De triangulis planis et sphaericis libri quinque : una cum tabulis sinuum, in quibus tota ipsorum triangulorum scientia ex primis fundamentis geometricarum ... continentur, quam multiplicem usum haec triangulorum doctrina omnibus ... adferat ... qui sana rerum intelligentia sunt instructi, in sequenti opere, quod complectitur ordinata astronomicorum et geometricorum problematum descriptionem (autore D. Santbech) ... deprehendere poterunt. (Tractatus Georgii Peurbachii super propositiones Ptolomaei de sinubus et chrodis) omnia nunc simul in lucem edita in gratiam matheseos studiosorum per Danielem Santbech.

Basel: Heinrich Petri & Peter Perna, 1561.

Rare augmented edition of “the first systematic treatise on plane and spheric trigonometry to be published in Europe. Although it drew heavily on Arabic sources, those earlier treatises had been either lost or forgotten by 1533 when Regiomontanuss work was first printed. Among the notable contents of this work are the sine law and perhaps the first European application of algebra to trigonometry. Indeed with De triangulis trigonometry was established as an independent discipline. Regiomontanus’ original purpose, however, had been to furnish astronomers with a mathematical technique essential for their studies, and in this De triangulis had a success perhaps greater than its author could have dreamed of. For in 1539 Georg Joachim Rheticus presented a copy of the work’s 1533 edition as a gift to Copernicus. The great astronomer had already written the trigonometrically-based portion of his De Revolutionibus without knowledge of his predecessor’s treatise. After reading the new book, Copernicus modified the presentation of several of his own indispensable theorems by inserting two leaves in the manuscript of the De Revolutionibus. Hence, Rheticus’ remark that Regiomontanus began the reconstruction of astronomy that Copernicus completed takes on a fuller meaning” (Rose, The Italian Renaissance of Mathematics, pp. 99-100).

This edition is augmented by two early allied treatises: ‘Tabula sinuum ad 6000000 partes per I. de Regiomonte computata’ and ‘Tractatus super propositiones Ptolemaei de sinubus et chordis’ by Peurbach. These contain trigonometric tables etc., not present in the first edition. This edition is also immeasurably improved by the extended treatise of Santbech, appearing here for the first time, which contains a wealth of information about astronomy in the first years after Copernicus. It addresses the use of instruments for astronomical observations, and the solution of various problems in measurement making use of the doctrine of triangles given in the first part, as well as occasionally citing Copernicus (e.g. pp. 46, 52).

The writing of De Triangulis was completed by 1464 but it was first published in 1533 at Nuremberg by Johann Schöner. A second edition of this work, published in 1541, contained the first appearance of the two additional tracts by Regiomontanus and Peurbach included here (but not the Santbech) and appears to be so rare that even Zinner, who cites it (no. 1900), gives it the wrong date (Basel, 1546) and may never have seen a copy.

Adams R-281; see Stillwell, Awakening 218; Cockle, Military Books, p. 23; see PMM 40; DSB 11: 348-52 & 15:478.

Folio (), pp [xvi] 146 [38]; [20] 294 [2]. Woodcut initials and numerous woodcut diagrams in text. Contemporary vellum (hinge of title and final leaf mended, some light occasional browning).

Item #2852

Price: $13,500.00