the participations of this subject, and establish the rare and the denfe as the principles of participations; in the fame manner thefe alfo affert, that diverfities are the caufes of other things. But they fay that these are three: figure, order, and position. For they affert that being differs by ryfmos, diathege, and trope: but of these rysmos is figure, diathege order, and trope pofition: for the letter a differs from the letter n in figure, but the fyllable an from na in order, and Z from N in position. But these men, in a manner fimilar to others, negligently omit to confider with refpect to motion, whence it is derived, and how it tubfifts in beings. And thus far, as we have faid, thofe prior to us appear to have investigated the two caufes of things.

CHAP. V.

BUT among these, and prior to these *, those who are called Pythagoræans, and who were the first that applied themselves to mathematics, gave the precedency to thefe difciplines; and, in confequence of being nourished in them, were of opinion that these are the principles of all beings. But fince among these disciplines numbers are first by nature, and it appeared to them that in numbers more fimilitudes both to things which are, and to things in generation, are seen, than in fire, earth, and water (for this particular property † of numbers is justice, that soul and intellect, and again another opportunity, and in a similar manner, as I may say, with respect to each of the reft); and further ftill, fince they perceived the participated properties and reasons of harmonies in numbers, and fince other things appeared in every refpect to be naturally affimilated to numbers, but numbers are the first elements of every nature; hence they conceived the elements of numbers § to

Aristotle, fays Alexander Aphrodifienfis, fpeaks in this manner because Pythagoras himfelf was a little prior to Democritus and Leucippus, and many of his auditors flourished at the fame time with these two philofophers.

+ The word here used by Aristotle for property, as also in many other parts of this work, is walos, which is literally paffion. It may therefore fuffice, once for all, to obferve that wherever Tabos and abn occur, they fignify participated property or properties. Plato alfo ufes wabos in this

fenfe.

‡ Aoyos, reason, wherever it occurs in Aristotle, either fignifies computation, in calculations and reckoning, or that inward intellectual difcurfus commonly called reasoning, or a certain productive and feminal principle, or that which is indicative and definitive of a thing: in the prefent paffage it fignifies a productive principle.

work.

Concerning the numbers of the Pythagoreans, fee the notes on the thirteenth book of this

be

be the elements of all things, and that all heaven is harmony and number and fuch things as are acknowledged to be evinced both in numbers and harmonies, these they collected together and adapted to the participated properties and parts of the heavens, and to the whole order of things. Likewife, if any thing was found any where to be much deficient, they supplied the defect, that the whole of their treatife might properly accord with itself. I fay, for instance, since the decad appears to be perfect, and to comprehend all the nature of numbers, hence they fay that the bodies which revolve in the heavens are ten; but as nine only are apparent, they make the tenth to be antichthon, or the oppofite earth. But these things are confidered by us more accurately in other places *.

However, we have related these things that we may understand from these men what the principles are which they establish, and how they fall into the above-mentioned caufes. For it appears that they also confidered number as a principle, as matter to beings, and as participated properties and habits. But they affert that the elements of number are the even and the odd; and that of these, the one is bounded, but the other infinite; and that the one is composed from both these, because it is both even and odd. They likewife affert that number confifts from the one, and that numbers, as we have faid, compose the whole of heaven. But others of these affert that there are ten principles, which are denominated according to co-ordination, viz.

BOUND, THE INFINITE:

THE ODD, THE EVEN:

THE ONE, MULTITUDE:

RIGHT HAND, LEFT HAND:

THE MASCULINE, THE FEMININE:

THE QUIESCENT, THAT WHICH IS IN MOTION:

THE STRAIGHT, THE CURVED:

LIGHT, DARKNESS:

GOOD, EVIL:

THE SQUARE, THE OBLONG.

Alcmæon the Crotonian appears to have entertained this opinion: and either he derived this dogma from them, or they from him. For Alemæon flourished when Pythagoras was an old man. But his doctrine was fimilar For he says that the multitude of human affairs re

to that of these men.

i. e. in his books de Cœlo.

ceives a twofold divifion (meaning into contrarieties), yet not diftinguished as they diftinguish them, but defined in a cafual manner: fuch as white, black; fweet, bitter; good, evil; the finall, the great. He therefore spoke indefinitely concerning the reft: but the Pythagoræans declare how many, and what are the contrarieties. Hence thus much may be understood from both, that contraries are the principles of beings; but from the Pythagoræans we learn the number and quality of these principles: yet it is not clearly determined by them how they may be applied to the above-mentioned causes. But they appear to difpofe the elements as in the fpecies of matter. For from these, as things inherent, they fay that effence is compofed and fashioned. From these things, therefore, the conceptions of the antients, who afferted that the elements of nature were many, may be fufficiently seen.

But there are some who have discoursed about the universe as if it were one nature: yet all of them have not discoursed after the fame manner, neither of that which subsists beautifully, nor of that which fubfifts according to nature. By no means, therefore, does the discourse concerning these men harmonise with the present fpeculation of causes. For they do not speak like certain physiologists, who, supposing being to be one, at the fame time generate from the one, as from matter; but their affertions are of a different nature. the phyfiologifts who contend that being is one, when they generate the universe, at the fame time add motion: but these men affert that the universe is immoveable. Thus far, however, a discourse about these men is adapted to the prefent inquiry. For Parmenides appears to have touched upon the one according to reafon, but Meliffus according to matter. Hence the former afferts that the universe is finite *, but the latter that it is infinite. But Xeno

For

phanes,

* The following remarkable paffage from Simplicius in Phyf. p. 7, on the concord of these antient philofophers refpecting the principles of things, will, I doubt not, be highly acceptable

to the liberal reader:

"Perhaps it will not here be improper to digrefs a little, and point out to the more ftudious how, though the antients appear to differ from each other in their opinions concerning the principles of things, yet at the same time they harmoniously agree. For fome of them discoursed concerning the intelligible and first principle of things, as Xenophanes, Parmenides, and Meliffus; Xenophanes and Parmenides, indeed, calling it one and finite : for it is necessary that the one should have a fubfiftence prior to multitude, and that the cause of bound and limitation to all things, should be rather defined according to bound than according to infinity; and that the every-way perfect, and which has received its proper end, fhould be definite, or rather fhould be the end, as it is the beginning of all things. For the imperfect being indigent, has not yet received the limitation

phanes, who was the first that introduced this doctrine (for Parmenides is faid to have been his difciple), did not affert any thing clearly; nor does he appear to have apprehended the nature of either of thefe, but, looking to the whole of heaven, he fays that the one is God. Thefe men, therefore, as we have said, are to be difmiffed in the prefent inquiry; two of them, indeed, entirely, as being a little too ruftic, viz. Xenophanes and Meliffus. But Parmenides appears to have feen more than thefe where to fpeak. For, befides being itself, he thought fit to confider non-being as nothing, and hence was neceffarily of opinion that being is one, and nothing elfe; concerning which doctrine we have spoken more clearly in our Phyfics. But being compelled to follow the phænomena, and conceiving that, according to reafon, the one had a fubfiftence, but, according to fenfe, the many, he again establishes two caufes and two principles, viz. the hot and the cold, or, in other words, fire and earth. But of these he difpofes the one, viz. the hot, according to being, but the other according to non-being.

From what has been faid, therefore, and from those wife men who adhered to reason, we now receive these particulars. From the firft indeed *, that

the

limitation of bound. This exception, however, must be made, that Xenophanes places it beyond motion and reft, and every anti-ordination, as being the cause of, and tranfcending, all things, in the fame manner as Plato in the firft hypothesis of his Parmenides. But Parmenides beholding it as fubfifting according to fame and fimilar (i. e. as having an effence perpetually the fame with, and fimilar to, itfelf), and as above all mutation, and perhaps energy alfo and power, celebrates it as immoveable, and alone as being exempt from all things. Meliflus too, in a fimilar manner, appears to have contemplated the immutability of this caufe, and to have evinced that he is infinite, as alfo unlegotten, from the never-failing nature of his effence and the infinity of his power."

The oppofition, therefore, of Ariftotle to the doctrine of thefe philofophers, is, as usual, directed to the literal and not to the true meaning of their affertions.

* Ariftotle here means those philofophers who fpeculated the fenfible order of things and investigated the elements of bodies, viz. Thales and Heraclitus, Anaximenes and Diogenes, Anaximander, Leucippus and Democritus. Of thefe, Thales afferted that the element of bodies was water, in confequence of furveying its prolific, nutritive, connective, vivific, and yielding nature; but Heraclitus, that it was fire, from regarding the vivific and demiurgic nature of this element. Anaximenes affirmed that it was air, from beholding the plastic power of this element, and the facility with which it pervades fire and water; and Anaximander, that it was of a middle nature, between fire and air, from the facility with which it receives mutation. And, laftly, Leucippus and Democritus called the elements of bodies atoms, in confequence of regarding the difference of their figures, pofition, and order. So that, as Simplicius juftly obferves of the antient philofophers, fome contemplated the intelligible, and others the fenfible, order of things. Some inveftigated

D

two.

the principle of things is corporeal (for water, and fire, and the like, are bodies); and of these fome affert that there is one, but others that there are many corporeal principles; but both agree in placing these principles as in the fpecies of matter. But from certain others who establish this caufe, we receive befides this the principle whence motion is derived; and according to fome there is one principle, but according to others there are two principles of this kind. As far, therefore, as to the Italic philofophers, and separate from them, others have spoken in a more becoming manner about these things, except, as we have faid, that they used two caufes; and of these some made the other caufe, or that whence motion is derived, to be one, but others to be The Pythagoreans, after the fame manner, faid that there are two principles. But thus much they added, which is peculiar to them, that they did not think the finite, and the infinite, and the one, were certain other natures, fuch as fire, or earth, or any other fimilar thing; but they were of opinion, that the infinite itself, and the one itself, are the effence of these things of which they are predicated and hence they afferted that number is the effence of all things. After this manner, therefore, they unfolded their opinion respecting these things, and began to speak about what a thing is, and to define; but they treated this affair in a very simple manner. For they defined fuperficially, and confidered that in which a given definition is first inherent, as the effence of the thing; just as if any one should think that the double and the duad are the fame, because the double first fubfifts in two. haps the double is not the fame with the duad: and if it be not, one thing will be many*; which confequence happens alfo to them. From thofe, therefore, who first philofophifed, and from others, thus much may be received. veftigated the proximate, and others the more primary, elements of bodies. Some, again, furveyed the more partial, but others the more total, prerogative of an elementary nature. And laftly others, exploring all the causes and concauses of things, fpeak differently from each other. in phyfiologifing, at the fame time that their affertions are not contrary to each other.

But per

* That is to fay, if things of which a definition is first truly predicated be the fame as the definitions which are predicated of them: but many definitions first accord with one thing (for the Pythagoreans, for inftance, called the number 7, both opportunity and Minerva); hence one and the fame number will be many things, fince many different definitions accord with it. There is, however, no abfurdity in admitting that one thing may be many: for every effentially producing caufe comprehends in itself, unitedly, all the multitude of which it is the cause, in the fame manner as the centre comprehends the fummits of all the radii of a circle.

CHAP.