Katherine Neal, “Mathematics and Empire, Navigation and Exploration: Henry Briggs and the Northwest Passage Voyages of 1631” Isis 93, no. 3 (September 2002): 435–453
Advances in mathematics played an important role in encouraging European exploration and the demands of exploration and the interest in its success in turn encouraged further development of mathematics. Mathematicians developed astronomical charts for mariners, invented navigational instruments, and drew maps. Perhaps most importantly, it was mathematicians who helped sailors figure out where they were when they were on the open sea. Until the fifteenth century, Katherine Neal explains, European “mariners had coasted close to land, using compass, rudder, lead, and line. The advent of oceangoing sailors began a revolution in navigational techniques, which now included observing the sun and stars and plotting one’s course on charts.” Mathematicians discovered that latitude could be determined by measuring the angle of the noonday Sun above the horizon with an astrolabe or cross staff. The print above shows the tools of navigation (compass, globe, astrolabe, cross staff) lighting the way for ships of discovery. This required a knowledge of angles and trigonometry. Sailors could find a line of latitude and sail across the Atlantic on it. Finding longitude was much harder and would not be possible for another century. Neal recounts that “fleets of ships sailing together could seldom agree on their location. Captain Luke Ward’s voyage of 1582 included a conference between ships in mid-Atlantic; they differed by nearly a hundred miles in their judgment of their east-westing.” Finding longitude required the development of spherical trigonometry to solve the triangles that were the results of the navigational measurements. Tables were constructed which solved triangles with a vast range of different angles. These were used with ephemerides, which were tables of the location of the Sun, planets and many stars for frequent time intervals in every day throughout the year. The development of mathematics made travel safer and more precise over the course of the sixteenth and seventeenth centuries; less risk to ships, cargo, and crew meant more profit, which meant greater incentives for kingdoms and companies to continue to explore.