Introductio geographica in Verneri annotationes / Horoscopium generale dignoscendis horis cuiuscumque generis aptissimum by APIAN, Peter - 1533

Ingolstadt: Apian, 1533. 1st Edition. Hardcover. Very Good. Astronomy, Geography, sine tables, instruments, trigonometry, geometry, Werner, Regiomontanus. Astronomy, Geography, sine tables, instruments, trigonometry, geometry, Werner, Regiomontanus. 1st Edition. Hardcover. Folio - over 12 - 15" tall. Introductio geographica in Verneri annotationes. Ingolstadt: (Peter) Apian, 1533. 88 unnumbered leaves. Signatures: A-E4 a4 b-c6 d8 e-h6 i8 k-l6 (D3 missigned E3). Title printed in red and black and with large woodcut illustration, full-size woodcut coat of arms on verso, historiated woodcut initials, several woodcut diagrams and illustrations in text. Generally crisp and clean internally with light even browning, small worm holes in gatherings A-B, light dampstaining toward lower gutter, light brown staining at upper third from gathering l towards end. [Bound with:] APIAN, Peter. Horoscopium generale dignoscendis horis cuiuscumque generis aptissimum. Ingolstadt: (Peter) Apian, 1533. 20 unnumbered leaves. Signatures: A-E4. Title printed in red and black and with large woodcut illustration, historiated woodcut initials, several woodcut diagrams and illustrations in text, single plate, duplicating the illustration on the title-page, tipped to gutter of final leaf of first work. Some damp- and brownstaining at inner margin which becomes stronger towards end (the final two leaves showing faint old mould spots, some softening of paper and slight surface abrasion affecting a few letters on final leaf recto). Two works in one volume. Folio (301 x 198 mm). Bound in 18th century three quarter vellum over colored paste paper, spine lettered in ink (boards soiled and rubbed, spine spotted, wear and bumping to corners and board edges, top of spine chipped, extremities rubbed, vellum over spine with a diagonal split), red-sprinkled edges, later endpapers. Still very good copy of two rare works by Apian. ----

I. FIRST EDITION (in the later published title edition, the place of printing and the year are missing on the title page) of Peter Apian's introduction to practical geometry and computational astronomy, dedicated to Johann Wilhelm von Laubenberg. The book contains, besides Johannes Werner's notes and Apian's upon them, a Latin translation of the first book of Ptolemy's Geography, a letter of Regiomontanus, and descriptions of three instruments invented by Apian himself, namely the "Radius astronomicus", the "Quadrans novus" (a height quadrant with various auxiliary divisions) and the "Torquetum" ("Turkish instrument"). Apian was a student of Johannes Werner in theoretical cartography. Werner's treatises, contained in Johannes Stabius' collection of writings on geography (1514), were "included almost unchanged in Apian's Introductio geographica (1533); Apian even used the proof sheets from the beginning of "In eundem primum librum.argumenta" to the end of "Joannis de Regiomonte epistola.de compositione et usu cuiusdam meteoroscopii," and admits in several places in his writings how much he had learned from Werner." (DSB, on Werner).
Of peculiar interest is the early description of the calculation of a sine table. Apian's "Introductio geographica (1533) contains both a sine table . . . and a description. The Instrumentum sinuum seu primi mobilis also contains a small table of arc sines, the earliest such table of which I am aware with clearly trigonometric intent." (G. van Brummelen, The Doctrine of Triangles: A History of Modern Trigonometry, Princeton University Press, 2021, p.12. "The first table of sines seems to have been printed in 1490, as part of Regiomontanus' Tabulae directionum profectionumque. It was only 30 pages long and gave the sines for every minute and to a radius of 60000. According to Folkerts, this table was probably computed before 1463-1464 [36, p. 234]. Most of the tables published during the 16th century are ultimately based on this table or on other tables constructed by Regiomontanus. Next came Peter Apian (1495-1552) who published his Introductio geographica in 1533." (D. Roegel, A reconstruction of the tables of Rheticus' Canon doctrinæ triangulorum (1551). [Research Report] 2010. inria-00543931, p.3).
Further references: VD 16, A 3090; Adams A 1294; Dodgson II, 385.3; Gunther 27 ff.; van Ortroy 101; Schottenloher, Apian 33; Zinner 1516; R. Gebhardt, Rechenmeister und Cossisten der frühen Neuzeit. TU Bergakademie Freiberg. Freiberg 1996, p.139).
II. FIRST AND ONLY EDITION of this little treatise on Apian's "horoscope", "an instrument not for astrological purposes, but for geodatic and chronometric purposes, which can be seen as an improvement of Peurbach's 'geometric square'" (Gunther). Among the woodcuts there are also some astronomical representations and illustrations for finger arithmetic.
References: VD 16, A 3085; Adams A 1290; Gunther 40; van Ortroy 100; Dodgson II, 386.2; Schottenloher, Apian 37; Zinner 1512; Houzeau-L. I, 2395.