This group properly belongs to Polynesia:  of the other islands in this quarter of the globe, which were discovered prior to the eighteenth century, Otaheite is supposed to have been discovered by Quiros in 1606.  His object was to discover the imagined austral continent; but his discoveries were confined to Otaheite, which he named Sagittaria, and an island which he named Terra del Esperitu Sancto, which is supposed to be the principal of the New Hebrides.  The Ladrones were discovered by Magellan in 1521.  The New Philippines, or Carolinas, were first made known by the accidental arrival of a family of their natives at the Philippines in 1686.  Easter island, a detached and remote country, which, however, is inhabited by the Polynesian race, was discovered by Roggewein in 1686.

Having thus exhibited a brief and general sketch of the progress of discovery, from the period when the Portuguese first passed the Cape of Good Hope to the beginning of the eighteenth century, we shall next, before we give an account of the state and progress of commerce during the same period, direct our attention to the state of geographical science in the sixteenth and seventeenth centuries.

We have already stated that the astrolobe, which had been previously applied only to astronomical purposes, was accommodated to the use of mariners by Martin Behaim, towards the end of the fifteenth century.  He was a scholar of Muller, of Koningsberg, better known under the name of Regiomontanus, who published the Almagest of Ptolemy.  The Germans were at this time the best mathematicians of Europe.  Walther, who was of that nation, and the friend and disciple of Regiomontanus, was the first who made use of clocks in his astronomical observations.  He was succeeded by Werner, of Nuremberg, who published a translation of Ptolemy’s Geography, with a commentary, in which he explains the method of finding the longitude at sea by the distance of a fixed star from the moon.  The astronomical instruments hitherto used were, with the exception of the astrolobe, those which had been employed by Ptolemy and the Arabians.  The quadrant of Ptolemy resembled the mural quadrant of later times; which, however, was improved by the Arabians, who, at the end of the tenth century, employed a quadrant twenty-one feet and eight inches radius, and a sextant fifty-seven feet nine inches radius, and divided into seconds.  The use of the sextant seems to have been forgotten after this time; for Tycho Brahe is said to have re-invented it, and to have employed it for measuring the distances of the planets from the stars.  The quadrant was about the same time improved by a method of subdividing its limbs by the diagonal scale, and by the Vernier.  The telescope was invented in the year 1609, and telescopic sights were added to the quadrant in the year 1668.  Picard, who was one of the first astronomers who applied telescopes to quadrants, determined the earth’s diameter in 1669, by measuring a degree of the meridian in France.