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In 1492 the Spanish monarchs funded Christopher Columbus's expedition to sail west to reach the Indies by crossing the Atlantic, which resulted in the Discovery of America.In 1498, a Portuguese expedition commanded by Vasco da Gama reached India by sailing around Africa, opening up direct trade with Asia.A military navigator might have bearing takers stationed at the gyro repeaters on the bridge wings for taking simultaneous bearings, while the civilian navigator must often take and plot them himself.While the military navigator will have a bearing book and someone to record entries for each fix, the civilian navigator will simply pilot the bearings on the chart as they are taken and not record them at all.The Trinidad sailed east from the Philippines, trying to find a maritime path back to the Americas, but was unsuccessful.The eastward route across the Pacific, also known as the tornaviaje (return trip) was only discovered forty years later, when Spanish cosmographer Andrés de Urdaneta sailed from the Philippines, north to parallel 39°, and hit the eastward Kuroshio Current which took its galleon across the Pacific. The term stems from the 1530s, from Latin navigationem (nom. of navigare "to sail, sail over, go by sea, steer a ship," from navis "ship" and the root of agere "to drive".

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The height of Polaris in degrees above the horizon is the latitude of the observer, within a degree or so.

Most other modern techniques rely on crossing lines of position or LOP.

Dead reckoning or DR, in which one advances a prior position using the ship's course and speed. It is generally accepted that only course and speed determine the DR position.

The fleet of seven ships sailed from Sanlúcar de Barrameda in Southern Spain in 1519, crossed the Atlantic Ocean and after several stopovers rounded the southern tip of South America.

Some ships were lost, but the remaining fleet continued across the Pacific making a number of discoveries including Guam and the Philippines.

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