What we know today as trigonometry began as a collection of mathematical techniques, both geometrical and arithmetical, for addressing astronomical problems, such as: how to measure the elevation of the Sun in the sky how to predict when a given star will rise, based on the regularity of its revolutions about an Earth-based observer or when an eclipse (solar or lunar) should occur. As Van Brummelen makes clear in The Mathematics of the Heavens and the Earth, the history of trigonometry up to the sixteenth century is to a large extent the history of astronomy. What makes it truly noteworthy, however, is what one will not find in its pages: astronomical problems. While it contained little brand-new mathematics, On Triangles was the first fully comprehensive treatment of trigonometry to appear in Europe.
Regiomontanus ’ De triangulis omnimodis ( On Triangles of Every Kind) was compiled decades earlier than De revolutionibus, in 1464, but it was not published until 1533. Johannes Müller / Regiomontanus (1436–1476). īut where Van Brummelen sees the transition from the early history of trigonometry to its modern phase in the shift of perspective between “the Earth-centered and Sun-centered universe ” of Copernicus’ (literally) world-changing De revolutionibus (1543), the classroom unit Regiomontanus and the Beginnings of Modern Trigonometry featured in this article highlights a pedagogically more useful transition in the history of trigonometry through excerpts from a much less “revolutionary” work by Johannes Müller, better known by the name Regiomontanus (1436–1476). Trigonometry proper began with the origins of the Ptolemaic geocentric system, and a nice breaking point is found with the beginning of Copernicus’s heliocentric model. In the preface to the first book of his two-volume history of trigonometry, The Mathematics of the Heavens and the Earth and The Doctrine of Triangles, Glen Van Brummelen discussed how he decided where to divide the two volumes:
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