lit 



OROANON. 



QROANON. 



100 



no demonstration at all (' Metaph.,' iv. 4.) Ami it U not ponible fur 

 tint thought to go through the infinite. (' Analyt Port.,' i. -J-.M 



(50.) And those things are true and fint which not through other 

 thing*, but through thenuelve* receive assent ; for it U not neoenary 

 in Mieutinc fint principle* for the " wherefore " to be inquired after, 

 but each of the principles miwt itaelf of iUelf receive ascent (' Top.; 

 i. 1.) And in two wan it if Decenary first to know : for as to come 

 thing* it ia neoeiMry first to admit that they are ; but as to others it 

 u necemry to understand what tho thing spoken of is ; and as to 

 others again both ; for example, in the proposition that either to affirm 

 or deny everything U true, we must assume the "U"; and in tlu< 

 triangle, that it signifies this particular thing ; and in the monad both, 

 both what it means and that it is. (' Analyt. Post.,' i. 1 .) 



(1.) But we assert that all science ia not demonstrative, but that 

 that of the immediate (tfufa) is incapable of demonstration. And that 

 this u a matter of necessity, ia clear ; for if it is necessary to under- 

 stand the prior and those things from which the demonstration comes, 

 and the immediate at any time enter into the demonstration, it is a 

 matter of necessity that the immediate are not capable of demonstration. 

 And this then we so affirm, and that there is not only science, but also 

 some first principle (Vx4) of science by which we know the terms 

 (tfoi). It U necessary not only to know first the first things, cither all 

 or some, but also to know them more : for always that through which 

 each thing is, is more (in a higher degree) ; for example, that through 

 which we love, is more love. So that if we know by the first things 

 and believe, those things also we know and believe more, since by 

 them we know also the things which come after. (' Analyt. Post,' i. 

 8. 2.) 



(52.) And an immediate proposition (wpArotris K^nroi) is a beginning 

 (afxi) of demonstration, and an immediate proposition is that to' which 

 there is no prior proposition. (' Analyt. Post.,' i. 2.) 



(53.) And of an immediate syllogistic beginning I call that the 

 Thesis which need not be demonstrated, and which it is not necessary 

 that he who is going to learn anything should possess ; but what he 

 who is going to learn anything must necessarily possess, is on axiom 

 (afkjia). (' Analyt. Post.,' i. 2.) 



(54.) The first things will be definitions (Upta/toi) incapable of 

 demonstration. For definition ia of what the thing is and of essence ; 

 but all demonstrations apjtear to go by hypothesis and to assume 

 what a thing is ; for example, mathematical demonstrations take for 

 granted what a unit ia and what odd is, and other kinds of demon- 

 stration in like manner. 



The definition ia a certain notification (ympurpiit) of essence. ('Analyt. 

 Post,' U. 3.) 



(55.) He who defines shows either what a thing is or what the name 

 means. (' Analyt. Post,' ii. 7.) 



All who in any way by a name give an account of a thing, mani- 

 festly do not give the definition of the thing, since every definition is 

 speech (\6yoi). (' Top.,' i. 3.) 



What a triangle means, the geometer assumes ; but that it is, he 

 proves. (' Analyt. Post,' ii. 7.) 



(56.) And it is necessary to investigate, when considering things 

 which are alike and do not differ, in the first place what they all have 

 in common, then again with respect to other things what things they 

 have which ore of the some genus as the former, and are the same as 

 pue another in species, but different from the first named. And when 

 in these things it has been found what they all have in common, and 

 in the other things in like manner, we must consider again if there is 

 anything in common in these things which have been token, until you 

 come to one notion (Arfyot) ; for this will be a definition of the thing. 

 But if a man does not come to one notion, but to two or more, it is 

 manifest that what is sought cannot be one, but more than one. For 

 example, if we should inquire what magnanimity fe, wc must consider 

 in the cose of some magnanimous persona whom we know, what one 

 thing they all have by which they are such. For example, if Alcibiades 

 is magnanimous, or Achilles, and Ajax, what one thing they have all in 

 common ? Non-endurance of insult ; for the first mode war, and the 

 second was enraged, and the third killed himself. 



Again in the case of others, such as Lyrander or Socrates; if indiffer- 

 ence in prosperity and adversity are the things that they have in 

 common, these two things I take and consider what same things ore 

 contained in the absence of all feeling (Awa&fa) as to fortune, and non- 

 endurance of insult If they have nothing hi common, there must be 

 two Bpecica (Ui() of magnanimity. (' Analyt. Post.,' ii. 13.) 



(57.) Of the things indeed which are in the definition, each will 

 extend further, but all will not extend further. For of necessity there 

 must be this essence (otiala) of the thing: for example, theru is number 

 in every Three (-rpuii), odd (npnriy), and the prime in both ways, both 

 so as not to be measured by any number and not to be composed of 

 numbers. This then is Three, number odd, and prime, and prime in 

 this manner : for of each of these things some are in all odd numbers 

 also, but the last is in Two olao, but all are in none. (' Analyt. Post./ 



(58.) And it ui necessary, when a person is labouring at any whole 

 thing, to divide the genus (ytw) into things indivisible in species, the 

 first ; for example, to divide number into Three and Two. (' An.-ilvt. 



post, 1 a is.) 



All genus u divided by differences which are opposed to one another 



in division, ai a living animal by the difference of quadruped and bird 

 and fish. (' Top.,' vi. 0.) 



That everything should fall under the division, if they be things 

 opposed in which there is no middle, is not an aasumption, for it in 

 necessary that everything should be in one of them, if there shall be a 

 difference (Jio^opd) in it (the genus). (' Analyt Post,' ii. 13.) 



It is requisite, moreover, to divide by privation (rrifqm), and those 

 who cut into two parts divide by privation. And there is no dif- 

 ference in privation, so for as it U privation, for it ia impossible tli.it 

 there should be species of a thing which does not exist; fr example, 

 of animals without feet or animals without wings, as then- i- in the 

 case of winged animals and quadrupeds. (' Do Partib. Animal.,' i. 3.) 



(59.) Definition (Apia/tat) consists of genus and differences (Suvpopwy). 

 ('Top.; IS.) 



It ia requisite that he who defines well define through genus and 

 differences, and these belong to those things which are plainly clearer 

 than and prior to the species (eJJos). 



And there ore three ways in which the definition is not from prior 

 things. Tho first ia, if through what is opposed that which is o| 

 is defined ; for example, if through evil good ia defined; for the opposed 

 exist by nature. But to some the knowledge of each of them appears 

 to be also the same, so that neither is one better known than the other. 

 But it should not escape notice that some things perhaps it i.-, not 

 possible to define otherwise ; for example, the double without the half, 

 and all those things which of themselves ore said in relation to any- 

 thing c*p6s n) : for in all such things to be is the same thing as to be 

 related to something in some manner, so that it U impossible without 

 the one to know the other ; wherefore it is necessary in the notion 

 (\oyos) of the one that the other also be included. 



Another way is, if a man uses the very thing which is defined. But 

 this escapes notice when he bos not used the name itself of the thing 

 defined : for example, if ho defined the sun to be a star which appear* 

 in the day-time ; for he who employs the word day employs the word 

 sun. And it is requisite, in order that such errors may be detected, to 

 exchange the name (owyta) for the notion (full speech, \6yos) : for 

 example, that day is the passage of the sun above the earth ; fur it is 

 manifest that he who has spoken of the passage of the sun above the 

 earth has spoken of the sun. So that he who has employed tho word 

 day has employed the word sun. A third way is, if that which is 

 opposed in division ia defined by that which ia opposed in division : for 

 example, that odd is greater than even by a unit. For things of the 

 same genus opposed in division exist by nature, and odd and even are 

 opposed in division ; for both are differences of number. (' Top.,' vi. 4.) 



(60.) To know what a thing is, is the same as to know why it ia. 

 What ia an eclipse ? Privation of light from the moon through the 

 earth intercepting (the light). What causes an eclipse ? or why is the 

 moon eclipsed ? Because the light fails, owing to the interposition of 

 the earth. What is symphony ? A proportion (\6yos) of numbers in 

 sounds high or deep (o{u, &apii). Why is the high symphonioua with 

 the deep ? Because the high and deep sounds have a proportion (\6yos) 

 of numbers. ('Analyt. Post.,' ii. 2.) 



(61.) We seek the cause after we know that a thing is ; but some- 

 times they are manifest at the same time also ; but it ia not possible to 

 know the cause before we know that the tiling exists. (' Analyt Post,' 

 ii. 8.) For it is impossible to know what a thing U when we ore in 

 ignorance whether it exists or not. 



And both the notion or expression (X<fyos) appears to give eviiVnee 

 to phenomena, and phenomena to the notion. ('De Coel.,' i. ".> 



(62.) The cause ia the middle (itimr), and in all things this is sought, 

 ('Analyt. Post.,' ii. 2.) 



(63.) Not only that a thing "is" ought the definition (Apurruds 

 \6yos) to show, as the most part of definitions declare, but tho 

 cause also ought to be in it, and to be clear. But the notions of the 

 definitions are as conclusions : for example, what ia quadrature .' 

 a rectangular equilateral figure being equal to a figure of unequal 

 And inch a ilrtinition ia an expression of the conclusion. I'.ut 1 1> 

 nitiou which says that quadrature is invention of a middle, tatea tho 

 cause of the thing. (' De Animal.,' ii. 2, 1.) 



(64.) And it appears that not only what a thing is, is useful towards 

 knowing the causes of the accidents of essences (run <ru/i/3/97)/rVa>i' rats 

 ovo-ioir), as in mathematics what a straight line is and what a curved 

 line is, or what a line and a plane are, is useful towards seeing how 

 many right angles the angles of a triangle are equal to ; bin 

 also the accidents help in a great degree to perceiving what the t Inn- 

 is ; for when wc ore able by the appearance (^Kurairfa) to give on 

 account of the accident* either of all or of the greater part, then i -on- 

 cerning the essence also we shall be able best to speak ; for of all 

 demonstration what a thing is (rj> rl limn), is the beginning. So that 

 in all definitions in which it does not happen that we can recogni 

 accident*, and cannot even form a conjecture of them cattily, it is mani- 

 fest that they ore all enunciated diolectically (5ioAimKt) and emptily 



TOJ). (' Do Animal.,' i. 1, 8.) 



(65.) And of some things some other thing is the cause, and of other 

 things not. 



Accordingly it is manifest that of those also which belong to the 

 class of what a thing " is," some are immediate (&ntaa) and first prin- 



Thin it whit the Uth Proposition of the Second Book of Euclid ihown. 



