Anaximander, the son of Praxiades, was a native of Miletus. He laid down as his principle and element that which is unlimited without defining it as air or water or anything else. He held that the parts undergo change, but the whole is unchangeable; that the earth, which is of spherical shape, lies in the midst, occupying the place of a centre; that the moon, shining with borrowed light, derives its illumination from the sun; further, that the sun is as large as the earth and consists of the purest fire.These astronomical discoveries belong properly to Anaxagoras.

He was the first inventor of the gnomon and set it up for a sundial in Lacedaemon,But see Herodotus ii. 109, who makes the Babylonians the inventors. as is stated by Favorinus in his , in order to mark the solstices and the equinoxes; he also constructed clocks to tell the time.

He was the first to draw on a map the outline of land and sea, and he constructed a globe as well.

His exposition of his doctrines took the form of a summary which no doubt came into the hands, among others, of Apollodorus of Athens. He says in his that in the second year of the 58th Olympiad547-546 b.c. Anaximander was sixty-four, and that he died not long afterwards. Thus he flourished almost at the same time as Polycrates the tyrant of Samos.There is a chronological difficulty in this statement of Diogenes, for Polycrates of Samos died in 522. The difficulty, however, disappears if the statement be taken to refer not to Anaximander but to Pythagoras. There is a story that the boys laughed at his singing, and that, when he heard of it, he rejoined, Then to please the boys I must improve my singing.

There is another Anaximander, also of Miletus, a historian who wrote in the Ionic dialect.

Anaximenes, the son of Eurystratus, a native of Miletus, was a pupil of Anaximander. According to some, he was also a pupil of Parmenides. He took for his first principle air or that which is unlimited. He held that the stars move round the earth but do not go under it. He writes simply and unaffectedly in the Ionic dialect.

According to Apollodorus he was contemporary with the taking of Sardis and died in the 63rd Olympiad.528-525 b.c.

There have been two other men named Anaximenes, both of Lampsacus, the one a rhetorician who wrote on the achievements of Alexander, the other, the nephew of the rhetorician, who was a historian.

Anaximenes the philosopher wrote the following letters:

Anaximenes to Pythagoras

Thales, the son of Examyas, has met an unkind fate in his old age. He went out from the court of his house at night, as was his custom, with his maidservant to view the stars, and, forgetting where he was, as he gazed, he got to the edge of a steep slope and fell over. In such wise have the Milesians lost their astronomer. Let us who were his pupils cherish his memory, and let it be cherished by our children and pupils; and let us not cease to entertain one another with his words. Let all our discourse begin with a reference to Thales.

And again:

Anaximenes to Pythagoras

You were better advised than the rest of us when you left Samos for Croton, where you live in peace. For the sons of Aeaces work incessant mischief, and Miletus is never without tyrants. The king of the Medes is another terror to us, not indeed so long as we are willing to pay tribute; but the Ionians are on the point of going to war with the Medes to secure their common freedom, and once we are at war we have no more hope of safety. How then can Anaximenes any longer think of studying the heavens when threatened with destruction or slavery? Meanwhile you find favour with the people of Croton and with the other Greeks in Italy; and pupils come to you even from Sicily.

Anaxagoras, the son of Hegesibulus or Eubulus, was a native of Clazomenae. He was a pupil of Anaximenes, and was the first who set mind above matter, for at the beginning of his treatise, which is composed in attractive and dignified language, he says, All things were together; then came Mind and set them in order. This earned for Anaxagoras himself the nickname of Nous or Mind, and Timon in his says of himFr. 24 d.: Then, I ween, there is Anaxagoras, a doughty champion, whom they call Mind, because forsooth his was the mind which suddenly woke up and fitted closely together all that had formerly been in a medley of confusion.

He was eminent for wealth and noble birth, and furthermore for magnanimity, in that he gave up his patrimony to his relations.

For, when they accused him of neglecting it, he replied, Why then do you not look after it? And at last he went into retirement and engaged in physical investigation without troubling himself about public affairs. When some one inquired, Have you no concern in your native land? Gently, he replied, I am greatly concerned with my fatherland, and pointed to the sky.

He is said to have been twenty years old at the invasion of Xerxes and to have lived seventy-two years. Apollodorus in his says that he was born in the 70th Olympiad,500-497 b.c. and died in the first year of the 88th Olympiad.428 b.c. He began to study philosophy at Athens in the archonship of Calliasi.e. 456 b.c.; but possibly the year 480 is meant, when Calliades was archon. when he was twenty; Demetrius of Phalerum states this in his list of archons; and at Athens they say he remained for thirty years.