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MUELLER, Johann (called Regiomontanus) (1436-1476). De Triangulis omnimodis libri quinque...accesserunt huc in calce pleraque D. Nicolai Cusani de Quadratura circuli. Edited by J. Schner. Nuremberg: Johann Petri, 1533.
Two parts in one volume, 2o (289 x 196 mm). Collation: A-Q4 R6; a-b6 c-l4. 118 leaves, R6 and l4 blank, paginated. Woodcut diagram on main title, numerous woodcut diagrams in text. (Some light browning and spotting.) Modern vellum. Provenance: Two circular ink stamps erased from title-page, covered with the following; Alphonse Land (17th-century inscription on slips pasted onto title-page, "ex libris Alphonsi Landi"); ink monogram on front pastedown.
FIRST EDITION OF THE FIRST PRINTED SYSTEMATIC WORK ON TRIGONOMETRY. De triangulis was Regiomontanus's most important scientific contribution. Completed in 1464, De triangulis remained in manuscript for nearly seventy years before being published in this edition, edited by J. Schner (1477-1547). It 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.
Adams R-289; BM/STC German, p. 631; Stillwell Science 218; Norman 1566.
Two parts in one volume, 2o (289 x 196 mm). Collation: A-Q4 R6; a-b6 c-l4. 118 leaves, R6 and l4 blank, paginated. Woodcut diagram on main title, numerous woodcut diagrams in text. (Some light browning and spotting.) Modern vellum. Provenance: Two circular ink stamps erased from title-page, covered with the following; Alphonse Land (17th-century inscription on slips pasted onto title-page, "ex libris Alphonsi Landi"); ink monogram on front pastedown.
FIRST EDITION OF THE FIRST PRINTED SYSTEMATIC WORK ON TRIGONOMETRY. De triangulis was Regiomontanus's most important scientific contribution. Completed in 1464, De triangulis remained in manuscript for nearly seventy years before being published in this edition, edited by J. Schner (1477-1547). It 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.
Adams R-289; BM/STC German, p. 631; Stillwell Science 218; Norman 1566.