The French mathematician and historian of science Paul Tannery (1843-1904) worked as an administrator in the state tobacco industry while researching and publishing on a wide variety of topics, including editions of Fermat and Descartes as well as of the Greek mathematician Diophantus of Alexandria. This 1893 work reviews the history of ancient Greek astronomy, beginning with a survey of what the Greeks actually meant by the use of the terms 'astronomy' and 'astrology', and going on to consider the work of Pythagoras and the other pre-Socratics, Aristotle and the Alexandrian mathematicians. At its core is a detailed analysis of Claudius Ptolemy's Almagest, which attempts to trace each of the Greek master's theories - on the sphericity and circumference of the earth, on the sun, moon and planets, and on the prediction of eclipses - back to its historical origins in Greek mathematical and philosophical thought.