Euclid's Elements of Geometry, Plane and Solid

To him are ascribed the 14th and 15th books of Euclid, contracted by Hypsicles. Hipparchus and Menelaus wrote the first books on chords in a circle, the latter six, the former twelve; for which discovery, so useful and necessary, no small praise and gratitude is owed to both. There are also extant three books of Menelaus on spherical triangles. The three very useful books on spherics by Theodosius of Tripoli are in everyone’s hands. And these, if you except Menelaus [Isidorus and Hypsicles], all lived before Christ.

In the year 70 after Christ came to light Claudius Ptolemy, prince of Astronomers, a man clearly marvelous, and (says Pliny) "beyond the nature of mortals." He was indeed most skilled not only in Astronomy but also in Geometry; which is witnessed by many other things written by him, and especially by his books on chords, contracted from the 6 of Menelaus and 12 of Hipparchus into 5 theorems. There are also extant Mathematical problems by the highly renowned philosopher Plutarch. Now, who is ignorant of the learned commentaries of Eutocius of Ascalon on Archimedes [and Apollonius]? By him, the inventions regarding the doubling of the cube by Philon, Diocles, Nicomedes, Sporus, and Heron, as excellent teachers of Mathematics, are recounted. And indeed, Heron’s genius was excellent in mechanics as well as in geometry. The doubling of the cube handed down by him is praised by Pappus (book 3, p. 7) above all others. The admirable works of Ctesibius of Alexandria, to whom we owe our pumps, are celebrated by Vitruvius, Proclus, Pliny, and Athenaeus. Geminus also holds a name of no small account among mathematicians, whom Proclus in some matters preferred even to Euclid himself.

Diophantus, also an Alexandrian, in Arithme-

* Error: For Pliny was earlier in age than Ptolemy.