Son of Aristocles, of Lampsacus, rhetor; pupil of Diogenes the Cynic and the grammarian Zoilus of Amphipolis, who abused Homer; teacher of Alexander of Macedon, and accompanied him on his campaigns.
When king Alexander was angry with the people of Lampsacus, this man got round him by the following trick. The people of Lampsacus were pro-Persian; Alexander was furiously angry, and threatened to do them massive harm. They, trying to save their women, their children and their homeland, sent Anaximenes to intercede. Alexander knew why he had come, and swore by the gods that he would do the opposite of what he asked; so Anaximenes said, 'Please do this for me, your majesty: enslave the women and children of Lampsacus, burn their temples, and raze the city to the ground.' Alexander had no way round this clever trick, and because he was bound by his oath he reluctantly pardoned the people of Lampsacus. Anaximenes also retaliated against Theopompus, son of Damostratus, in an ingenious though malicious way. Since he was a sophist and could imitate the style of the sophists, he wrote a book addressed to the Athenians and Spartans, a defamatory treatise, exactly imitating him. He attached Theopompus' name to it, and sent it to the cities. As a result, hostility to Theopompus was increased throughout Greece. Moreover, no one before Anaximenes had invented improvised speeches.
Source: “Anaximenes.” Suda On Line. Tr. Malcolm Heath. 27 January 2000. 2 March 2014. <http://www.stoa.org/sol-entries/alpha/1989>.
57. On coming to Myndus and finding the gates large, though the city itself was very small, he cried, “Men of Myndus, bar your gates, lest the city should run away.” Seeing a man who had been caught stealing purple, he said:
Fast gripped by purple death and forceful fate.
When Craterus wanted him to come and visit him, “No,” he replied, “I would rather live on a few grains of salt at Athens than enjoy sumptuous fare at Craterus's table.” He went up to Anaximenes the rhetorician, who was fat, and said, “Let us beggars have something of your paunch; it will be a relief to you, and we shall get advantage.” And when the same man was discoursing, Diogenes distracted his audience by producing some salt fish. This annoyed the lecturer, and Diogenes said, “An obol's worth of salt fish has broken up Anaximenes' lecture-class.”
Source: The Lives and Opinions of Eminent Philosophers, by Diogenes Laertius, Literally translated by C.D. Yonge. London: Henry G. Bohn, 1853 | Life of Anacharsis only, Lives of the Eminent Philosophers by Diogenes Laërtius, translated by Robert Drew Hicks, Wikisource