The investigation of the much discussed problem of the «homoeomeries» of Anaxagoras was initially stimulated by the need to meet a «practical» problem: should the word ομοιομέρειαι, often presumed to be a technical term of Anaxagoras, be an entry in the «Lexicon of the philosophical and scientific terms of the Presocratics» now in the preparation by the «Research Center for Greek Philosophy» at the Academy of Athens? The word does not occur in Anaxagoras’ extant fragments. However, among the many instances of its application to Anaxagorean physics in the testimonia, one explicit attribution by Simplicius (59 A 45 DK) is exceptionally important and should be taken into serious consideration, since Simplicius is our main authority for Anaxagoras’ physical fragments. Actually Diels (though not Lanza) spaces the term in this instance; and this conventional indication of its authenticity commits us to making an entry of it in the lexicon, unless we are convince by close research that it is spurious. And, although most modern scholars, contrary to the ancient tradition, consider this a single lapsus calami on the part of the otherwise reliable Simplicius, and hold the term to be a later development, some others still believe that Anaxagoras must have used it, while the minority take no sides on the question. The disagreement, moreover, concerning the meaning of the word, both as a substantive and an adjective (consistently fathered on Anaxagoras by Aristotle in the latter form) is still greater and no unanimity has been attained as to what term, if any, in the extant fragments was referred to by ομοιμέρειαι. One possible interpretation of Simplicius’ reference containing the presumed term, which might terminate but not solve the problem, could be to regard Aristotle and Anaxagoras as the grammatical subject of the parenthetical clause άπερ ομοιομερείας καλεί, although the former never used the term in its substantive form, but he said that Anaxagoras considered τα ομοιομερή as elements (59 A 46). This is not completely improbable, given Simplicius’ abstruse style and the subordinate construction of the long complicated period in which the clause occurs. Yet the assumption seems quite unorthodox syntactically and cannot be seriously defended. On other hand, since most of the evidence makes it to father the term of Anaxagoras, in spite of the almost unanimous consensus of the Peripatetic and Atomist doxographical tradition, the only solution that appears to be open is to dispute the trustworthiness of Simplicius in this particular case and to do away with the term as far as the lexicon is concerned. But even if we deny the authenticity of the term, a problem still remains concerning the clarification of other words most unanimously accepted as technical terms of Anaxagoras’ physics, such as χρήματα, σπέρματα, μοίραι, εναντία etc., so long as it is not made quite clear which word of the fragments renders Anaxagoras’ ultimate material realities, whether these may be considered as «elements» or not. The consideration of the testimonia is indispensable for an answer to this question, which brings again to therefore the problem of the homoeomerous (things or bodies) or of the homoeomeries. Since complete disagreement prevails about many issues of Anaxagoras’ physical philosophy and all sorts of reconciliations have been tried between the Anaxagoras of the fragments and the Anaxagoras of the tradition, an exhaustive survey of the available bibliography was judged indispensable as a prerequisite both for the clarification of Anaxagoras’ physical terminology and the justification of the theses advanced in this paper. Thus, before attempting an inquiry into some pre-aristotelian texts, a sample analysis of Aristotle’s critique of Anaxagoras’ physics in comparison with the related commentaries of the Commentators and in particular Simplicius’ and a brief exposition of Lucretius’ full reference to Anaxagoras’ homoeomerian rerum, I presented the main theses on the usage, the meaning and the equivalence of the term advanced by Tannery, Zeller, Burnet, Bailey, Cornford, Vlastos, Lanza Raven, Veicos, Muggler, Boussoulas, Stokes, Strang, Schwabe, Cherniss, Cleve, Zafiropulo, Sambursky, Reesor, Gershenson – Greenberg, and Schofield. Peck’s, Leon’s, Guthrie’s, Mathewson’s, Kerferd’s and Furley’s views weer very helpful to my approach and particular theses, but my conclusions, reached through another method, are different in many details. In my effort to answer the central questions of Anaxagoras’ physics I tried to find out what Plato considered to be Anaxagoras’ material substances as distinct from the νούς. As a matter of fact Plato referring to Anaxagoras speaks of no other material principles than «all things» (πάντα τα πράγματα) set in order by the νους. This expression corresponds to what the testimonia describe as «νουν αποκρίνοντα τας ομοιομερείας». In Protagoras 329d-333d and 349c however we find reference to things having similar and dissimilar parts, which anticipates the Aristotelian distinction (with the same examples); but the term is not used and there is no mention of Anaxagoras. Protagoras, in any case, a near contemporary of Anaxagoras, has also spoken of χρήματα, and this is important, Nor is the term met in the Hippocratic treatise Περί διαίτης which betrays close imitation of Anaxagoras’ wording and style; and the same is true of the echoes of Anaxagoras in some published lines of the Derveni papyrus. Actually the term in question as an adjective together with similar compound words does not occur before Aristotle. But how did it occur to Aristotle to say that Anaxagoras’ «elements» were τα ομοιομερή ? And on what grounds did the Commentators and especially Simplicius – who either had the Περί Φύσεως itself or some epitome of it – unquestionably accept Aristotle’s rendering as automatically applying to Anaxagoras, alternating it with the corresponding substantive ομοιομέρειαι, (perhaps from atomist assumptions), even though in all probability Anaxagoras had not used the word? Was Aristotle so unreliable as to read into Anaxagoras an idea which at first sight contradicts the basic principles of the latter’s physics (i.e. if the homoeomereity is taken to imply homogeneity), and did the Commentators follow him slavishly? I order to answer this question I discussed Aristotle’s method of «articulating» Anaxagoras’ «vague» and «incomplete» thought described in Metaphysics 989 a 30ff., (with Alexander of Aphrodisias’ commentaries) and his critique of Anaxagoras in Physics A4 together with the Commentators’ (especially Simplicius’) commentaries on the chapter. Thus, apart from the innovation of considering Anaxagoras’ «elements» as τα ομοιομερή, both the positive and destructive account of Anaxagoras’ physics given by Aristotle does complete justice to our philosopher, and all other theses attributed to him are in full agreement with what we read in fragments. It should be mentioned that these fragments are nothing else than Anaxagorean quotations cited by Simplicius for corroboration and clarification of Aristotle’s account. And, granted this «genetic» dependence of the actual quotations on Aristotle’s account, it is surprising that some scholars are so eager to reject the Aristotelian evidence as incompatible with theses advanced in the fragments. Though not following Aristotle’s interpretation unquestionably, and not citing any quotation containing the term in question – which also claims that the term was not used by Anaxagoras himself – Simplicius does not seem to deny the authorship of the term, he uses it himself as a noun or adjective either as if it was coined by Anaxagoras or fully described his primary elements. This means that the term was unanimously held to render the structure of the Anaxagorean elementary substances very satisfactorily, and, since Aristotle did not engage in doxography but in interpretation, he seemed to have successfully «articulated» Anaxagoras’ vague language and thought. Which word of Anaxagoras, however, did Aristotle read as ομοιομερή? The ultimate material realities are in Anaxagoras’ fragments denoted as χρήματα in the original mixture, as αποκρινόμενα and διακρινόμενα, when separated off and distinguished by the νούς, and as πάντα in reference το their structure. Among them there were elements (γη), opposites, and numberless seeds (σπέρματα) of all kinds (fr. 4), Since σπέρματα and ενάντια were well established physical terms, Aristotle had no reason to substitute in their place the term ομοιομερή. The χρήματα were the novelty of Anaxagoras, too vague a word to denote elementary substances. These are said by Anaxagoras to contain portions of all things. On the other hand, Aristotle was facilitated in the rendering because the ομοιομερή had already a place in his own system, denoting natural substances, intermediate between the elements and the organic parts. And, since he did not find in Anaxagoras any substances more elementary than his own ομοιομερή, because for Anaxagoras all things, qualitatively differentiated, were equally real, he was fully entitled to specify as ομοιομερή the Anaxagorean χρήματα conceived of infinitesimal magnitude and in seminal form and having the opposites as their ingredients. Although Simplicius in his Commentary on the De caelo (603, 17-19) says that Anaxagoras called τα ομοιομερή σπέρματα (a testimony inexcusably missing from the editors because, if taken at its face value, would reinforce the current consideration of the σπέρματα aw Anaxagoras’ primary elements), the term σπέρματα does not seem to cover all that was real for Anaxagoras nor to the emphasized by him as his own original technical term. It was early considered to apply to the atomist physics. As to the meaning of the ομοιομερή, I believe that the definition given in Physics 203a 23 (μίγμα ομοίως τω παντί) renders best the structure of the term as Anaxagorean and not as Aristotelian, although I see no inconsistency to this sense in the connotation met in Gen. et Corr. 314a 18 (ως έκαστου συνώνυμον το μέρος) nor in Aetius’ definition of the ομοιμέρειαι in 59 A 46 DK. The great advantage of the term might have appeared to Aristotle to be its susceptibility to having many meanings. For it would thus best describe the vague Anaxaogrean χρήματα which expresses most of the basic principles of Anaxagoras’ physics. A thing is homoeomeorus both with all things present in the original mixture (in virtue of the principle of universal mixture) and with the specific whole of which it is a part (in virtue of the principle of the predominance of the similar parts), while due to its seminal form it is homoeomerous dynamically with the thing which will develop out of it. Indicative of the many senses of the term is also Lucretius’ whole account of Anaxagoras’ homoeomoria (De rerum natura I, 836-930). Its alternative use with the χρήματα is shown in Sextus Empiricus’ reference (IX 6) and Michael Psellos’ commentary on Aristotle’s Physics (ad locum). Anyway, I do not see any decisive inconsistency between the Anaxagoras of the fragments and that of the doxographical and scholarly tradition apart from terminological matters. In no case do the principles of homoeomereity imply any homogeneity of Anaxagoras’ material realities. Only νους is explicitly said to be alike, i.e. homogeneous. The principle of homoeomereity (similarity of the parts with the Whole, with the specific whole and with one another) does not contradict the principles of universal mixture and of predominance, but it should be understood as combination of both. In Anaxagoras’ molecular theory of matter there are no other material realities more elementary than the «things» themselves in their variety. Yet these things in their function as primary elements should be considered in infinitesimal magnitude and in seminal form, somewhat like the material «forms» of all the things that exist and are equally real. These things, when separated off by the νους from the original mixture, in which everything was present, could be regarded as homoemerous or as homoeomeries in order to constitute the διακόσμησις according to the decrees of νους. Therefore, with regard to the main questions of my inquiry I conclude that the term was not used by Anaxagoras and thus no entry of it should be made in the lexicon of the Presocratics; that it has many meanings depending on the aspect from which it is seen to function as descriptive of the constituents of the material reality; and that the corresponding term in the extant fragments was in all probability the χρήματα, which occurs about twelve times in the actual quotations and is implied in the crucial phrase «εν παντί παντός μοίρα ενέστι», which might have given rise to the much discussed term. It could be possible to father the term on the «Anaxagoreans» if we had more information about them. For a proper account of Anaxagoras’ physical theory it is necessary to read again all the secondary evidence and particularly Simplicius.