two hundred eighty eight, and two hundred fifty six; so that either of the intervals is Toniaeon: and there remaineth that which is betweene two hundred forty three, and two hundred fifty six, which is not a Demytone, but lesse: for two hundred eighty eight, is more than two hundred fifty six, by thirty two; and two hundred forty three, more than two hundred sixteene, by twenty seven; and two hundred fifty sixe more than two hundred forty three, by 13: and both these are lesser than the advantages or surplussages by halfe: and therefore Diatessaron is found to be of two tones and a 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, and not of two and a halfe. And thus you see the demonstration of this: and so it is no hard matter to understand by that which we have delivered: what is the reason [ 40] why Plato having said, that intervals sesquialterall, sesquitertian and sesquioctaves are made by filling the sesquitertians with sesquioctaves; made no mention of the seqsuialterons, but hath left them behind, namely, for that the sesquialter is filled, when one putteth a sesquioctave to asesquitertiall, or rather a sesquitence to a sesquioctave.

These things thus shewed in some sort by way of demonstration: now to fill the intervals, and to interject the Medieties if none before had shewed the meanes and maner how, I would leave you to do it for your exercise: but the same having beene done already by many worthy personages, and principally by Crantor, Clearchus, and Theodorus, all borne in the city Soli: It will not be impertinent to deliver somewhat as touching the difference betweene them; for Theodor us maketh not two files of nnmbers as the other doe, but rangeth them all in the same [ 50] line directly one after another, to wit, the duple and the triple: and principally he groundeth and fortifieth himselfe by this position (which they so call) of the substance drawen out in length, making two branches as it were from one trunke, and not foure of twaine: then he saith, that the interpositions of the Medieties ought so to take place; for otherwise there would be a trouble and confusion: and anon passeth immediately from the first duple to the first triple, when they should be that which ought to fulfill the one and the other. On the other side, there maketh for Crantor, the position and situation of plaine numbers with plaine, squares with

squares, and cubes with cubes, which are set one against another in opposite files, not accor∣ding to their range, but alternatively, * * * * * * * * * * * * * * * * * * * * 1.2 which is of one sort as Idea or forme: but that which is divided by bodies, is the subject and the matter; and the mixture of them both in common, is that which is complet and perfect.

As touching then the substance indivisible, which is alwaies one and of the same sort; wee are not thus to thinke, that it admitteth no division for the smalnesse thereof, like to those lit∣tle bodies called Atomi: but that of it which is simple, pure, and most subject to any passion or alteration whatsoever, alwaies like it selfe, and after one maner, is said to be indivisible, and to have no parts; by which simplicity, when it commeth to touch in some fort, such things as be [ 10] compounded, divisible, and caried to and fro, it causeth that diversitie to cease, restreineth that multitude, and by meanes of similitude, reduceth them to one and the same habitude. And if a man be disposed to call that which is divisible by bodies, matter, as subject unto it, and parti∣cipating the nature thereof, using a certeine homonymie or equivocation, it mattereth not much, neither skilleth it as touching the thing in question: but those who would have the corporall matter to be mixed with the indivisible substance, be in a great errour: first, because Plato hath not now used any names thereof, for that he hath evermore used to call it a recepta∣cle to receive all, and a nurse, not divisible by bodies, but rather a body divided into individu∣all particulars. Againe, what difference would there be, betweene the generation of the world, and of the soule, if the constitution of the one and the other, did consist of matter and things [ 20] intelligible?

Certes, Plato himselfe as one who would in no wife admit the soule to be engendred of the body, saith: That God put all that which was corporall within her; and then, that without forth the same was enclosed round about with it: In sum, when he had framed and finished the soule according to proportion, he inferreth and annexeth afterwards a treatise of matter, which be∣fore when he handled the creation of the soule, he never required nor called for, because crea∣ted it was without the helpe of matter.

The like to this may be said by way of confutation against Posidonius and his sectaries; for very farre they went not from matter; but imagining that the substance of tearmes and extre∣mities, was that which he called divisible by bodies, and joining with the intelligible, they af∣firmed [ 30] and pronounced, that the soule is the Idea of that which is distant every way, and in all the dimensions, according to the number which conteineth harmony, which is very erroni∣ous: For the Mathematicks (quoth he) are situate betweene the first intelligible and sensible things: but the soule having of intelligible things an eternall essence, and of sensible objects, a passible nature: therfore meet it is that it should have a middle substance between both. But he was not ware, that God after he had made and finished the soule, used the bounds & termes of the body, for to give a forme to the matter, determining the substance thereof dispersed, and not linked or conteined within any limits, by environing it with superficies, composed of tri∣angles, all joined together. And yet more absurd than that it is, to make the soule an Idea, for that the soule is alwaies in motion; but the Idea is immooveable, neither can the Idea be mix∣ed [ 40] with that which is sensible, but the soule is alwaies linked fast with the body: besides, God did imitate Idea as one who followed his patterne; but he wrought the soule as his piece of worke: And that Plato held the soule not to be a number, but rather a thing ordeined by num∣ber, we have already shewed and declared before.

But against both these opinions and their patrons, this may be opposed in common: That neither in numbers nor in tearmes and limits of bodies, is there any apparence or shew of that puissance, whereby the soule judgeth of that which is sensible; for the intelligence and facultie that it hath, was drawen from the participation and societie of the intelligible principle: But opinions, beliefs, assents, imaginations, also to be passive and sensitive of qualities inherent in bodies, there is no man will thinke that they can proceed from unities, pricks, lines, or super∣ficies: [ 50] and yet not onely the soules of mortall men have the power to judge of all the exterior qualities perceptible by the senses; but also the very soule of the world, as Plato saith, when it returneth circularly into her selfe, and toucheth any thing that hath a substance dissipable and apt to be dispersed; as also when it meeteth with ought that is indivisible, by mooving herselfe totally, she telleth in what respect any thing is the same, and in what regard divers and different; whereto principally ech thing is meet, either to doe or to suffer, where, when, and how it is affected, alwel in such as are engendred, as in those that are alwais the same. Moreover,

making a certeine description with all of the ten predicaments, hee declareth the same more cleerely afterwards: True reason (quoth he) when it meeteth with that which is sensible, and if therewith the circle of the other goeth directly to report the same, throughout the whole soule thereof, then there be engendred opinions and beliefes that be firme and true: but when it is conversant about that which is intelligible and discoursing by reason, and the circle likewise of the same, turning roundly with facility, doth shew the same, then of necessity there is bred per∣fect and accomplisht science; and in whatsoever these two things be infused, if a man call it otherwise than soule, he saith any thing rather than the truth: whence commeth it then that the soule had this motion opinative, which comprehendeth that which is sensible, divers and diffe∣rent from the other intellective that endeth in science? Hard it were to set this downe, unlesse [ 10] a man firmly presuppose that in this place, and at this present, he composeth not the soule sim∣ply, but the soule of the world, with the parts above mentioned, of a better substance, which is indivisible; and of a woorse that he calleth divisible by bodies; which is nothing else, but an imaginative & opinionative motion, affected & accordant to that which is sensible, not engen∣dred, but as the other of an eternall subsistance: for nature having the 〈◊〉〈◊〉 vertue, had also the facultie opinionative: but the intellective power is unmoveable, impassible, founded & set upon that substance, which abideth alwaies in one sort: whereas the other is divisible and wandering, in as much as it toucheth a matter that is alwaies floting, carried to and fro and dissi∣pable. For the matter sensible had before time no order at all, but was without all forme, bound or limitation whatsoever, and the faculty therein had neither expresse opinions articulate and [ 20] distinct, nor her motions all certaine and composed in order: but for the most part resembling turbulent and vaine dreames, troubling that which was corporall, unlesse haply they fell upon a∣ny thing that was better. For betweene two it was, having a nature conformable, and accordant to the one ond the other: chalenging matter by that which is sensitive, and by the judiciall part those things which are intelligible. And this declareth he himselfe in these proper termes: By my reckoning (quoth he) let this be the summe of the whole account that these three things had their being three waies before the heaven was, to wit, essence, space, and generation. As for space or place, he calleth matter by that name, as it were the seat, and otherwhiles a receptacle: the essence, that which is intelligible; and the generation of the world as yet not made, can be no other thing but a substance subject to motions and alterations, situate betweene that which imprinteth a forme and which is imprinted, dispensing and distributing the images from thence [ 30] hither: which is the reason it was called divisible, for that of necessitie both the sensitive must be divided and goe with the sensible, and also the imaginative with the imaginable. For the sensitive motion being proper unto the soule mooveth toward the sensible without: but the in∣telligence & understanding was of it selfe, stable, firme and immovable: howbeit being infused once into the soule and become master and lord thereof, it rolleth and turneth upon it selfe, and accomplisheth a round & circular motion, about that which is alwaies permanent, and touch∣ing that principally which is, and hath being. And therefore hard was the mixtion and associa∣tion which mingled the divisible with the indivisible, that which is every way moovable, with that which never mooveth, and forcing in one word the other to meet and joine with the same. [ 40] So the other was not motion, no more than the same was station; but the beginning both of Di∣versity and also of Identity or The samenesse: for the one and the other descend from divers principles, to wit, the same from unity, and the other, from binary, and were at the first mingled 〈◊〉〈◊〉 here in the soule; as tied by numbers, proportions and medieties harmonicall: and the other being imprinted into the same, maketh difference: but the same infused into the other, causeth order; as it appeareth manifestly in the first powers of the soule, to wit, the faculties of moving and of judging. As for motion, it sheweth incontinently about the heaven, diversity in identity by the revolution of the planets, and identity in dive sity by the setled order & situation of the fixed starres: sor in these, the same beareth sway and is more predominant; but contrari∣wise, the other, in those that be neerer to the earth. But judgement hath two principles, to wit, [ 50] understanding, from the same, for judging of things universall; and sense, from the other, to judge of particulars. Now reason is mingled of them both, being intelligence in things generall and intelligible; but opinion onely in matters sensible, using for instruments, both the fansies and imaginations betweene, and also the memories; whereof the former make the other in the same; but the latter, the same in the other. For intelligence is the motion of the intelligent a∣bout that which is stable and permanent; but opinion is the mansion of the sentient about that which moveth. As for imagination or fansie, being a connexion of opinion to the sense, the

same, placeth it in memorie; and contrariwise, the other stirreth it in the difference and distincti∣on of that which is past, and that which is present, touching both identity and diversitie toge∣ther.

Now the better to understand the proportion wherewith he made the soule, we must take 〈◊〉〈◊〉 patterne and example, from the constitution of the bodie of the world: for whereas the two ex∣tremes, to wit, pure fire and earth, were by nature hard to be tempered one with another; or∣to say more truely, impossible to be mixed and incorporate together: he placed in the 〈◊〉〈◊〉 betweene, aire before fire, and water before earth: and so contempered first these two meane e∣lements, and afterwards by their helpe, the other extremes also, which he fitted and framed to∣gether, both with the said meanes, and also with themselves one with another. And heere a∣gaine, [ 10] the same and the other, being contrary puissances and extremities, fighting one against the other as meere enemies, he brought together, not immediatly by themselves, but by put∣ting betweene other substances, to wit, the indivisible, before the same, and the divisible before the other, according as in some sort the one had affinitie and congruency with the other: af∣terwards when these were mixed together, he contempered likewise the extreames, and so warped and wove, as one would say, the whole forme of the soule, making as farre as it was pos∣sible, of things unlike, semblable, and of many one. But some there bee who give out, that 〈◊〉〈◊〉 was not well said of Plato: That the nature of the other, was hard to bee mixed and tempered; considering (say they) that it is not altogether insusceptible of mutation, but a friend to it, and rather the nature of the same, being firme and hard to be turned and remooved, admitteth not [ 20] easily any mixture, but flieth and rejecteth it, to the end that it may remaine simple, pure, and without alteration: but they who reproove this, are ignorant that the same, is the Idea of such things as be alwaies of one sort; and the other, the Idea of those that change. Also that the effect of this, is evermore to divide, separate, and alter that which it toucheth; and in a word, to make many of one: but the effect of that is, to conjoine and unite by similitude, many things there∣by into one forme and puissance. Thus you see what be the powers and faculties of the soule of this universality, which entring into the fraile, mortall, and passible instruments of bodies, however they be in themselves incorruptible, impatible and the same; yet in them now appec∣reth more the forme of an indeterminate duality: but that forme of the simple unitie, sheweth it selfe more obscurely, as deepely setled within: howbeit for all that, hardly shall one see and [ 30] perceive in a man, either passion altogether void of reason, or motion without understanding, wherein there is no lust, no ambition, no joy or griefe: and therefore some philosophers there be, who would have the perturbations of the mind to be reasons; as if forsooth, all disire, sorow, and anger, were judgements. Others also doe hold, that all vertues be passions: for in 〈◊〉〈◊〉 (say they) there is foure, intemperance, pleasure, injustice, lucre. Howbeit, the soule being both contemplative, and also active at once, as it doth contemplate universal thing; so it practi∣seth particulars, seeming to conceive the one by intelligence, and to perceive the other by sense: common reason meeting alwaies the same, in the other, and likewise, the other, in the same, endevoureth verily to sever by divers bonds and partitions, one from many; and the indivisible from the divisible, but it can not bring it so about, as to be purely in the one or the other, for [ 40] that the principles be so enterlaced one within another, and hudled pell-mell together.

In which regard, God hath appointed a certeine receptacle for the same, and the other, of a di∣visible, and indivisible substance, to the end, that in diversity there should be order; for this was as much as to be engendred. Seeing that without this, the same should have had no diversitie, and consequently no motion nor generation; neither should the other have had order, and so by consequence also, neither consistence nor generation: for if it should happen to the same, to be divers from the other, and againe, to the other, to be all one with the same; such a communi∣on and participation, would bring foorth of it selfe nothing generative, but require some third matter to receive them, and to be digested and disposed by them. And this is that which God ordeined and composed first, in defining and limiting the infinity of nature, mooving about [ 50] bodies, by the firme steadinesse of things intellectuall. And like as there is one kinde of bru∣tish voice, not articulate nor distinct, and therefore not significant; whereas speech consisteth in voice, that giveth to understand what is in the minde: and as harmony doeth consist of ma∣ny sounds and intervals; the sound being simple and the same, but the intervall a difference and diversitie of sounds, which when they be mixed and tempered together, make song and melo∣dy: Even so the passible part of the soule, was infinit, unstable, and disordinate; but afterwards became determinate, when tearmes and limits were set to it, and a certeine forme expelled to

that divisible and variable diversity of motion. Thus having conceived and comprised the same, and the other, by the similitudes and dissimilitudes of numbers, making accord of difference: thereof the life of the universall world became wise and prudent, the harmony consonant, and reason drawing with her 〈◊〉〈◊〉 , tempered with grace and perswasion, which the common sort call fatall destiny; Empedocles named concord and discord together: Heraclitus the oppo∣site tension and harmony of the world, as of a bow or harpe, wherein both ends bend one a∣gainst another: Parmemdes, light and darknesse: Anaxagoras, understanding and infinitie: Zoroastes, God, and the devill; tearming the one Oromasdes, and the other Arimanius: But Euripides did not well to use the disjunctive for the copulative, in this verse,

Jupiter, natures necessity, Or humane minde, whether he be?

For in truth, that puissance which pierceth and reacheth through all things, is both necessitie, [ 10] and also a minde. And this is it which the Aegyptians would covertly give us to understand, un∣der the vaile of their mysticall fables, that when Horus was condemned and dismembred, his spirit and bloud was given and awarded to his father, but his flesh and grease to his mother: But of the soule there is nothing that remaineth pure and sincere, nothing unmixt and apart from others; for as Her aclitus was woont to say: Hidden harmony, is better than the apparant: for that therein, God who tempered it, hath bestowed secretly and concealed, differences and diversities: and yet there appeereth in the unreasonable part, turbulent perturbations, in the rea∣sonable setled order: in senses necessitie and constreint; in the understanding full power and [ 20] entier libertie: but the terminant and defining power, loveth the universall and indivisible, by reason of their conjunctions and consanguinity. Contrariwise, the dividing puissance, en∣clineth and cleaveth to particulars by the divisible. The totall universalitie joieth in a setled or∣der, by the meanes of the same, and againe, so farre foorth as need is, in a mutation by the meanes of the other: but the difference of inclinations to honesty or dishonesty, to pleasure, or displeasure; the ravishments and transportations of the spirit in amorous persons, the com∣bats in them, of honour against voluptuous wantonnesse; doe evidently shew, and nothing so much, the commixion of the nature divine and impassible with the mortall and passible part in bodily things; of which himselfe calleth the one the concupiscence of pleasure ingenerate and inbred in us, the other an opinion induced from without, desirous of the soveraigne good: [ 30] for the soule of it selfe produceth and yeeldeth passibility; but the participation of understan∣ding commeth to it without foorth, 〈◊〉〈◊〉 by the best principle and cause, which is God: so the very nature of heaven is not exempt from this double societie and communion; but that a man may see how otherwhiles it doth encline and bend another way, by the revolution of the the same which is more predominant, and so doth governe the world: and a portion of time will come, like as it hath beene often heeretofore, when as the wisedome thereof shall be dul∣led and dazeled, yea and laid asleepe, being filled with the oblivion of that which is meet and decent for it: and that which from the beginnings is familiar and conformable to the body, shall draw, weigh downe, and turne backe the way and course of the whole universality on the right hand: but breake and undoe the forme thereof quite it shall not be able, but reduce it againe to [ 40] the better, and have a regard unto the first pattern of God, who helpeth the endevours thereof, and is ready to reforme and direct the same.

Thus it is shewed unto us in many places, that the soule is not altogether the worke of God; but having a portion of evill inbred in her, she hath bene brought into order and good dispose by him who hath limited infinity by unity; to the end that it should becom a substance bounded within the owne tearmes: and hath set by the meanes of the same and the other, order, change, dif∣ference, and similitude: and hath contracted and wrought a society, alliance and amity of all things one with another, as farre as possible it was, by the meanes of numbers and proportions. Of which point, albeit you have heard much speech, and read many books and writings; yet I shall not doe amisse, but greatly to the purpose, if briefely I discourse thereof. First setting [ 50] downe the words of Plato.

God (quoth he) deducted first from the universall world, one part: and then double so much: afterwards a third portion, to wit, the one, and halfe of the second, and the triple of the first: Soone after a fourth, to wit, the double of the second: & anon a fift, namely the triple of the third: After that a sixt, to wit, the octuple of the first, and a seventh, which was the first seven twenty fold. This done he filled the double and triple intervals; cutting from them also certaine parcels from thence, which he interjected berweene these: in such sort as in every intervall there were two medieties: the one surmounting, and surmounted by the same

portion of the extremites: the other, surmounting by equall number, one of the extremities and surmounted of another by the like. But seeing the intervals carry the proportions sesquial∣terall, sesquitercian and sesquioctave: of these ligaments in the first precedent distances, he fil∣led up all the sesquiterces with the intervall of the sesquioctave, leaving of each of them one part: And this distance of the part or number being left of number to number, it had for the tearmes and bonds thereof in proportion to that which is betweene, two hundred fiftie six, and two hundred forty three.

Here first and formost a question is mooved as touching the quantity of these numbers: and secondly, concerning the order: and thirdly, of their power. For the quantity and sum: what they be which he taketh in the duple intervals? For the order, to wit, whether they ought to be set and disposed all in one range, as Theodor us did? or rather as Cran∣tor, [ 10] in the figure of the letter lamda. 〈◊〉〈◊〉 . setting upon the point or top thereof unity or the first, & then in one file apart, the duples, and the triples in another, for the use and power, namely what they conferre to the constitution and composition of the soule. As concerning the first, we will reject those who say, that it sufficeth in these proportions to cōsider of what nature be the inter∣vals, and of what the midieties which fill them up, in what numbers soever a man may suppose that they have places capable betweene of the proportions aforesaid: for that the doctrine go∣eth after the same maner. And albeit that which they say, were true, yet the proofe and demon∣stration thereof is but slender without examples, and hindreth another speculation, wherein there is contained a pleasant kinde of learning and philosophy. If then, beginning at unity, we put apart by them selves the numbers duple and the triple as he himselfe teacheth us, there will be [ 20] of the one side two, foure, and eight, on the other, three, nine, and twenty seven; which are in all seven, taking the unity as common, and proceeding forward in multiplication unto fowre. For it is not in this place onely, but also in many others, where the consent and agreement is very evident, that is betweene the quarternary and the septenary. And as for that quaternity of the Pythagoreans so much voiced and so highly by them celebrated, it is of thirty six, which hath this admirable matter in it above all others, that it is compounded of the fowre first even numbers, & of the fowre first od numbers: and it ariseth by the fourth couple or conjugation of number, ranged in order one after the other. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

For the first is of one and two: the second of one and three which be od. For setting one in [ 30] the first place, as indifferent and common to both; then taketh he eight, and twenty seven, shewing and as it were pointing with the finger, what place he giveth to the one and the other kinde.

But to treat hereof after a more exact and exquisit maner, appertaineth unto others: But that which remaineth is proper to the subject matter in hand. For it was not upon any ostenta∣tion of skill and sufficiencie in the Mathematicall arts that Plato hath inserted within a treatise of naturall philosophy, this Arethmeticall and harmonicall medieties, but as a discourse verie meet and fit to serve for the composition and constitution of the soule; howsoever there bee some who seeke for these proportions in the swiftnesse more or lesse of the wandring sphaeres; others rather in their distances; some in the magnitudes of the starres; and others a∣gain, [ 40] after a more curious maner, in the Diamiters of the Epicycles, as if that creatour had in re∣gard thereof, and for this cause applied and fitted the soule distributed into seven parts, unto the celestiall bodies. Many there be moreover who bring hither and accomodate to this matter the Pythagoreans inventions, tripling the distances of bodies from the midst: which they doe after this maner, setting upon fire unity; and upon the earth opposit unto ours, three; upon the earth nine; upon the Moone twenty seven; upon Mercurie fowre-score and one; upon Ve∣nus two hundred forty three; and upon the Sun himselfe 729. for that it is both quadrat and cube: which is the reason that they call the sun also one while quadrat and another while cube: and after the same sort they reduce the other starres by way of triplation. But these philosophers doe miscount greatly, and stray farre from reason and proportion indeed, if so be that Geome∣tricall [ 50] demonstrations do availe ought: yet in comparison of them, well fare they who goe to worke another way; and albeit they prove not their positions exactly, yet (I say) they come neerer to the marke, who give out, that the Diameter of the sunne, compared to the Diameter of the earth, is in the same proportion that twelve is to one: that the Diameter or Dimetient line of the earth is triple to that of the moone: and the least fixed starre that is to be seene, hath no lesse a Diameter, than the third part of the Diameter of the earth: also that the totall globe of the earth, compared with the sphaere of the moone, carieth the proportion of twentie

seven to one: The Diameters of Venus and the earth, are in double proportion, but their globes or sphaeres beare octuple proportion, to wit, eight for one. Semblably, the intervall of the ecleptory, and the shadow which causeth the eclipse, is triple to the Diameter of the moone. Also the latitude of the moones declination from the Zodiaque on either side, is one twelfth part: likewise that the habitudes and aspects of her to the sunne, in distances triqueter, or qua∣drangular, take the formes and figurations either of the halfe moone, at the first quarter, or else when she swelleth and beareth out on both sides: but after she hath passed sixe signes of the Zodiaque, she maketh a full compasse, and resembleth a certeine harmonicall symphonie of Diapason in Hexatonos. And forasmuch as the sunne about the solstices or tropicks, as well of summer as winter mooveth least, & most slowly; but contrariwise, about the two equinoxes [ 10] in Spring and Autumne, most swiftly, and exceeding much: the proportion of that which he taketh from the day, and putteth to the night, or contrariwise, is after this maner in the first thirty daies; for in that space after the solstice in winter, hee addeth to the day the sixt part of that exuperance, whereby the longest night surmounteth the shortest day: and in another thir∣tie daies following after that, a third part, and so forward in the rest of the daies one halfe, until you come to the aequinox, in fextuple and triple intervals, to make even the inequality of the times. But the Chaldeans say, that Spring in regard of Autumne carieth proportion Diatessa∣ron, in respect of winter Diapente, and in comparison of summer Diapason: But if Euripides hath well limited the foure quarters of the yeere when he said:

For summer hot, foure moneths or deined be, [ 20] For winter colde likewise are other foure: Shorter is rich Autumne by one 〈◊〉〈◊〉 , And pleasant Spring whiles it remaines in floure.

then the seasons doe change after the proportion Diapason. Some attribute to the earth, the place of the musicall note Proslambanomenos: unto the moone Hypate: unto Mercurie and Lucifer Diatonos and Lichanos: the sunne they set upon Mese (they say) containing Diapason in the middes, distant from the earth one fifth or Diapente, and from the sphaere of the fixed starres a fourth, or Diatesseron. But neither the prety conceited imagination of these toucheth the trueth any way, nor the reckoning and account of those other, commeth precisely to the point. Well, those who affirme that these devices agree not to the minde of Plato, are yet of [ 30] opinion, that those other agree very well to the propositions described in the Tablature of musicians, which consisteth of five tetrachords, to wit, the first Hypaton, as one would say, of base notes; the second, Meson, that is to say, of meanes; the third, Synemmenon that is to say, of conjuncts; the fourth, Diezeugmernon, that is to say, of disjuncts; & the fift, Hyperbolaeon, to wit, of the high and excellent notes: semblably, say they: The planets be set in five distan∣ces, where of the one is from the moone unto the sunne, and those which have the same revolu∣tion with him, as Mercurie and Venus; a second, from these three unto the firie planet Mars; the third, from thence to Jupiter; the fourth, from him to Saturne; and the fift reacheth unto the starry skie: so that the founds and notes which determine the five terrachords, answere to the proportion of the planets or wandring starres. Moreover, we know very well, that the an∣cient [ 40] musicians, did set downe no more notes but two Hypates, three Netes, one Mese, and one Parame: so as their musicall notes were equall in number to the planets: but our moderne ma∣sters of musicke, have added that which is called Proslambanomenos, namely, lower by one note than Hypate, and enclining to the base: and so the whole composition they made Dis∣diapason; not keeping and observing the order of the consonances according to nature, for Diapente is before Diatesseron, by adding one note or tone to Hypate toward the base; where∣as it is certeine that Plato tooke one note to it toward the treble; for hee saith in his books of Common-wealth: That every one of the eight sphaeres hath a sirene sitting upon it, causing the same to turne about, and that ech one of them hath a severall and proper voice of their owne: but of altogether there is contempered a certeine harmonie: these sirenes being dispo∣sed [ 50] to solace themselves, sing for their pleasure divine and heavenly tunes, dauncing withall a sacred daunce, under the melodious consent of eight strings: as also there were eight princi∣pall tearmes at first of proportions double and triple; counting for one of these tearmes or li∣mits unitie to either part: but the more auncient sort have given unto us nine muses, to wit, eight as Plato himselfe saith, about the celestiall bodies, and the ninth about the terrestriall, cal∣led foorth from the rest to dulce and set them in repose, in stead of errour, trouble, and inequa∣lity. Consider now I pray you, whether the soule being become most just and most wise, doth

not manage the heaven and celestiall things by the accords and motions therein? And thus en∣dued she is by proportions harmonicall; the images where of are imprinted upon the bodies and visible parts of the world which are seene: but the first and principall power is visibly inser∣ted in the soule which sheweth herselfe accordant & obeisant to the better & more divine part, all the rest consenting likewise thereto. For the soveraigne creatour, finding a disorder and con∣fusion in the motions of this disordinate and foolish soule, being evermore at discord with her selfe, divided and separated some; reconciled and reunited others; using thereto numbers and proportions; by meanes where of, the most deafe bodies, as blocks and stones, wood, barks of trees, and the very rennets and mawes of beasts, their guts, their galles and sinewes, being fra∣med, contempered, and mixed together in proportion, exhibite into us the figures of statues [ 10] woonderfull to see to, and drogues and medicines most effectuall, yea and sounds of musicall instruments right admirable. And therefore Zeno the Citiean, called foorth yong men to see and beholde minstrels playing upon flutes and hautboies: That they might heare (quoth he) and learne, what sweet sounds and melodious noises, hornes, pieces of wood, canes and reeds do yeeld, yea and whatsoever matters els musicall instruments be made of, when they meet with proportions and accords. As for that which the Pythagoreans were woont to say and affirme, namely, that all things resembled number, it would aske a long discourse for to declare it. But that all the gods who were before at discord and debate, by reason of their dissimilitude, and whatsoever els jarred, grew to accord and consonance one with another, where of the cause was the contemperature, moderation and order of number and harmonie, the very Poets were not [ 20] ignorant of, who use to call such things as be friendly, 〈◊〉〈◊〉 and pleasing, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉: but adversa∣ries and enemies they terme 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, as if discord and enmitie were nothing els but dispropor∣tion: and verily that Poet whoever he was, that made a funerall dittie for Pindarus, when he said thus of him,

〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉. To strangers kinde he was and affable, To citizens friendly and pliable.

shewed very well, that he held it for a singular vertue to be sociable, and to know how to sort and agree with others: like as the same Pindar us himselfe,

When God did call, he gave attendance, [ 30] And never bragd of all his valiance,

meaning and signifying Cadmus. The olde Theologians and Divines, who of all Philosophers are most ancient, have put into the hands of of the images of the gods, musicall instruments, minding nothing lesse thereby, than to make this god or that a minstrell, either to play on lute or to sound the flute, but because they thought there was no greater piece of worke than ac∣cord and harmonicall symphonic could beseeme the gods. Like as therefore, hee that would seeke for sesquitertian, sesquialterall or double proportions of Musicke, in the necke or bridge, in the belly or backe of a lute, or in the pegs and pinnes thereof, were a ridiculous foole (for howsoever these parts ought to have a symmetrie and proportion one to another in regard of length and thicknesse; yet the harmonie where of we speake, is to be considered in the sounds [ 40] onely.) Even so, probable it is, and standeth with great reason, that the bodies of the starres, the distances and intervals of sphaeres, the celeritie also of their courses and revolutions, should be proportionate one unto the other, yea and unto the whole world, as instruments of musicke well set and tuned, albeit the just quantitie of the measure be unknowen unto. But this we are to thinke, that the principall effect and efficacie of these numbers and proportions, which that great and sovereigne Creatour used, is the consonance, accord, and agreement of the soule in it selfe; with which she being endowed, she hath replenished both the heaven it selfe, when she was setled thereupon, with an infinite number of good things; and also dispo∣sed and ordeined all things upon the earth, by seasons, by changes and mu∣tations, tempered and measured most excellently well and with sur∣passing [ 50] wisdome, aswell for the production and generation of all things, as for the preservation and safety of them, when they were crea∣ted and made.

Notes

• * 1.1

  〈◊〉〈◊〉 and 〈◊◊〉〈◊◊〉 .
• * 1.2

  Heere is a 〈◊〉〈◊〉 ; 〈◊◊〉〈◊◊〉 .