PTOLEMAEUS, Claudius; WERNER, Johannes.

In hoc opere haec co[n]tinentur: Noua translatio primi libri Geographiæ Cl. Ptolomæi Geographia quæ quidem translatio verbum habet e verbo fideliter expressum Præceptio super plana terraru[m] orbis descriptione Libellus de quatuor terrarum orbis in plano figurationibus Epistola ad Bessarionem de compositione et usu cuiusd. meteoroscopii Libellus Ioannis Verneri Nurenbergen[si] de quatuor aliis planis terrarum orbis descriptionibus propositio ... De his quæ geographiæ debent adesse Georgii Amirucii oposculum In Georgii Amirucii Constantinopolitani opusculum: Ioannis Verneri Nurenbergen[si] appendices Ad Bessarionem Cardinalem Nicenum ac patriarcham Co[n]stantinopolitanum: de compositione Metheoroscopii.

Nuremberg: Jo. Stuchs, 1514.

First edition of Werner’s “most famous work on astronomy and geography” (MacTutor), an extremely rare and highly influential work on cartography and navigation, notable for several ‘firsts’: it contains the first published direct translation of any part of Ptolemy’s Geography from the original Greek; the first publication of the Werner map projection, which was widely used for world and continental maps through the sixteenth and seventeenth centuries, notably by Mercator, Oronce Finé and Ortelius; the invention of the lunar distance method of longitude determination, which was the principal method used by navigators until the second half of the 18^th century; and the invention, and first illustration, of the cross-staff, an instrument designed to make the necessary astronomical observations at sea. “Werner’s mathematical and astronomical work has been quite undeservedly neglected by historians” (North, p. 61). Werner was at the heart of a tight knit circle of mathematical practitioners in Nuremberg, Ingolstadt, Vienna and Tübingen who were largely responsible for establishing mathematics as a discipline in the central European universities. Werner’s edition of the first and part of the seventh book of Ptolemy’s Geography, the Nova translatio Primi Geographiae, was the first translation from the Greek since the original translation made by Jacobus Anglicus around 1406. Werner stated clearly that his rationale for the undertaking lay in the many errors contained in Anglicus’s edition and in the succeeding ones, which were all based on Anglicus’s rendering of the Greek text. Werner had access to the papers of Regiomontanus, which were part of the scientific library of his former mentor Bernhard Walther and had been inherited by Werner’s friend and neighbour Albrecht Dürer who purchased the library, along with Walther’s house, in 1509. These papers may have included Regiomontanus’s notes for his own translation of the Geography which he had planned but failed to complete before his death in 1476. Werner’s greatest personal input in this edition were his mathematical notes to the first book, where he criticized Ptolemy, often on the grounds that taking him literally would result in “deforming the earth’s shape”. Drawing inspiration from Ptolemy and from astronomical usage, Werner also made an original contribution to cartographical projections with his Libellus de quatuour terrarum orbis en plano figurationibus ab codem Ioanne Verneo novissime compertis et enarratis. Here Werner gave a theoretical discussion of two generalizations of Ptolemy’s second conic projection. His Propositio IV modifies Ptolemy’s methodology by requiring that lengths be preserved on all parallels, represented by concentric arcs, and on all radii. Werner further modified the projection in a way that makes the North Pole the centre of what in modern terms would be called a system of polar coordinates. In Propositio V he also requires that a quadrant of the equator have the same length as the radius between a pole and the equator. These modifications provided the first solution to the problem of representing the surface of a sphere within a finite area. OCLC locates only three copies in America (Folger, University of Illinois and John Carter Brown). No copies located in auction records since 1981 (and only 3 copies before).

“The collection dated 1514 contains Werner’s works on mathematical geography. In the commentary on the first book of Ptolemy’s Geography, Werner explains the basic concepts of spherical geography and then turns to the measurement of degrees on the sphere. When determining the declination of the sun, he refers to the tables compiled by Georg von Peuerbach and Domenico Maria. Werner’s method is interesting in that it determines simultaneously the longitude and the latitude of a place (ch. 3, annotation 8): For the first time it was possible for two sites the locations of which are being sought to be found by a combined series of observations. Since for the determination of latitude it is necessary merely to observe the upper and lower culmination of a circumpolar star, but not the position of the sun, quite a few sources of errors were removed. The fourth chapter deals with the determination of the difference in longitude of two places, which can be obtained by simultaneous observation of a lunar eclipse. Another method is based in the determination of the distance of a zodiac star from the moon as seen from two places (ch. 4, annotation 8). This method of calculating the distances to the moon requires only the determination of the angular distances, which can be carried out by means of the Jacob’s staff, and the precise knowledge of the true and mean motions of the moon. This method soon replaced the older ones and was then used as the principal method for determining longitude in nautical astronomy.

“The methods used by Werner enabled him to improve or to explain certain details of the ancient geographers, especially those of Marinus. Warner’s remarks in chapters 7–10 refer to Marinus’ determination of places, which he proves to be often incorrect, or to the sea voyages mentioned and explained by Marinus. Werner demonstrated a knowledge of the existence and direction of the trade winds and explained their origin. In addition, he tried to present a theoretical proof of approximate formulas for the determination of distances that were used in navigation.

“Warner’s contributions to cartography are based on his criticism of Marinus: they can be found at the end of the commentary on Ptolemy and in the ‘Libellus quatuor terrarum orbis …’ The remarks on chapter 24 of the Geography lead us to believe that Werner understood the two projections used by Ptolemy (simple conic projection and modified spherical projection) and developed them. The treatise on four other projections of the terrestrial globe, which is dedicated to Pirkheimer, contains more new ideas. In it Werner outlines the principles of stereographic projection and emphasizes that any point on the surface of the sphere can be chosen as the center of projection. In addition, Werner develops three cordiform map projections that resemble one another; the second gives an equal-area projection of the sphere. The idea of an equivalent projection occurred earlier in the works of Bernard Sylvanus, but Werner and Johannes Stabius were the first to work it out mathematically. Later, Oronce Fine, Peter Apian, and Gerardus Mercator adopted the cordiform projection. It is not known whether Werner designed a map of the world.

“Werner’s work in geography gained widespread recognition. Peter Apian, in particular, was a student of Werner’s in theoretical cartography. The treatises contained in the collection dated 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, under Werner).

The ‘lunar distance’ method of determining longitude, first published in the present work, exploits the fact that the moon moves relative to the fixed stars owing to its rotation about the earth. By measuring the angular distance of the moon from certain stars it is possible to determine the local time, and hence the longitude. In proposing this method, it seems that Werner may have been inspired by a letter of Amerigo Vespucci written in 1502 where he wrote: “I maintain that I learned [my longitude] … by the eclipses and conjunctions of the Moon with the planets”. When Werner suggested these ideas they were not really practical as sufficiently precise ephemerides were not available. To make the necessary measurements Werner designed and advocated the use of the cross-staff, an instrument which measured with precision angles in degrees of arc. Werner wrote:

‘Our aim is to find the distance in longitude between two distant places. The geographer will be in one of these places and will measure with a cross-staff the distance of the Moon from a star on the Ecliptic. If then we divide this distance by the velocity of the Moon per hour, we will know at what time in the future the Moon will be in conjunction with this body’ (translation from MacTutor).

The cross-staff is “an early navigation instrument for measuring the meridian altitude of the sun or a star to establish latitude at sea. Its precise origins are obscure but the principle is clearly the same as that of the Jacob’s staff (with which the cross-staff is often confused), a medieval instrument first referred to in 1342 in a treatise by the Catalan Jew Levi ben Gerson, and used principally by surveyors and for military purposes for distance measurement. The cross-staff measured with precision angles in degrees of arc and its use at sea seems to have been first proposed, somewhat earlier than contemporary technology warranted, by the astronomer Johannes Werner who had suggested the use of lunar distances to find longitude at sea … By the middle of that century the Portuguese in their southward exploration by sea of the Atlantic Ocean were using the instrument, which was eventually to displace both the seaman's quadrant and astrolabe. The cross-staff comprises a square-cut wooden staff about 76 centimetres (30 in) in length with, at right angles to the shaft, a cross-piece known as the transversal that could slide up and down the staff. The instrument was aimed at the body being observed, much as a crossbow might be aimed, with one end on the observer's cheekbone. The staff was graduated to give the observer the angle of elevation, that is, the altitude of the body” (Oxford Reference).

A decade later, Apianus was advocating the use of Werner’s cross-staff to measure lunar distances in his Cosmographicus liber (Landshut, 1524), and by the mid-sixteenth century Portuguese navigators were using it in their southward exploration by sea of the Atlantic Ocean. It was eventually to displace both the seaman’s quadrant and astrolabe.

The Werner map projection, the fourth of the new projections Werner describes in this book, draws lines of latitude as concentric circular arcs centred on the pole, with arc lengths equal to their lengths on the globe, and placed symmetrically and equally spaced across the vertical central meridian. The two representations at the sides of the antipodal meridian come together near the North Pole, and overall the map forms a heart shape (hence ‘cordiform’). The Werner projection reflects the fact that lines of latitude are shorter nearer the poles than those near the equator. To achieve this, it keepc the central meridian straight and preserves distances along it, while transforming other meridians into curves; this has the effect of distorting shapes, in particular those towards the sides of the map, but helps remind the viewer of the curvature of the earth’s surface. The Werner projection represents areas correctly but distorts angles and distances, although distances along each parallel and along the central meridian are correct, as are all distances from the north pole.

Werner also included in his work a treatise by the Greek scholar George Amiroutzes (1400-70), who was born in Trebizond and studied at Constantinople. His wide knowledge of science, medicine, philosophy and theology earned him the epithet the Philosopher. “After the fall of Trebizond in 1461, Mehmed II (1432-81), noting that the maps of Ptolemy divided the world into excessively small sections, commissioned Amiroutzes to produce one overall map on a single canvas – a task the scholar carried out, for all its proclaimed difficulties, to the best of his abilities. The final work gave indications of direction, scale, and distances, and it was accompanied by a ‘treatise,’ the content of which is not described and that does not seem to have come down to us in Greek. However, in 1514 Johannes Werner published in Nuremberg a Latin version of the Geography, including a commentary and a treatise by Amiroutzes under the title De his quae geographiae debent adesse, which may have been the text that accompanied the map drawn for Mehmed II. The content here is purely mathematical, and the essential problem considered is that of the variation in the degree of longitude, the resolution of which was considered indispensable for the resolution of two further issues, one scientific and the other practical: how to establish the relative distance between cities and between cities and the ends of the world and how to provide means for planning swift and efficient military operations. This is the only fifteenth-century treatise to deal with such questions, and the fact that this Latin translation was published by Werner in Nuremberg should lead us to wonder if its contents were known to Georg von Peuerbach and Johannes Regiomontanus” (Dalché, p. 337).

The present work concludes with an Appendix which reprints a letter from Regiomontanus (1436-76) to Cardinal Bessarion (1403-72), who had commissioned Peurbach and Regiomontanus to produce a new Latin translation of the Almagest, in which Regiomontanus describes his ‘meteoroscope’ (the first printed description of the device). “It was the technical bent of Regiomontanus’s genius that led to the development of the meteoroscope, an instrument that provided an easy way of establishing coordinates. His treatise ‘De compositione metheoroscopii’ has comedown to us in the form of a letter to Bessarion. In effect, this instrument was an armillary sphere with a movable horizon and meridian (so that the pole could be raised or lowered), within which moved the hour ring and the equator. A moving quarter circle ran from the horizon to the zenith of the meridian, all of the circles and rings were graduated in degrees, and two openings were made on opposite sides of the hour ring. This instrument made it possible to determine the latitude and longitude of one place with respect to another whose coordinates and distance in miles were known. We do not know if Regiomontanus actually constructed and used a meteoroscope; the important point is that its design is an adaptation of that for the astrolabe given in Ptolemy’s Almagest. Thus this meteoroscope was the concrete result of the philological method Regiomontanus followed, involving the comparison of classical texts in order to improve the design and manufacture of instruments” (Dalché, p. 341). A tract on the meteoroscope, which Regiomontanus wrote in 1462 or 1463, appeared on his Programme, a trade list of works he intended to publish, but he died before he could accomplish the printing.

“While still a student in Nuremberg, Werner (1468-1522) was drawn to the exact sciences and later said that he was intended for the study of mathematics from his early childhood. He enrolled at the University of Ingolstadt on 21 September 1484; and in 1490 he was appointed chaplain in Herzogenaurach. While studying in Rome (1493-1497) Werner was ordained a priest and met Italian scholars. By then his knowledge of mathematics, astronomy, and geography had increased; and he was allowed to inspect scientific manuscripts. He owned a Menelaus manuscript and was acquainted with unpublished works by Jabir ibn Aflah (Geber) and Theodosius. Werner probably acquired his excellent knowledge of Greek in Italy. After his return to Nuremberg he celebrated his first mass in the church of St. Sebald on 29 April 1498 … Since his pastoral duties were rather limited, he devoted much of his time to scientific study. His works brought him recognition from such Nuremberg scholars as Willibald Pirkheimer (1470-1530), Sebald Schreyer (1446-1520), and Cardinal Matthäus Lang (1468-1540). He was friendly with Bernhard Walther (ca. 1430-1504) and the choirmaster Lorenz Beheim (1457[?]– 1521) from Bamberg, as well as Albrecht Dürer, who occasionally asked his advice on mathematical problems. Werner enjoyed an excellent reputation even among scholars from Vienna: in 1514 the mathematician and imperial historiographer Johannes Stabius arranged the publication of a collection of writings on geography [offered here] that included works by Werner” (DSB). The work is dedicated to the Nuremberg merchant Schreyer and the wealthy lawyer and humanist Pirckheimer, who was to publish his own translation of Ptolemy’s Geography in 1525.

VD 16, P5208. Not in Adams or BL STC German. Dalché, The Reception of Ptolemy’s Geography (End of the Fourteenth to Beginning of the Sixteenth Century), in: The History of Cartography (Woodward, ed.), Vol. 3: Cartography in the European Renaissance, Part 1 (2007), pp. 285–364. North, ‘Werner, Apian, Blagrave and the Meteoroscope,’ British Journal for the History of Science 3 (1966-7), pp. 57-65.

Folio (311 x 208 mm), ff. [68] (some marginal water staining to the first 10 leaves, otherwise fine and clean. Later limp vellum.

Item #3080

Price: $75,000.00