Who was Anaxagoras?
Like Thales before him, Anaxagoras was born in what's now Turkey. Anaxagoras was born around 500 BC in a city called Clazomenae, in the Persian Empire. When he was a child, Clazomenae participated in the Ionian Revolt and soon became part of the Athenian Empire.
Anaxagoras seems to have been born into a rich family, and he probably went to school, but later he chose to be poorer so he could spend his time studying instead of running his family's business. When Anaxagoras grew up, he went to Athens, which was essentially his capital city. He lived in Athens most of his life. He became friends with Pericles and Euripides, and he must have known Socrates.
Anaxagoras' most important idea was that people should not trust their senses (seeing and hearing) or their common sense to tell them about the world, but they should always use logic and reason to figure out the truth instead.
Sometimes this idea led Anaxagoras to some funny conclusions. For instance, he said that snow must have some darkness in it, as well as whiteness, or how could it turn into dark water when it melted? But he was able to use his logic to figure out correctly what caused eclipses.
Anaxagoras' ideas upset a lot of people in Athens who said he didn't believe in the Greek gods (and maybe he didn't). He was arrested, and only escaped being sentenced to death by the jury because his friend Pericles helped him. He had to leave Athens, and he died soon after in Lampsacus (near Troy), about 428 BC. Only fragments of the books Anaxagoras wrote survive today - most of them were lost or destroyed.
Almost a hundred years later, Aristotle said that he had gotten the beginnings of his science from Anaxagoras' work.
Greek and Roman Science, by Don Nardo (1998). Nardo has written a lot of good books about the ancient world for kids; this one is no exception.
Ancient Science: 40 Time-Traveling, World-Exploring, History-Making Activities , by Jim Wiese (2003). Activities, as the title says - how to make your own sundial, and so on. The author is a science teacher.
Early Greek Science: Thales to Aristotle, by Geoffrey Lloyd (1974).
History of Greek Mathematics: From Aristarchus to Diophantus, by Thomas L. Heath (1921, reprinted 1981). A lot of Euclid, but also describes who the other major Greek mathematicians were and what they did.
Episodes from the Early History of Mathematics, by Asger Aaboe (1997).