Incunabula and the Keio University Library Collection


Regiomontanus, Tabulae directionum et profectionum (Augsburg: Erhard Ratdolt, 2 Jan. 1490)

Tabulae directionum et profectionum. Tabella sinus recti (Ed: Joannes Angelus)

IIIF Drag-n-dropIIIF Manifest

Regiomontanus (1436-76) was an astronomer and mathematician of the fifteenth century born in Königsberg, Germany. His name was originally Johannes Müller, but he called himself Johannes de Monteregio, from a Latinized version of the name of his birthplace, and then later 'Regiomontanus'. He studied astronomy under Georg von Peuerbach (1423-69) at the University of Vienna and made a close Latin translation of the works of Ptolemy, and thereby sought to reform the faulty astronomy of the time. It was also Regiomontanus who first made a serious study of trigonometry.

After moving to Nuremberg in 1471, he found a patron to enable him to build the first substantial astronomical observatory in Germany. A printing shop was also established at the patron's house, where a record of Regiomontanus' observations of the daily movements of the heavenly bodies, which he had kept for thirty-two years, was printed in 1474 (see also IKUL 035). This included the times of the new and full moons and the eclipses; Christopher Columbus was said to have used it to foretell the eclipse in Jamaica. Regiomontanus died (probably of the Black Death) during a trip to Rome in 1476, where he had been invited to go by the Pope in order to work on reforming the calendar.

This posthumous work, edited by Joannes Angelus, contains calculation tables for the zodiacal constellations and for the angular distances (or 'phase difference') from the sun on every longitude, as well as tables of tangents which appeared in print for the first time. Eleven editions had been issued by 1626.

Ratdolt (d. 1527 or 1528) was trained as a printer in Venice, and ran a printing shop in his native town, Augsburg, from 1486. He pioneered the craft of making illustrated printed books: a calendar which he produced with his partners in 1476 was the first European title-page to have printed borders. However, only letters are used on the title-page of this book. The text is printed forty lines to a page in gothic type, of a very common Venetian form and size. The format is quarto, and most quires are in eight leaves; each of the first four leaves of a quire bears a signature which consists of a letter and an Arabic numeral – for example, 'a2'. No catchword is used. There are only tables after sig. d1v (fol. 23v). All the figures are represented using Arabic numerals enclosed by a pair of full stops, as in '.8.'.

The decorative initials have been printed using woodblocks, in an elegant Venetian style: the white letters are surrounded by arabesque patterns on a black background. On sig. s6r (fol. 140r), a printed and rubricated printer's device occupies the whole page.

The presence of many manuscript notes indicates that this copy has been heavily used; a table of contents is written on the title-page, and there are many annotations in brown ink in the margins and tables. Sadly, however, some of them were chopped off at the time of rebinding.



Regiomontanus, Johannes (Müller, Johann, of Königsberg)
Place of Publication
Erhard Ratdolt


Date of Publication

18th-century vellum over paper boards.

Bibliographical Notes

156 leaves; some woodcut initials; some contemporary marginalia; a printer's device printed in black and red on s6r.

Goff R112, HC13801* (incl H 15206*), BMC II 383, IJL 256, IJL2 323, PP41
Acquisition Year