"The third century before Christ, which opens with... Euclid and closes with the death of Apollonius, is the most brilliant era in the history of Greek mathematics. But the great mathematicians of that century were geometricians... It was not till after... nearly 1800 years that the genius of Descartes opened the way to any further progress in geometry... [R]oughly... during the next thousand years Pappus was the sole geometrician of great ability; and... almost the only other pure mathematicians of exceptional genius were Hipparchus and Ptolemy who laid the foundations of trigonometry, and Diophantus who laid those of algebra."