Peter Apianus's trigonometry and geography

Petrus Apianus [Peter Apian] was a German humanist known for his work in mathematics, astonomy, and cartography.  This is the title page of his Instrumentum sinuum sive primi (1534), the most accurate sine table published up until this time.  It contains sines for every minute of arc computed using a decimally divided radius of 100 subunits.

This page of Instrumentum directly precedes a listing of sine values. Apianus illustrates and explains the nomogram employed to graphically determine his sine and versed sine values [versed sine ø = 1 - cos ø ].

Title page of Petrus Apianus’ A Geographical Introduction (1534).  In this book, he reviews the theories of Vernerus [Johannes Werner (1468-1522), a Nuremburg priest and mathematician who devised a method of using lunar observations to find longitude] and explains the applications of trigonometry (i.e. sines and chords) in geography.