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 equinoxes—all bequeathed to them by Hipparchus, and preserved for them by Ptolemy. The system of Ptolemy was the navigator's text-book in the Middle Ages; and the Almagest, the Arabic translation of his work, was the foundation of astronomical knowledge. It was to learned men, well versed in the Almagest, that Alfonso X. of Castille, had entrusted the preparation of the astronomical tables which are called after him, and which, after they had remained in manuscript for about two hundred years, were first printed in 1483. Before the accession of Henry VII., Georg Peurbach and Johann Müller, better known as Regiomontanus, had lived and done their work, and the latter had not only constructed valuable instruments, but had also published his "Ephemerides," with tables of the sun's declination calculated for the years from 1475 to 1566.

It was, however, in the lifetime of Henry VII. that greater progress was made than in any previous period of thrice the duration, and the chief authors of this remarkable progress were the two celebrated navigators, Martin Behaim, of Nuremberg, and Christopher Columbus.

Behaim, a merchant, was a pupil of Regiomontanus, and a student of the Almagest. While in Portugal, he adapted for João I., as an instrument of navigation, the astrolabe, which had previously been used only in astronomy. A graduated metal ring, held so as to hang as a plummet, with a movable limb across it, fitted with two perforated sights, enabled the seaman to observe the angle between the horizon and the sun at noon; and with this, and the daily declination of the sun, as given by Regiomontanus, the discovery of the latitude involved only a simple calculation. This seems to have been about the year 1483. Not many years elapsed ere a more suitable instrument for observing the sun's altitude was devised. This was the cross-staff, the first known description of which dates from 1514, and is by Werner of Nürnberg. After accompanying Diogo Cão on his West African voyage in 1484-85, and then living for a time in the Azores, Behaim returned to Nürnberg, and constructed his great globe, concerning