1012b“Beginning”1 means: (a) That part of a thing from which one may first move; eg., a line or a journey has one beginning here , and another at the opposite extremity. 1013a(b) The point from which each thing may best come into being; e.g., a course of study should sometimes be begun not from what is primary or from the starting-point of the subject, but from the point from which it is easiest to learn. (c) That thing as a result of whose presence something first comes into being; e.g., as the keel is the beginning of a ship, and the foundation that of a house, and as in the case of animals some thinkers suppose the heart2 to be the “beginning,” others the brain,3 and others something similar, whatever it may be. (d) That from which, although not present in it, a thing first comes into being, and that from which motion and change naturally first begin, as the child comes from the father and mother, and fighting from abuse. (e) That in accordance with whose deliberate choice that which is moved is moved, and that which is changed is changed; such as magistracies, authorities, monarchies and despotisms. (f) Arts are also called “beginnings,”4 especially the architectonic arts. (g) Again, “beginning” means the point from which a thing is first comprehensible, this too is called the “beginning” of the thing; e.g. the hypotheses of demonstrations. (“Cause” can have a similar number of different senses, for all causes are “beginnings.” ) It is a common property, then, of all “beginnings” to be the first thing from which something either exists or comes into being or becomes known; and some beginnings are originally inherent in things, while others are not. Hence “nature” is a beginning, and so is “element” and “understanding” and “choice” and “essence” and “final cause”—for in many cases the Good and the Beautiful are the beginning both of knowledge and of motion.
“Cause” means: (a) in one sense, that as the result of whose presence something comes into being—e.g. the bronze of a statue and the silver of a cup, and the classes5 which contain these; (b) in another sense, the form or pattern; that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 and number in general is the cause of the octave—and the parts of the formula. (c) The source of the first beginning of change or rest; e.g. the man who plans is a cause, and the father is the cause of the child, and in general that which produces is the cause of that which is produced, and that which changes of that which is changed. (d) The same as “end”; i.e. the final cause; e.g., as the “end” of walking is health. For why does a man walk? “To be healthy,” we say, and by saying this we consider that we have supplied the cause. (e) All those means towards the end which arise at the instigation of something else, as, e.g. fat-reducing, purging, drugs and instruments are causes of health; 1013bfor they all have the end as their object, although they differ from each other as being some instruments, others actions. These are roughly all the meanings of “cause,” but since causes are spoken of with various meanings, it follows that there are several causes (and that not in an accidental sense) of the same thing. E.g., both statuary and bronze are causes of the statue; not in different connections, but qua statue. However, they are not causes in the same way, but the one as material and the other as the source of motion. And things are causes of each other; as e.g. labor of vigor, and vigor of labor—but not in the same way; the one as an end , and the other as source of motion . And again the same thing is sometimes the cause of contrary results; because that which by its presence is the cause of so-and-so we sometimes accuse of being, by its absence, the cause of the contrary—as, e.g., we say that the absence of the pilot is the cause of a capsize, whereas his presence was the cause of safety. And both, presence and privation, are moving causes. Now there are four senses which are most obvious under which all the causes just described may be classed. The components of syllables; the material of manufactured articles; fire, earth and all such bodies; the parts of a whole; and the premisses of a syllogistic conclusion; are causes in the material sense. Of these some are causes as substrate: e.g. the parts; and others as essence : the whole, and the composition, and the form. The seed and the physician and the contriver and in general that which produces, all these are the source of change or stationariness. The remainder represent the end and good of the others; for the final cause tends to be the greatest good and end of the rest. Let it be assumed that it makes no difference whether we call it “good” or “apparent good.” In kind , then, there are these four classes of cause. The modes of cause are numerically many, although these too are fewer when summarized. For causes are spoken of in many senses, and even of those which are of the same kind, some are causes in a prior and some in a posterior sense; e.g., the physician and the expert are both causes of health; and the ratio 2:1 and number are both causes of the octave; and the universals which include a given cause are causes of its particular effects. Again, a thing may be a cause in the sense of an accident, and the classes which contain accidents; e.g., the cause of a statue is in one sense Polyclitus and in another a sculptor, because it is an accident of the sculptor to be Polyclitus. 1014aAnd the universal terms which include accidents are causes; e.g., the cause of a statue is a man, or even, generally, an animal; because Polyclitus is a man, and man is an animal. And even of accidental causes some are remoter or more proximate than others; e.g., the cause of the statue might be said to be “white man” or “cultured man,” and not merely “Polyclitus” or “man.” And besides the distinction of causes as proper and accidental , some are termed causes in a potential and others in an actual sense; e.g., the cause of building is either the builder or the builder who builds. And the same distinctions in meaning as we have already described will apply to the effects of the causes; e.g. to this statue, or a statue, or generally an image; and to this bronze, or bronze, or generally material.6 And it is the same with accidental effects. Again, the proper and accidental senses will be combined; e.g., the cause is neither “Polyclitus” nor “a sculptor” but “the sculptor Polyclitus.” However, these classes of cause are in all six in number, each used in two senses. Causes are (1.) particular, (2.) generic, (3.) accidental, (4.) generically accidental; and these may be either stated singly or (5, 6) in combination7; and further they are all either actual or potential. And there is this difference between them, that actual and particular causes coexist or do not coexist with their effects (e.g. this man giving medical treatment with this man recovering his health, and this builder with this building in course of erection); but potential causes do not always do so; for the house and the builder do not perish together.
“Element” means (a) the primary immanent thing, formally indivisible into another form, of which something is composed. E.g., the elements of a sound are the parts of which that sound is composed and into which it is ultimately divisible, and which are not further divisible into other sounds formally different from themselves. If an element be divided, the parts are formally the same as the whole: e.g., a part of water is water; but it is not so with the syllable. (b) Those who speak of the elements of bodies similarly mean the parts into which bodies are ultimately divisible, and which are not further divisible into other parts different in form. And whether they speak of one such element or of more than one, this is what they mean. (c) The term is applied with a very similar meaning to the “elements” of geometrical figures, and generally to the “elements” of demonstrations; for the primary demonstrations which are contained in a number of other demonstrations 1014bare called “elements” of demonstrations.8 Such are the primary syllogisms consisting of three terms and with one middle term. (d) The term “element” is also applied metaphorically to any small unity which is useful for various purposes; and so that which is small or simple or indivisible is called an “element.” (e) Hence it comes that the most universal things are elements; because each of them, being a simple unity, is present in many things—either in all or in as many as possible. Some too think that unity and the point are first principles. (f) Therefore since what are called genera9 are universal and indivisible (because they have no formula), some people call the genera elements, and these rather than the differentia, because the genus is more universal. For where the differentia is present, the genus also follows; but the differentia is not always present where the genus is. And it is common to all cases that the element of each thing is that which is primarily inherent in each thing.
“Beginning” means: (a) That part of a thing from which one may first move; eg., a line or a journey has one beginning here , and another at the opposite extremity.
ὥστʼ εἴπερ ἀδύνατα ἐκεῖνα, καὶ ταῦτα ἀδύνατον εἶναι. ἔτι δὲ φανερῶς ἀντιφάσεις εἰσὶν ἃς οὐχ οἷόν τε ἅμα ἀληθεῖς εἶναι—οὐδὲ δὴ ψευδεῖς πάσας· καίτοι δόξειέ γʼ ἂν μᾶλλον ἐνδέχεσθαι ἐκ τῶν εἰρημένων. ἀλλὰ πρὸς πάντας τοὺς τοιούτους λόγους αἰτεῖσθαι δεῖ, καθάπερ ἐλέχθη καὶ ἐν τοῖς ἐπάνω λόγοις, οὐχὶ εἶναί τι ἢ μὴ εἶναι ἀλλὰ σημαίνειν τι, ὥστε ἐξ ὁρισμοῦ διαλεκτέον λαβόντας τί σημαίνει τὸ ψεῦδος ἢ τὸ ἀληθές. εἰ δὲ μηθὲν ἄλλο τὸ ἀληθὲς φάναι ἢ ὃ ἀποφάναι ψεῦδός ἐστιν, ἀδύνατον πάντα ψευδῆ εἶναι· ἀνάγκη γὰρ τῆς ἀντιφάσεως θάτερον εἶναι μόριον ἀληθές. ἔτι εἰ πᾶν ἢ φάναι ἢ ἀποφάναι ἀναγκαῖον, ἀδύνατον ἀμφότερα ψευδῆ εἶναι· θάτερον γὰρ μόριον τῆς ἀντιφάσεως ψεῦδός ἐστιν. συμβαίνει δὴ καὶ τὸ θρυλούμενον πᾶσι τοῖς τοιούτοις λόγοις, αὐτοὺς ἑαυτοὺς ἀναιρεῖν. ὁ μὲν γὰρ πάντα ἀληθῆ λέγων καὶ τὸν ἐναντίον αὑτοῦ λόγον ἀληθῆ ποιεῖ, ὥστε τὸν ἑαυτοῦ οὐκ ἀληθῆ (ὁ γὰρ ἐναντίος οὔ φησιν αὐτὸν ἀληθῆ), ὁ δὲ πάντα ψευδῆ καὶ αὐτὸς αὑτόν. ἐὰν δʼ ἐξαιρῶνται ὁ μὲν τὸν ἐναντίον ὡς οὐκ ἀληθὴς μόνος ἐστίν, ὁ δὲ τὸν αὑτοῦ ὡς οὐ ψευδής, οὐδὲν ἧττον ἀπείρους συμβαίνει αὐτοῖς αἰτεῖσθαι λόγους ἀληθεῖς καὶ ψευδεῖς· ὁ γὰρ λέγων τὸν ἀληθῆ λόγον ἀληθῆ ἀληθής, τοῦτο δʼ εἰς ἄπειρον βαδιεῖται.—φανερὸν δʼ ὅτι οὐδʼ οἱ πάντα ἠρεμεῖν λέγοντες ἀληθῆ λέγουσιν οὐδʼ οἱ πάντα κινεῖσθαι. εἰ μὲν γὰρ ἠρεμεῖ πάντα, ἀεὶ ταὐτὰ ἀληθῆ καὶ ψευδῆ ἔσται, φαίνεται δὲ τοῦτο μεταβάλλον (ὁ γὰρ λέγων ποτὲ αὐτὸς οὐκ ἦν καὶ πάλιν οὐκ ἔσται)· εἰ δὲ πάντα κινεῖται, οὐθὲν ἔσται ἀληθές· πάντα ἄρα ψευδῆ· ἀλλὰ δέδεικται ὅτι ἀδύνατον. ἔτι ἀνάγκη τὸ ὂν μεταβάλλειν· ἔκ τινος γὰρ εἴς τι ἡ μεταβολή. ἀλλὰ μὴν οὐδὲ πάντα ἠρεμεῖ ἢ κινεῖται ποτέ, ἀεὶ δʼ οὐθέν· ἔστι γάρ τι ὃ ἀεὶ κινεῖ τὰ κινούμενα, καὶ τὸ πρῶτον κινοῦν ἀκίνητον αὐτό.
(b) The point from which each thing may best come into being; e.g., a course of study should sometimes be begun not from what is primary or from the starting-point of the subject, but from the point from which it is easiest to learn. (c) That thing as a result of whose presence something first comes into being; e.g., as the keel is the beginning of a ship, and the foundation that of a house, and as in the case of animals some thinkers suppose the heart to be the “beginning,” others the brain, and others something similar, whatever it may be. (d) That from which, although not present in it, a thing first comes into being, and that from which motion and change naturally first begin, as the child comes from the father and mother, and fighting from abuse. (e) That in accordance with whose deliberate choice that which is moved is moved, and that which is changed is changed; such as magistracies, authorities, monarchies and despotisms. (f) Arts are also called “beginnings,” especially the architectonic arts. (g) Again, “beginning” means the point from which a thing is first comprehensible, this too is called the “beginning” of the thing; e.g. the hypotheses of demonstrations. (“Cause” can have a similar number of different senses, for all causes are “beginnings.” ) It is a common property, then, of all “beginnings” to be the first thing from which something either exists or comes into being or becomes known; and some beginnings are originally inherent in things, while others are not. Hence “nature” is a beginning, and so is “element” and “understanding” and “choice” and “essence” and “final cause”—for in many cases the Good and the Beautiful are the beginning both of knowledge and of motion.
“Cause” means: (a) in one sense, that as the result of whose presence something comes into being—e.g. the bronze of a statue and the silver of a cup, and the classes which contain these; (b) in another sense, the form or pattern; that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 and number in general is the cause of the octave—and the parts of the formula. (c) The source of the first beginning of change or rest; e.g. the man who plans is a cause, and the father is the cause of the child, and in general that which produces is the cause of that which is produced, and that which changes of that which is changed. (d) The same as “end”; i.e. the final cause; e.g., as the “end” of walking is health. For why does a man walk? “To be healthy,” we say, and by saying this we consider that we have supplied the cause. (e) All those means towards the end which arise at the instigation of something else, as, e.g. fat-reducing, purging, drugs and instruments are causes of health;
ἡ δὲ ὅθεν ἂν κάλλιστα ἕκαστον γένοιτο, οἷον καὶ μαθήσεως οὐκ ἀπὸ τοῦ πρώτου καὶ τῆς τοῦ πράγματος ἀρχῆς ἐνίοτε ἀρκτέον ἀλλʼ ὅθεν ῥᾷστʼ ἂν μάθοι· ἡ δὲ ὅθεν πρῶτον γίγνεται ἐνυπάρχοντος, οἷον ὡς πλοίου τρόπις καὶ οἰκίας θεμέλιος, καὶ τῶν ζῴων οἱ μὲν καρδίαν οἱ δὲ ἐγκέφαλον οἱ δʼ ὅ τι ἂν τύχωσι τοιοῦτον ὑπολαμβάνουσιν· ἡ δὲ ὅθεν γίγνεται πρῶτον μὴ ἐνυπάρχοντος καὶ ὅθεν πρῶτον ἡ κίνησις πέφυκεν ἄρχεσθαι καὶ ἡ μεταβολή, οἷον τὸ τέκνον ἐκ τοῦ πατρὸς καὶ τῆς μητρὸς καὶ ἡ μάχη ἐκ τῆς λοιδορίας· ἡ δὲ οὗ κατὰ προαίρεσιν κινεῖται τὰ κινούμενα καὶ μεταβάλλει τὰ μεταβάλλοντα, ὥσπερ αἵ τε κατὰ πόλεις ἀρχαὶ καὶ αἱ δυναστεῖαι καὶ αἱ βασιλεῖαι καὶ τυραννίδες ἀρχαὶ λέγονται καὶ αἱ τέχναι, καὶ τούτων αἱ ἀρχιτεκτονικαὶ μάλιστα. ἔτι ὅθεν γνωστὸν τὸ πρᾶγμα πρῶτον, καὶ αὕτη ἀρχὴ λέγεται τοῦ πράγματος, οἷον τῶν ἀποδείξεων αἱ ὑποθέσεις. ἰσαχῶς δὲ καὶ τὰ αἴτια λέγεται· πάντα γὰρ τὰ αἴτια ἀρχαί. πασῶν μὲν οὖν κοινὸν τῶν ἀρχῶν τὸ πρῶτον εἶναι ὅθεν ἢ ἔστιν ἢ γίγνεται ἢ γιγνώσκεται· τούτων δὲ αἱ μὲν ἐνυπάρχουσαί εἰσιν αἱ δὲ ἐκτός. διὸ ἥ τε φύσις ἀρχὴ καὶ τὸ στοιχεῖον καὶ ἡ διάνοια καὶ ἡ προαίρεσις καὶ οὐσία καὶ τὸ οὗ ἕνεκα· πολλῶν γὰρ καὶ τοῦ γνῶναι καὶ τῆς κινήσεως ἀρχὴ τἀγαθὸν καὶ τὸ καλόν.
αἴτιον λέγεται ἕνα μὲν τρόπον ἐξ οὗ γίγνεταί τι ἐνυπάρχοντος, οἷον ὁ χαλκὸς τοῦ ἀνδριάντος καὶ ὁ ἄργυρος τῆς φιάλης καὶ τὰ τούτων γένη· ἄλλον δὲ τὸ εἶδος καὶ τὸ παράδειγμα, τοῦτο δʼ ἐστὶν ὁ λόγος τοῦ τί ἦν εἶναι καὶ τὰ τούτου γένη (οἷον τοῦ διὰ πασῶν τὸ δύο πρὸς ἓν καὶ ὅλως ὁ ἀριθμός) καὶ τὰ μέρη τὰ ἐν τῷ λόγῳ. ἔτι ὅθεν ἡ ἀρχὴ τῆς μεταβολῆς ἡ πρώτη ἢ τῆς ἠρεμήσεως, οἷον ὁ βουλεύσας αἴτιος, καὶ ὁ πατὴρ τοῦ τέκνου καὶ ὅλως τὸ ποιοῦν τοῦ ποιουμένου καὶ τὸ μεταβλητικὸν τοῦ μεταβάλλοντος. ἔτι ὡς τὸ τέλος· τοῦτο δʼ ἐστὶ τὸ οὗ ἕνεκα, οἷον τοῦ περιπατεῖν ἡ ὑγίεια. διὰ τί γὰρ περιπατεῖ; φαμέν. ἵνα ὑγιαίνῃ. καὶ εἰπόντες οὕτως οἰόμεθα ἀποδεδωκέναι τὸ αἴτιον. καὶ ὅσα δὴ κινήσαντος ἄλλου μεταξὺ γίγνεται τοῦ τέλους,
for they all have the end as their object, although they differ from each other as being some instruments, others actions. These are roughly all the meanings of “cause,” but since causes are spoken of with various meanings, it follows that there are several causes (and that not in an accidental sense) of the same thing. E.g., both statuary and bronze are causes of the statue; not in different connections, but qua statue. However, they are not causes in the same way, but the one as material and the other as the source of motion. And things are causes of each other; as e.g. labor of vigor, and vigor of labor—but not in the same way; the one as an end , and the other as source of motion . And again the same thing is sometimes the cause of contrary results; because that which by its presence is the cause of so-and-so we sometimes accuse of being, by its absence, the cause of the contrary—as, e.g., we say that the absence of the pilot is the cause of a capsize, whereas his presence was the cause of safety. And both, presence and privation, are moving causes. Now there are four senses which are most obvious under which all the causes just described may be classed. The components of syllables; the material of manufactured articles; fire, earth and all such bodies; the parts of a whole; and the premisses of a syllogistic conclusion; are causes in the material sense. Of these some are causes as substrate: e.g. the parts; and others as essence : the whole, and the composition, and the form. The seed and the physician and the contriver and in general that which produces, all these are the source of change or stationariness. The remainder represent the end and good of the others; for the final cause tends to be the greatest good and end of the rest. Let it be assumed that it makes no difference whether we call it “good” or “apparent good.” In kind , then, there are these four classes of cause. The modes of cause are numerically many, although these too are fewer when summarized. For causes are spoken of in many senses, and even of those which are of the same kind, some are causes in a prior and some in a posterior sense; e.g., the physician and the expert are both causes of health; and the ratio 2:1 and number are both causes of the octave; and the universals which include a given cause are causes of its particular effects. Again, a thing may be a cause in the sense of an accident, and the classes which contain accidents; e.g., the cause of a statue is in one sense Polyclitus and in another a sculptor, because it is an accident of the sculptor to be Polyclitus.
οἷον τῆς ὑγιείας ἡ ἰσχνασία ἢ ἡ κάθαρσις ἢ τὰ φάρμακα ἢ τὰ ὄργανα· πάντα γὰρ ταῦτα τοῦ τέλους ἕνεκά ἐστι, διαφέρει δὲ ἀλλήλων ὡς ὄντα τὰ μὲν ὄργανα τὰ δʼ ἔργα. τὰ μὲν οὖν αἴτια σχεδὸν τοσαυταχῶς λέγεται, συμβαίνει δὲ πολλαχῶς λεγομένων τῶν αἰτίων καὶ πολλὰ τοῦ αὐτοῦ αἴτια εἶναι οὐ κατὰ συμβεβηκός (οἷον τοῦ ἀνδριάντος καὶ ἡ ἀνδριαντοποιητικὴ καὶ ὁ χαλκὸς οὐ καθʼ ἕτερόν τι ἀλλʼ ᾗ ἀνδριάς· ἀλλʼ οὐ τὸν αὐτὸν τρόπον ἀλλὰ τὸ μὲν ὡς ὕλη τὸ δʼ ὡς ὅθεν ἡ κίνησις), καὶ ἀλλήλων αἴτια (οἷον τὸ πονεῖν τῆς εὐεξίας καὶ αὕτη τοῦ πονεῖν· ἀλλʼ οὐ τὸν αὐτὸν τρόπον ἀλλὰ τὸ μὲν ὡς τέλος τὸ δʼ ὡς ἀρχὴ κινήσεως). ἔτι δὲ ταὐτὸ τῶν ἐναντίων ἐστίν· ὃ γὰρ παρὸν αἴτιον τουδί, τοῦτʼ ἀπὸν αἰτιώμεθα ἐνίοτε τοῦ ἐναντίου, οἷον τὴν ἀπουσίαν τοῦ κυβερνήτου τῆς ἀνατροπῆς, οὗ ἦν ἡ παρουσία αἰτία τῆς σωτηρίας· ἄμφω δέ, καὶ ἡ παρουσία καὶ ἡ στέρησις, αἴτια ὡς κινοῦντα.—ἅπαντα δὲ τὰ νῦν εἰρημένα αἴτια εἰς τέτταρας τρόπους πίπτει τοὺς φανερωτάτους. τὰ μὲν γὰρ στοιχεῖα τῶν συλλαβῶν καὶ ἡ ὕλη τῶν σκευαστῶν καὶ τὸ πῦρ καὶ ἡ γῆ καὶ τὰ τοιαῦτα πάντα τῶν σωμάτων καὶ τὰ μέρη τοῦ ὅλου καὶ αἱ ὑποθέσεις τοῦ συμπεράσματος ὡς τὸ ἐξ οὗ αἴτιά ἐστιν· τούτων δὲ τὰ μὲν ὡς τὸ ὑποκείμενον, οἷον τὰ μέρη, τὰ δὲ ὡς τὸ τί ἦν εἶναι, τό τε ὅλον καὶ ἡ σύνθεσις καὶ τὸ εἶδος. τὸ δὲ σπέρμα καὶ ὁ ἰατρὸς καὶ ὁ βουλεύσας καὶ ὅλως τὸ ποιοῦν, πάντα ὅθεν ἡ ἀρχὴ τῆς μεταβολῆς ἢ στάσεως. τὰ δʼ ὡς τὸ τέλος καὶ τἀγαθὸν τῶν ἄλλων· τὸ γὰρ οὗ ἕνεκα βέλτιστον καὶ τέλος τῶν ἄλλων ἐθέλει εἶναι· διαφερέτω δὲ μηδὲν αὐτὸ εἰπεῖν ἀγαθὸν ἢ φαινόμενον ἀγαθόν.—τὰ μὲν οὖν αἴτια ταῦτα καὶ τοσαῦτά ἐστι τῷ εἴδει, τρόποι δὲ τῶν αἰτίων ἀριθμῷ μέν εἰσι πολλοί, κεφαλαιούμενοι δὲ καὶ οὗτοι ἐλάττους. λέγονται γὰρ αἴτια πολλαχῶς, καὶ αὐτῶν τῶν ὁμοειδῶν προτέρως καὶ ὑστέρως ἄλλο ἄλλου, οἷον ὑγιείας ὁ ἰατρὸς καὶ ὁ τεχνίτης, καὶ τοῦ διὰ πασῶν τὸ διπλάσιον καὶ ἀριθμός, καὶ ἀεὶ τὰ περιέχοντα ὁτιοῦν τῶν καθʼ ἕκαστα. ἔτι δʼ ὡς τὸ συμβεβηκὸς καὶ τὰ τούτων γένη, οἷον ἀνδριάντος ἄλλως Πολύκλειτος καὶ ἄλλως ἀνδριαντοποιός, ὅτι συμβέβηκε τῷ ἀνδριαντοποιῷ Πολυκλείτῳ εἶναι·
And the universal terms which include accidents are causes; e.g., the cause of a statue is a man, or even, generally, an animal; because Polyclitus is a man, and man is an animal. And even of accidental causes some are remoter or more proximate than others; e.g., the cause of the statue might be said to be “white man” or “cultured man,” and not merely “Polyclitus” or “man.” And besides the distinction of causes as proper and accidental , some are termed causes in a potential and others in an actual sense; e.g., the cause of building is either the builder or the builder who builds. And the same distinctions in meaning as we have already described will apply to the effects of the causes; e.g. to this statue, or a statue, or generally an image; and to this bronze, or bronze, or generally material. And it is the same with accidental effects. Again, the proper and accidental senses will be combined; e.g., the cause is neither “Polyclitus” nor “a sculptor” but “the sculptor Polyclitus.” However, these classes of cause are in all six in number, each used in two senses. Causes are (1.) particular, (2.) generic, (3.) accidental, (4.) generically accidental; and these may be either stated singly or (5, 6) in combination; and further they are all either actual or potential. And there is this difference between them, that actual and particular causes coexist or do not coexist with their effects (e.g. this man giving medical treatment with this man recovering his health, and this builder with this building in course of erection); but potential causes do not always do so; for the house and the builder do not perish together.
“Element” means (a) the primary immanent thing, formally indivisible into another form, of which something is composed. E.g., the elements of a sound are the parts of which that sound is composed and into which it is ultimately divisible, and which are not further divisible into other sounds formally different from themselves. If an element be divided, the parts are formally the same as the whole: e.g., a part of water is water; but it is not so with the syllable. (b) Those who speak of the elements of bodies similarly mean the parts into which bodies are ultimately divisible, and which are not further divisible into other parts different in form. And whether they speak of one such element or of more than one, this is what they mean. (c) The term is applied with a very similar meaning to the “elements” of geometrical figures, and generally to the “elements” of demonstrations; for the primary demonstrations which are contained in a number of other demonstrations
καὶ τὰ περιέχοντα δὲ τὸ συμβεβηκός, οἷον ἄνθρωπος αἴτιος ἀνδριάντος, ἢ καὶ ὅλως ζῷον, ὅτι ὁ Πολύκλειτος ἄνθρωπος ὁ δὲ ἄνθρωπος ζῷον. ἔστι δὲ καὶ τῶν συμβεβηκότων ἄλλα ἄλλων πορρώτερον καὶ ἐγγύτερον, οἷον εἰ ὁ λευκὸς καὶ ὁ μουσικὸς αἴτιος λέγοιτο τοῦ ἀνδριάντος, ἀλλὰ μὴ μόνον Πολύκλειτος ἢ ἄνθρωπος. παρὰ πάντα δὲ καὶ τὰ οἰκείως λεγόμενα καὶ τὰ κατὰ συμβεβηκός, τὰ μὲν ὡς δυνάμενα λέγεται τὰ δʼ ὡς ἐνεργοῦντα, οἷον τοῦ οἰκοδομεῖσθαι οἰκοδόμος ἢ οἰκοδομῶν οἰκοδόμος. ὁμοίως δὲ λεχθήσεται καὶ ἐφʼ ὧν αἴτια τὰ αἴτια τοῖς εἰρημένοις, οἷον τοῦδε τοῦ ἀνδριάντος ἢ ἀνδριάντος ἢ ὅλως εἰκόνος, καὶ χαλκοῦ τοῦδε ἢ χαλκοῦ ἢ ὅλως ὕλης· καὶ ἐπὶ τῶν συμβεβηκότων ὡσαύτως. ἔτι δὲ συμπλεκόμενα καὶ ταῦτα κἀκεῖνα λεχθήσεται, οἷον οὐ Πολύκλειτος οὐδὲ ἀνδριαντοποιὸς ἀλλὰ Πολύκλειτος ἀνδριαντοποιός. ἀλλʼ ὅμως ἅπαντά γε ταῦτʼ ἐστὶ τὸ μὲν πλῆθος ἕξ, λεγόμενα δὲ διχῶς· ἢ γὰρ ὡς τὸ καθʼ ἕκαστον ἢ ὡς τὸ γένος, ἢ ὡς τὸ συμβεβηκὸς ἢ ὡς τὸ γένος τοῦ συμβεβηκότος, ἢ ὡς συμπλεκόμενα ταῦτα ἢ ὡς ἁπλῶς λεγόμενα, πάντα δὲ ἢ ὡς ἐνεργοῦντα ἢ κατὰ δύναμιν. διαφέρει δὲ τοσοῦτον, ὅτι τὰ μὲν ἐνεργοῦντα καὶ τὰ καθʼ ἕκαστον ἅμα ἔστι καὶ οὐκ ἔστι καὶ ὧν αἴτια, οἷον ὅδε ὁ ἰατρεύων τῷδε τῷ ὑγιαζομένῳ καὶ ὅδε ὁ οἰκοδόμος τῷδε τῷ οἰκοδομουμένῳ, τὰ δὲ κατὰ δύναμιν οὐκ ἀεί· φθείρεται γὰρ οὐχ ἅμα ἡ οἰκία καὶ ὁ οἰκοδόμος.
στοιχεῖον λέγεται ἐξ οὗ σύγκειται πρώτου ἐνυπάρχοντος ἀδιαιρέτου τῷ εἴδει εἰς ἕτερον εἶδος, οἷον φωνῆς στοιχεῖα ἐξ ὧν σύγκειται ἡ φωνὴ καὶ εἰς ἃ διαιρεῖται ἔσχατα, ἐκεῖνα δὲ μηκέτʼ εἰς ἄλλας φωνὰς ἑτέρας τῷ εἴδει αὐτῶν, ἀλλὰ κἂν διαιρῆται, τὰ μόρια ὁμοειδῆ, οἷον ὕδατος τὸ μόριον ὕδωρ, ἀλλʼ οὐ τῆς συλλαβῆς. ὁμοίως δὲ καὶ τὰ τῶν σωμάτων στοιχεῖα λέγουσιν οἱ λέγοντες εἰς ἃ διαιρεῖται τὰ σώματα ἔσχατα, ἐκεῖνα δὲ μηκέτʼ εἰς ἄλλα εἴδει διαφέροντα· καὶ εἴτε ἓν εἴτε πλείω τὰ τοιαῦτα, ταῦτα στοιχεῖα λέγουσιν. παραπλησίως δὲ καὶ τὰ τῶν διαγραμμάτων στοιχεῖα λέγεται, καὶ ὅλως τὰ τῶν ἀποδείξεων· αἱ γὰρ πρῶται ἀποδείξεις καὶ ἐν πλείοσιν ἀποδείξεσιν ἐνυπάρχουσαι,
are called “elements” of demonstrations. Such are the primary syllogisms consisting of three terms and with one middle term. (d) The term “element” is also applied metaphorically to any small unity which is useful for various purposes; and so that which is small or simple or indivisible is called an “element.” (e) Hence it comes that the most universal things are elements; because each of them, being a simple unity, is present in many things—either in all or in as many as possible. Some too think that unity and the point are first principles. (f) Therefore since what are called genera are universal and indivisible (because they have no formula), some people call the genera elements, and these rather than the differentia, because the genus is more universal. For where the differentia is present, the genus also follows; but the differentia is not always present where the genus is. And it is common to all cases that the element of each thing is that which is primarily inherent in each thing.
αὗται στοιχεῖα τῶν ἀποδείξεων λέγονται· εἰσὶ δὲ τοιοῦτοι συλλογισμοὶ οἱ πρῶτοι ἐκ τῶν τριῶν διʼ ἑνὸς μέσου. καὶ μεταφέροντες δὲ στοιχεῖον καλοῦσιν ἐντεῦθεν ὃ ἂν ἓν ὂν καὶ μικρὸν ἐπὶ πολλὰ ᾖ χρήσιμον, διὸ καὶ τὸ μικρὸν καὶ ἁπλοῦν καὶ ἀδιαίρετον στοιχεῖον λέγεται. ὅθεν ἐλήλυθε τὰ μάλιστα καθόλου στοιχεῖα εἶναι, ὅτι ἕκαστον αὐτῶν ἓν ὂν καὶ ἁπλοῦν ἐν πολλοῖς ὑπάρχει ἢ πᾶσιν ἢ ὅτι πλείστοις, καὶ τὸ ἓν καὶ τὴν στιγμὴν ἀρχάς τισι δοκεῖν εἶναι. ἐπεὶ οὖν τὰ καλούμενα γένη καθόλου καὶ ἀδιαίρετα (οὐ γὰρ ἔστι λόγος αὐτῶν), στοιχεῖα τὰ γένη λέγουσί τινες, καὶ μᾶλλον ἢ τὴν διαφορὰν ὅτι καθόλου μᾶλλον τὸ γένος· ᾧ μὲν γὰρ ἡ διαφορὰ ὑπάρχει, καὶ τὸ γένος ἀκολουθεῖ, ᾧ δὲ τὸ γένος, οὐ παντὶ ἡ διαφορά. ἁπάντων δὲ κοινὸν τὸ εἶναι στοιχεῖον ἑκάστου τὸ πρῶτον ἐνυπάρχον ἑκάστῳ.
φύσις λέγεται ἕνα μὲν τρόπον ἡ τῶν φυομένων γένεσις, οἷον εἴ τις ἐπεκτείνας λέγοι τὸ υ, ἕνα δὲ ἐξ οὗ φύεται πρώτου τὸ φυόμενον ἐνυπάρχοντος· ἔτι ὅθεν ἡ κίνησις ἡ πρώτη ἐν ἑκάστῳ τῶν φύσει ὄντων ἐν αὐτῷ ᾗ αὐτὸ ὑπάρχει· φύεσθαι δὲ λέγεται ὅσα αὔξησιν ἔχει διʼ ἑτέρου τῷ ἅπτεσθαι καὶ συμπεφυκέναι ἢ προσπεφυκέναι ὥσπερ τὰ ἔμβρυα· διαφέρει δὲ σύμφυσις ἁφῆς, ἔνθα μὲν γὰρ οὐδὲν παρὰ τὴν ἁφὴν ἕτερον ἀνάγκη εἶναι, ἐν δὲ τοῖς συμπεφυκόσιν ἔστι τι ἓν τὸ αὐτὸ ἐν ἀμφοῖν ὃ ποιεῖ ἀντὶ τοῦ ἅπτεσθαι συμπεφυκέναι καὶ εἶναι ἓν κατὰ τὸ συνεχὲς καὶ ποσόν, ἀλλὰ μὴ κατὰ τὸ ποιόν. ἔτι δὲ φύσις λέγεται ἐξ οὗ πρώτου ἢ ἔστιν ἢ γίγνεταί τι τῶν φύσει ὄντων, ἀρρυθμίστου ὄντος καὶ ἀμεταβλήτου ἐκ τῆς δυνάμεως τῆς αὑτοῦ, οἷον ἀνδριάντος καὶ τῶν σκευῶν τῶν χαλκῶν ὁ χαλκὸς ἡ φύσις λέγεται, τῶν δὲ ξυλίνων ξύλον· ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων· ἐκ τούτων γάρ ἐστιν ἕκαστον διασωζομένης τῆς πρώτης ὕλης· τοῦτον γὰρ τὸν τρόπον καὶ τῶν φύσει ὄντων τὰ στοιχεῖά φασιν εἶναι φύσιν, οἱ μὲν πῦρ οἱ δὲ γῆν οἱ δʼ ἀέρα οἱ δʼ ὕδωρ οἱ δʼ ἄλλο τι τοιοῦτον λέγοντες, οἱ δʼ ἔνια τούτων οἱ δὲ πάντα ταῦτα. ἔτι δʼ ἄλλον τρόπον λέγεται ἡ φύσις ἡ τῶν φύσει ὄντων οὐσία, οἷον οἱ λέγοντες τὴν φύσιν εἶναι τὴν πρώτην σύνθεσιν,
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