Shakespeare writes “the moon’s an arrant thief, and her pale fire she snatches from the sun” (Timon of Athens, Act 4, Scene 3). He is, of course correct. The moon merely reflects sunlight, and produces no light of its own. One way of telling this is that moonlight actually displays the same telltale absorption spectrum as sunlight:
Our eyes tend to perceive moonlight as “blueish” or “silvery,” but that is because of the way our eyes work at low light levels. Long-exposure photographs under moonlight, like this one, look much like daytime shots:
Anaxagoras (499–428 BC) seems to have been the first to discover that the moon shines only by reflected light:
Anaxagoras also explained that solar eclipses occur when the moon moves between the earth and the sun. Total solar eclipses are dark precisely because the moon produces no light of its own:
Scientific Gems 
Long before this Anaxagoras was born this was already been known by Enoch. So it was not Anaxagora made the discovery. You may want to read Book of Enoch Chapter 77( Book available on Apple and Google App)
The Book of Enoch we have was written after Anaxagoras.