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Mathematical Treasures - Peter Apianus's Trigonometry and Geography

Frank J. Swetz and Victor J. Katz


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 illustrated and explained 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 reviewed the theories of Vernerus, or Johannes Werner (1468-1522), a Nuremburg priest and mathematician who devised a method of using lunar observations to find longitude, and explained applications of trigonometry (specifically, sines and chords) in geography.


Convergence's Mathematical Treasures also include images from Apian's 1545 Cosmographia, extended from his original 1524 edition by Gemma Frisius.



Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Peter Apianus's Trigonometry and Geography," Convergence (January 2011)


Mathematical Treasures from the Smith and Plimpton Collections at Columbia University