Regiomontanus (Johannes Müller) De triangulis

Regiomontanus (Johannes Müller) De triangulis planis et sphaericis libri quinque..., second edition, collation: *4 a-o6 p8 : *6 A4 B-Z6 AA6 BB4 CC6, woodcut device to title, engraved historiated initials and woodcut illustrations, 20th century ink provenance note and bookplate to pastedown, first few ff. damp-stained, title with small repairs and reinforced at inner margin, short marginal tears to N¹ and N³ not affecting text, final ff. browned and repaired, occasional light spotting and browning, contemporary vellum, spine with manuscript title in raised bands (mostly chipped away), small contemporary labels to spine and cover, partially removed, [Adams R-281; Norman 1566], tall 8vo (315 x 210mm), Basel, Heinrich Petri & Peter Perna, [1561].

⁂ The second, much augmented edition of the first systematic treatise on plane and spherical trigonometry to be published in Europe. Though it was completed in 1464, it remained a manuscript until 1533 where it was first published in Nuremberg by Johann Petri. Regiomontanus's monumental work on triangles was the first printed systematization of the subject as a branch of mathematics independent of astronomy, and contains the earliest statement of the cosine law for spherical triangles, stating the proportionality of the sides of a plane triangle to the sines of the opposite angle. This fundamental proposition of spherical trigonometry appears as theorem 2 in book V of the treatise. In the second part, Regiomontanus proves the errors of Nicolaus de Cusa's theory of squaring the circle, which had a profound effect on the history of navigation (Adams). His contributions were instrumental in the development of Copernican heliocentrism in the decades following his death.