REGIOMONTANUS (1436–1476). De triangulis omnimodis. Edited by Johannes Schöner. Nuremberg: Johann Petri, 1533.

Leonardo Botallo’s copy. First edition of the first printed trigonometry textbook. Regiomontanus’s most important scientific contribution, On Triangles was completed in 1464 before being edited by Johannes Schöner (1477–1547) for this edition, its first appearance in print. It was when writing his epitome of Ptolemy’s Almagest (see lot 125), Regiomontanus realized the important role that trigonometry would play in making astronomical discoveries and the need for a systematic text on solving triangles. He wrote De triangulis to fill this need, writing in his introduction: “quisquis siderum motus admiraris, haec triangulorum theoremata in primis legenda sunt: quippe quorum disciplina omnibus Astronomicis, nonnullisque Geometricis quaesitis ianuam pandit” (whoever wonders at the motion of the stars must first read these theorems on triangles: for their study opens the door to all astronomical inquiries and some geometrical) (this edition, p. 5). On this copy the title has been inscribed along the top and bottom edges indicating that it was stored horizontally as common in medieval and early modern libraries.

This copy was owned by the 16th-century Italian physician Leonardo Botallo after whom the foramen Botalli and ductus Botalli are named in human anatomy.

Folio (302 × 197mm). Woodcut trigonometric diagram on title-page and further trigonometry cuts throughout, typeset mathematical tables and calculations (occasional spotting most prominent on title-page, small burn on title-page but no loss of text, faint marginal dampstains in few quires). Contemporary vellum over paper boards, contemporary title inscriptions on upper cover and top and bottom edges (corners worn, small worming through boards and endpapers); custom modern quarter calf box. Provenance: Leonardo Botallo (1530–c.1587; ownership inscription on title-page “Leonardi à Bottallis Astensis”) – Owen Gingerich (bookplate).