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All those who have written histories bring to this point their account of the development of this science. Not long after these men came Euclid, who brought together the Elements, systematizing many of the theorems of Eudoxus, perfecting many of those of Theatetus, and putting in irrefutable demonstrable form propositions that had been rather loosely established by his predecessors. He lived in the time of Ptolemy the First, for Archimedes, who lived after the time of the first Ptolemy, mentions Euclid. It is also reported that Ptolemy once asked Euclid if there was not a shorter road to geometry that through the Elements, andEuclid replied that there was no royal road to geometry.He was therefore later than Plato's group but earlier than Eratosthenes and Archimedes, for these two men were contemporaries, as Eratosthenes somewhere says. Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the so-called Platonic figures. (Proclus, ed. Friedlein, p. 68, tr. Morrow)

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