Insights An Introduction to Theorema Primum

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The discussion introduces the concept of "Copernican geometry," emphasizing its significance in Nicolaus Copernicus's work, particularly in "De Revolutionibus Orbium Coelestium." It highlights the geometric principles underlying Copernicus's revolutionary ideas, focusing on the importance of straight lines, arcs, and triangles in his proofs. The text critiques Euclid's Elements for lacking methods to derive sides from angles and vice versa, noting that arcs are essential for accurate measurements. This analysis aims to explore the geometric foundations that supported Copernicus's heliocentric model. The exploration of these geometric concepts will continue in future articles.
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Introduction
Whilst no doubt most frequenters of “Physics Forums” will be familiar with Nicolaus Copernicus as the scientist who advanced the (at the time) radical thesis that the Earth revolved around the sun rather than vice versa, a perhaps less well-known aspect of his work is the “nuts and bolts” geometry underlying his ground-breaking treatise: “De Revolutionibus Orbium Coelestium” (On the Revolutions of the Heavenly Spheres).  In this article (and perhaps others to follow), we analyse “Copernican geometry” in light of its stated intent:
Because the proofs which we shall use in almost the entire work deal with straight lines and arcs, with plane and spherical triangles, and because Euclid’s Elements, although they clear up much of this, do not have what is here most required, namely how to find the sides from the angles and the angles from the sides, since the angle does not measure the subtending straight line – just as the line does not measure the angle – but the arc does...

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