(Jacοby FGrHist. 72, Usener, Quaest. Anaxim. 6 sq., Blass II2 378 sq.)
1. Dion. Hal. Isaei I p. 122, 3 Us.-R.: Ἀναξιμένην δὲ τὸν Λαμψακηνὸν ἐν ἁπάσαις μὲν ταῖς ἰδέαις τῶν λόγων τετράγωνόν τινα εἶναι βουλόμενον (καὶ γὰρ ἱστορίας γέγραφε καὶ περὶ τοῦ ποιητοῦ συντάξεις καταλέλοιπε καὶ τέχνας ἐξενήνοχεν, ἧπται δὲ καὶ συμβουλευτικῶν καὶ δικανικῶν ἀγώνων), οὐ μέντοι τέλειόν γε ἐν οὐδεμιᾷ τούτων τῶν ἰδεῶν ἀλλʼ ἀσθενῆ καὶ ἀπίθανον ὄντα ἐν ἁπάσαις θεωρῶν.
Inter Isocratem et Alcidamanta positus παραγγελμάτων τεχνικῶν συγγραφεὺς καὶ ἀγωνιστὴς λόγων ῥητορικῶν a Dionysio nominatur ad Amm. 2, I p. 259, 3 sq. Ἀναξιμένης aliique eiusdem aetatis οὐθὲν οὔτε καινὸν οὔτε περιτεὸν ἐπετήδευσαν sec. eundem de Dem. p. 143, 7 sq.
2. Paus. VI 18 (3) 5: ἐπεφύκει μὲν αὐτὸς σοφιστὴς καὶ σοφιστῶν λόγους μιμεῖσθαι (sc. Ἀναξιμένης)… (6) οὐ μὴν οὐδὲ εἰπεῖν τις αὐτοσχεδίως Ἀναξιμένους πρότερός ἐστιν εὑρηκώς.
Artis verba p. 85, 20 (38 p. 99, 9 H.) συνεθίζειν αὑτοὺς τούτοις ἅπασιν ἐξ ἑτοίμου χρῆσθαι confert Usener l. l. p. 21.
3. Philod. rhet. II p. 254, 20 S.: ἀλλ’] ὅταν δὴ λέγωσιν ὥσπερ Ἀναξιμένης, ὡς οὐκ ἄν ποτε προσῇσαν τοῖς ῥητορικοῖς ἀργύριον διδόντες, εἰ μὴ τὸ δημηγορεῖν καὶ δικολογεῖν [ἐκ τῆ]ς τέχνης αὐτῶν [περιε]γίνετο τελείως, [ἀνα]στρέφονται παχέ[ως].
Cf. Philod. I p. 31, 3: εἰ μὴ τέχνην μ[εθώ]δευον ὀ[ρθῶς, οὔποτ’] ἂν πολλοὶ [προ]σῇεσαν αὐ[το]ῖ[ς] μισθοὺς διδόντες.
4. Ibid. II p. 165, 22 S.: λείπε[τʼ] οὖν ἀπόδει[ξις,] δι’ ἧς Ἀναξιμένης [ἔφασ]κε [τὸ συλ]λόγισμα... (28) ὥσθʼ οὗτος μ[άλιστα δύν]αται πείθειν [κατά γε] τοῦτον ὁ ῥήτωρ, οὗ [ἔστι τὸ?] καθόλου.
5. Hypoth. Isocr. Hel.: βέλτιον δὲ λέγειν, ὥσπερ ὁ Μαχάων, ὅτι πρὸς Ἀναξιμένην τὸν Λαμψακηνὸν γράφει. φέρεται δὲ ἐκείνου λόγος, Ἑλένης ἀπολογία μᾶλλον οὖσα ἤπερ ἐγκώμιον.
6. Philod. rhet. I p. 215, 1 S.: εἰ μέντοι γε τῶν θεῶν καὶ τῶν ἡρώων ἐγκώμια δύνασθαι ποιεῖν ἐπαγγέλλονται, τῶν δʼ ἀνθρώπων τοὺς μὲν εὐλογεῖν, τοὺς δὲ δυσφημεῖν καὶ τοὺς αὐτούς, ὅταν πρ[ο]έλωνται, ποιεῖν ἑκάτ[ε]ρον, ἡ[μ]εῖς [φ]ήσομεν, χ]ωρὶς τοῦ καὶ ἀναισθήτων οὐχ οἷον ἀλόγων ζώων αὐτοὺς ἐγκώμια πεπ[οι]ηκέναι, διότι θεῶν μὲν οὐδεὶς οὐδʼ ἡρώων ἐγκωμίου δεῖτα[ι] τοῦ παρʼ ἀνθρώπων, ἔστιν τε πὰν ἔλαττον αὐτῶν καὶ τὸ κατατευχθέν, ἀπρεπέστατον δὲ τὸ γεινόμενον ὑπὸ τῶν σοφιστῶν. διὸ καὶ λέγουσιν Ἀριστοτέλην ἤ τινα μέντοι πρὸς Ἀναξιμένην ἤ τινα δήποτʼ εἰπεῖν τῶν σοφιστῶν εἴτε Ἀ[ρ]τέμιδος εἴτʼ Ἀθηνᾶς ἐγκώμιον γράψαντα καὶ σεμνυνόμενον· οὐκ οἴει γάρ, εἰπ[εῖ]ν, ἐάν ποτʼ ἔρις γένηται τῶν θεῶν ὡς πρό[τ]ερον, ἐρεῖν τὴν Ἀφροδείτην· καλὸν γὰρ ἐγκώμιόν σου καὶ ὁ δεῖνα ἐποίησεν;
7. Stob. Flοr. Γʼ XXXVIII 45 (III p. 718 H.): τοῦ αὐτοῦ (i. e. Ἀναξιμένους)· ὅσοι γὰρ τὰ καλῶς ῥηθέντα ἢ πραχθέντα διὰ φθόνον οὐκ ἐπαινοῦσι, πῶς οὗτοι ἂν τοῖς ἔργοις ὠφελήσειαν;
Putes <τοῖς λόγοις ἢ> τοῖς ἔργοις. Ex aliquo encomio, ut videtur.
8. Stοb. Flοr. Δʼ L 91 (V p. 1055 H.): Ἀναξιμένους· τοῖς γὰρ ἀστείοις πρεσβύταις, ὅσον αἱ κατὰ τὸ σῶμα ἡδοναὶ ἀπομαραίνονται, τοσοῦτον αἱ περὶ τοὺς λόγους ἐπιθυμίαι πάλιν αὔξονται, καὶ τοσούτῳ βεβαιότερον αὐτοῖς παρέχει τὸ λέγειν τι χρήσιμον 5 τοῖς ἄλλοις καὶ παρʼ ἑτέρων αὐτοὺς ἀκούειν· ὥστε τὰς μὲν ἀπὸ τῶν βρωτῶν καὶ ποτῶν καὶ ἀφροδισίων ἡδονὰς γινομένας ἰδεῖν ἔστιν οὐχ οὕτως εἰς τὸ παραχρῆμα εὐφραινούσας ὡς ὕστερον λυπούσας· ἡ δὲ περὶ τοὺς λόγους ἡδονὴ καὶ μάθησις ἔν τε τῷ παραυτίκα εὐφραίνει καὶ πρὸς τὸν ἄλλον βίον τοὺς μανθάνοντας ἡδέως 10 παρασκευάει.
4 παρέχει sc. τὸ γῆρας 5 αὐτοῖς M 6 alterum καὶ om. A 9 διάγειν ἡδέως MA
Cf. Plato rei p. 328 D, Aristot. rhet. 1389 b 13 sq.
9. Quint. inst. 3, 4, 9: Anaximenes iudicialem et contionalem generalis partes esse voluit, septem autem species: hortandi, dehortandi, laudandi, vituperandi, accusandi, defendendi, exquirendi, quod ἐξεταστικόν dicit: quarum duae primae deliberativi, duae sequentes demonstrativi, tres ultimae iudicialis generis sunt partes.
Hoc testimonio usus primus P. Victorius rhetoricam ad Alexandrum, vulgo Aristoteli tributam, Anaximenis esse coniecit.
1. Dionysius of Halicarnassus, On Isaeus p. 122.3: [Isaeus] observed that Anaximenes of Lampsacus, while he wanted to be accomplished in every form of composition (for he wrote history, left behind treatises on Homer, published on rhetorical theory and also participated in political and forensic debates), he nevertheless became fulfilled in none of these forms, but was weak and unconvincing in all of them.
Dion. Hal. To Ammonius 2.1 p. 259, 3 f. names a ‘writer of teaching treatises and competitor in rhetorical speeches’ inserted between Isocrates and Alcidamas. The same author On Demosthenes p. 143, 7 f. reports that ‘Anaximenes’ and others among his contemporaries ‘did not practice anything new or outstanding’.
2. Pausanias 6.18.(3)6: He had a natural aptitude for rhetoric and for imitating the style of rhetoricians. […] Moreover, Anaximenes was the first to compose extemporary speeches.
Usener ibid. p. 21 compares the words of the treatise p. 85.20 (38 p. 99.9 H.): ‘they accustomed themselves to making use of all these things on the spot.’
3. Philodemus, On Rhetoric p. 254.20: But when they make the same claim as Anaximenes, that people did not use to approach orators offering money unless their speaking in public or in court came out perfectly due to their art, they are grossly mistaken.
4. Ibid. p. 165.22: There remains only the exposition, though which Anaximenes claimed happens the summary […] so that, according to this author, that orator can persuade best who masters the whole.
5. Hypothesis to Isocrates’ Helena: It is more accurate to say, as does Machaon, that [Isocrates] is writing in rivalry against Anaximenes of Lampsacus. A speech by the latter is known that is a defense of Helena rather than a praise.
6. Philodemus, Rhetoric p. 215.1: If they proclaim that they are able to write praises of gods and heroes and, as far as humans are concerned, to praise some and denigrate others and that they can do either thing to the same people when they so desire, we shall say the following (apart from the fact that they wrote praises, not just for brute animals, but for inanimate objects): None of the gods or heroes needs to be praised by a human, and even all of what hits the mark is less than they are; so what the sophists have done is totally inappropriate. This is why Aristotle, or whoever that was, is said to have said to Anaximenes, or whoever else that was, who had written a praise of either Artemis or Athena and took great pride in it: “Don’t you know that, should there arise a strife among gods as in the past, Aphrodite will say: ‘Nice praise of yours that gut wrote!’”
7. Stobaeus, Anthology: From the same author [Anaximenes]: “All those who do not praise good words or actions out of envy – how would these people be useful through actions?
You would expect ‘through <words or> actions.’ Apparently these words stem from some encomium.
8. Ibid.: From Anaximenes: “The more the bodily pleasures of cultivated old people vanish, the stronger their desires relating to speech grow again and the more likely  [their age] makes it for them to say something of use to others and to have such things said to them by others. So the pleasures coming from eating and drinking and sexual lust can be seen not so much to make one happy in the present moment as to cause pain afterwards; the pleasure relate to the art of speaking and the learning of it both cause joy in the present and make those who learn it happy for the rest of their life.”
9. Quintilian 3.4.9: Anaximenes claimed that the judicial and the deliberative were general parts, and the kinds were seven: exhortation, dissuasion, praise, blame, accusation, defense, inquiry, which he calls exetastikon. The first two are parts of the deliberative genre, the following two of the demonstrative, the last three of the judicial.
Based on this testimony, P. Victorius surmised for the first time that Anaximenes was the author of the Rhetoric to Alexander, which was generally attributed to Aristotle.