Nor were the laws of optics and the correction of the illusions of sight neglected. Euclid wrote a work on the subject which is now lost; but the praise of it by competent men of the Alexandrian school shows that it was on a level with his other scientific productions. To our educated public, the work of the Greeks in most fields is known at least by hearsay; the great library of Greek mathematics, scores of volumes, some of which are only quite recently published, is, except for Euclid, absolutely unknown. Yet from it is derived not only the scanty knowledge of science that filtered through the Romans into Western Europe, but also that adopted by the Arabs, and which in translations from Arabic versions came from them into awakening Italy and Germany and France. But let me add that now, when their discoveries in pure mathematics are being weighed by the light of expert knowledge, we are assured by all those really competent to judge that in no field of learning have the old Greeks shown their amazing originality and acuteness more signally than in higher arithmetic and in higher geometry. The great fathers of the exact sciences are therefore in arithmetic the Pythagoreans, whose history is too obscure to mention from it any single name before Archytas, Euclid, and Theon of Smyrna; in geometry, Euclid; in mechanics, Archimedes; in conic sections, Apollonius of Perga; in hydrostatics, Heron; in astronomy, Eudoxus and Hipparchus; last, but not least, in higher arithmetic and algebra, Diophantus; all of these were, moreover, men who did not confine themselves to any single department, but promoted accurate thinking in many. These, and others hardly less great, have left a record and a legacy to posterity second to none in its mighty consequences.