[Colophon:] Antwerp: G[regorius de] Bonte & Louvain: P[ierre] Phalèse, 1545.
First edition, very rare, of Gemma Frisius’s remarkable astronomical treatise, the most significant early text on the astronomer’s cross-staff, with an early favourable discussion of Copernicus’s De revolutionibus (1543), and the first printed illustration of the camera obscura – Tycho Brahe learned of the camera obscura from his copy of this book and used it in his observations. The cross-staff was an instrument permitting the measurement of the angular separation of two objects, of use in astronomy, navigation, perspective and surveying..
First edition, very rare, of Gemma Frisius’s remarkable astronomical treatise, the most significant early text on the astronomer’s cross-staff, with an early favourable discussion of Copernicus’s De revolutionibus (1543), and the first printed illustration of the camera obscura – Tycho Brahe learned of the camera obscura from his copy of this book and used it in his observations. The cross-staff was an instrument permitting the measurement of the angular separation of two objects, of use in astronomy, navigation, perspective and surveying. Gemma’s treatise contains a number of technical innovations, alongside detailed, finely illustrated descriptions of how to make and use the instrument. D. W. Waters (The Art of Navigation in England in Elizabethan and early Stuart Times, p. 135) notes that Gemma’s modification of the cross-staff directly influenced the northern navigations in the 16th century. Gemma Frisius (1508-1555) has been identified by Tredwell & Barker (p. 144) as one of the few Copernicans before 1600. “Focusing on the astronomical content of De radio astronomico, we encounter a strong emphasis on contemporary astronomical reform. Gemma’s demonstrations of the instrument’s use were frequently presented as either new astronomical advances, or confirmations of Copernican astronomy. A fine example is Gemma’s use of the cross-staff to verify the longitude and latitude of Mars, which he linked to a critique of the accuracy of Alfonsine planetary theory … [Gemma] advocated the systematic empirical verification of star positions in De radio astronomico … [His] method contributed to Gemma’s reputation among other admirers of Copernicus. In the preface to his Ephemerides novae for 1551, Rheticus claimed that his master Copernicus had urged him to observe the fixed stars. ‘And if the most learned Gemma Frisius,’ Rheticus continued, ‘holds the opinion that this is where action is needed, I think that he, like a new Copernicus for our age, casts the foundation of this science’” (Vanden Broeke, pp. 150 & 155-156). Gemma also describes in the present work the use of the pinhole camera, or camera obscura, in solar observation, and the book contains the first printed illustration of this instrument. “Tycho’s career in observational astronomy began with the acknowledgement that the best method for eclipse measurements is the use of a pinhole camera. Tycho learned about this technique from Reiner Gemma Frisius’s De radio astronomico et geometrico liber (Antwerp and Louvain, 1545), in which Gemma Frisius described his observation of a solar eclipse in 1544” (Wlodarczyk, p. 298). Tycho owned a copy of De radio, which he ‘borrowed’ from the Bavarian ducal library (Mosley, p. 173). Only the Horblit-Streeter copy (in a modern binding) has appeared in British/American auctions in the last 50 years (Sotheby’s, September 20, 1984, lot 642, £880; Christie’s New York, April 17, 2007, lot 225, $8,400).
In the preface to De radio, Gemma emphasized the relevance of the cross-staff to geography, optics, geometry, and astronomy. The first four chapters describe the construction of Gemma’s version of the instrument. The cross-staff, or Jacob staff, was invented by the Jewish astronomer Levi ben Gerson in the fourteenth century. It was used by Regiomontanus for astronomical observations and Ryff illustrated its use in measuring the heights of towers in 1447, but it was only adopted as an important instrument in surveying and navigation in the course of the sixteenth century. Its use continued throughout Europe until the mid-seventeenth century.
“In its basic form [the cross-staff] consists of two pieces of wood: one is called the Staff or the Radius, hand held such that one end is near the eye and the other end extends along the axis of vision; the other is called the Crosspiece or Transversary, attached at its midpoint perpendicularly to the Radius and allowed to slide along the radius. The observer then positions the instrument such that a star is visible at each end of the crosspiece; a simple geometric argument leads to the angular separation of the two stars … Levi ben Gerson’s original design, accepted by many of his successors, required that crosspieces of different lengths be used in observing stars of different angular separations, such that the crosspiece could be keep at about arm’s length. Indeed, the observation is subject to great error when the crosspiece is close to the eye. In effect, this error is due to the sensitivity of the cotangent function to small displacements on the Radius near the eye … One of Gemma’s innovations concerned the design of a single crosspiece that could be used for all separations, both great and small. The crosspiece is here fitted with several pinnules that can slide along it so that the effective length of the crosspiece can be varied without replacing one crosspiece by another. In the simplest case a pinnule is fitted at each end of the crosspiece such that one star is seen on the inner edge of one pinnule and the other star is seen on the inner edge of the other pinnule. In Gemma’s design the crosspiece is graduated so that one can determine the distance between the two inner edges of the pinnules, and the Radius is also graduated” (Goldstein (1987), pp. 168-169). When John Dee returned from his studies with Gemma at Louvain in 1547, one of the instruments he brought back was a cross-staff, subsequently donated to Trinity College Cambridge (though long since lost). Very few early examples survive, though the British Museum has a version in brass by Gemma’s nephew Gualterus Arsenius.
Chapters 5-15 describe and illustrate with numerous woodcuts the use of the cross-staff in surveying and perspective. “The key figure responsible for bringing to light the full potential of this instrument as a perspective aid is Gemma Frisius … Of particular interest for us is his Radii astronomici et geometrici structura, first published in 1545 …
Gemma Frisius’s treatise had an enormous impact. One intimation of this is found in G. P. Gallucci’s Fabrica et uso di diversi stromenti di astronomia et cosmografia (1598). Here Gemma Frisius’s comments concerning the staff as perspective aid in topographical drawing are repeated almost verbatim and without direct acknowledgement” (Veltman, pp. 344-345).
But perhaps the most interesting part of De radio is chapters 16-23, in which Gemma gives examples of astronomical observations made using the cross-staff, and the conclusions he draws from them. Gemma reported in De radio the following observations made at Louvain: Comet, 1532 and July 1533; Conjunction of the Moon and the star Spica, 12 June 1540; Solar eclipse, 24 January 1544 and 9 June 1545; Lunar diameter, 15 December 1542 and 27 October 1544; Solar diameter, 27 October 1544; Solar altitude, 24 January 1544 and 24 October 1544; Position of Mars, 31 October 1544.
In 1531, 1532 and 1533, three conspicuous comets appeared; Gemma includes his observations of the last two in De radio. Peter Apian of Ingolstadt found that all three cometary tails pointed directly away from the Sun. “Several scholars in subsequent years accepted and elaborated Apian’s theory of antisolarity. The Louvain professor Gemma Frisius supported Apian’s findings concerning the comet of 1533 with his own observations. He also explicitly made the connection between the sixteenth-century discovery of antisolarity and the theory of the Presocratics Hippocrates of Chios and Aeschylus, that the tail of a comet is nothing but reflected rays of the Sun. Unlike the ancients, however, Gemma thought the cometary tails to be due, not to reflection, but to refraction … Gemma later recorded his own observations of the comet in his De radio astronomico, where he endorsed Apian’s discovery of the antisolarity of cometary tails and expounded his theory that the comet’s tail was an effect of refraction. Although Gemma, like almost every physician of his age, was well versed in astrology, his treatment of the comet of 1533, as put down in his De radio astronomico, was in no way astrological” (van Nouhuys, pp. 116 & 149-150). As explained slightly later by Jean Pena, Gemma’s view was that the nucleus of the comet (to use the modern term) was like a glass lens which focused the Sun’s rays, the resulting beam of light constituting the comet’s tail.
Gemma viewed the solar eclipse of 1544 using a hole in one wall of a pavilion to project the Sun’s image onto the opposite wall, on which it appears inverted and reversed. This is depicted in the famous and much-reproduced woodcut on fol. 31v, the first illustration of a camera obscura (and so of any kind of camera) in print. “[Gemma] refers to Erasmus Reinhold’s commentary on Peurbach’s Theoricae novae planetarum for the idea of observing a solar eclipse with a camera obscura. Tycho Brahe mentions this passage from Gemma Frisius’s book and he also built a Jacob staff according to Gemma Frisius’s instructions” (Goldstein (2012), p. 143). The term ‘camera obscura’ was actually coined by Kepler, who had been introduced to the device by his teacher Maestlin, and who used one of his own design to view a solar eclipse on the market place in Graz on 30 June 1601. (Infamously, while Kepler was busy making these observations a thief stole his purse containing thirty silver florins.) Kepler realised that, in order to put astronomical observations on a firmer footing, it was necessary to understand the way the camera obscura works. He presented his theory of pinhole images in his Ad vitellionum paralipomena (1604).
Many references to Copernicus are found in chapter 16 of De radio. In §5 and §6, Gemma describes a problem with Ptolemy’s lunar theory he has been able to demonstrate using the cross-staff. In §5, “we learn that Ptolemy’s theory leads us to expect that the diameter of the Moon at half-Moon phase be twice that at full-Moon phase (or, equivalently, that the areas are in the ratio of four to one), contrary to experience. In this regard he cites a passage from Regiomontanus’s Epitome, V.22: ‘But it is surprising that the Moon does not appear so great at quadrature, when it is at the perigee of its epicycle, whereas if the entire disk were visible, it should appear four times its apparent size at opposition, when it is in the apogee of the epicycle.’ [In §6,] Gemma cites his observation of the lunar diameter on 15 December 1542 to demonstrate that he was aware of this difficulty in Ptolemy’s lunar theory before the publication of Copernicus’s De revolutionibus in 1543, leading us to believe it was an independent discovery. However, the citation from Regiomontanus … strongly suggests such dependence, albeit indirect” (ibid., pp. 176-177).
In §8, “Gemma describes an experiment with the use of the Radius to prove that the lunar diameter at full-Moon does not vary with its altitude. The phenomenon in question is known as the ‘Moon Illusion’, i.e., that the full Moon at the horizon appears to the naked eye to be much larger than when it is high in the sky, but that when it is measured no difference is discerned. In the Almagest, Ptolemy suggests that the Sun may appear larger on the horizon than when it is high in the sky because of the magnifying effect of the atmosphere and its moisture; this view was invoked to explain the Moon Illusion until well into the seventeenth century, despite alternative explanations as early as Ptolemy’s Optics later taken up by Ibn al-Haytham and others” (ibid., p. 178). Gemma’s failure to detect any change on the lunar diameter with altitude provided him with his first argument against the existence of atmospheric refraction. (The Moon Illusion is now viewed as a psychological phenomenon rather than a physical one.)
“The final remark in the chapter, that the distance between stars is unaffected by their altitude, implies that atmospheric refraction does not exist. Ptolemy had already described atmospheric refraction in his Optics: this phenomenon was widely known in the Middle Ages and the Renaissance despite the absence of attempts to measure its effect. Gemma’s remark was cited by Jean Pena [Euclidis Optica et Catoptrica, 1557] to prove that air reaches from our eyes to the fixed stars without any change in density, and hence the Aristotelian distinction between the sublunary and the superlunary domains had to be abandoned. Tycho Brahe was most displeased to learn that Pena had preceded him in arriving at the view that there are no Aristotelian solid spheres in the heavens. For, whereas Brahe had reached this conclusion based on careful observations of the new star of 1572 and the comet of 1577, Pena had relied upon a false argument, namely the absence of atmospheric refraction. [Tycho’s later, more accurate, observations showed that the distance between neighbouring stars in the sky did, in fact, vary slightly with their altitude.] The dissolution of the Aristotelian spheres was clearly an important event in the scientific revolution and, in a curious way, Gemma Frisius may have played a role in it” (ibid.).
Further references to Copernicus can be found elsewhere in De radio. Gemma “had read and painstakingly annotated the chapters of De revolutionibus dealing with trigonometry [see Gingerich, Census, pp. 146-150] and referred to Copernicus, together with Euclid and Regiomontanus, for the explanation of the geometrical and trigonometrical properties of his radius [ff. 35v-36r] … [Frisius] pointed out the importance of Copernicus’s solar and lunar theory for the exact determination of eclipses, observing, in chapter 17, ‘On the magnitude of eclipses’, that this was the only astronomical issue that really fascinates ignorant people [ff. 29v-30r] … In chapter 19, Frisius explained how to ascertain the positions of planets and comets using his astronomical staff. There he assessed that Copernicus’s emendation of the Martian theory allowed the inaccuracies of the Alfonsine Tables to be overcome [ff. 34r-v]. In chapter 22, ‘Longitudes determined through the position of the Moon’, Frisius determined the longitude of Leuven with respect to Cracow, which is the meridian to which Copernicus referred. This choice documents, once again, his profound respect for the work of the Polish astronomer. All of these implicit and explicit references show that Frisius had read De revolutionibus accurately and extensively. Still, he did not openly declare his position on terrestrial motion in De radio … he focused on those aspects of De revolutionibus that were immediately relevant to this topic: observation, the computational reliability of astronomical tables, the computation of ephemerides, and the accuracy of heavenly parameters” (Omodeo, pp. 125-127).
“Gemma may have heard about Copernicus’ theories even before their publication. He was briefly a client of Johann Flaschbinder (known from the place of his birth by the Latin name ‘Dantiscus’) who later became Bishop of Ermland and Copernicus’ superior. However, Gemma received a copy of the First Account [i.e., Rheticus’s Narratio prima], probably in 1540, and later made extensive annotations in a copy of On the Revolutions [see Gingerich, Census, pp. 146-150]. In addition to praising Copernicus in letters written to Dantiscus in the early 1540s, Gemma endorsed physical Copernicanism in a 1555 letter published as a preface to an astronomical work by Ioannes Stadius [Ephemerides novae, 1556]. He notes the increased accuracy of Copernican calculations, for example in determining the time of the equinox. Gemma then argues that Copernicus can explain things that Ptolemy can only assume, for example that the superior planets are always at the perigee of their epicycles (and hence in the middle of a retrogression) when they are diametrically opposite to the Sun in the sky. Gemma describes Copernicus’ result as a demonstration of the true causes of the phenomenon … Gemma not only asserts the physical reality of Copernicus’ cosmic scheme but claims that it provides scientific explanations of previously unexplained facts according to the highest standards accepted at the time” (Tredwell & Barker, p. 146).
After Gemma’s text, De radio astronomico concludes with a table for laying out sundials by Georg Peurbach (1423-1461), Tabula gnomonica, published here for the first time. Peurbach is well known for his Theoricae novae planetarum, which went through some 14 editions between 1460 and 1581, and for the Epitome of the Almagest, which he started to write but which was completed by his student Regiomontanus after his death. But Peurbach also wrote about and constructed sundials, including a hinged, portable sundial with a compass whose dial for the first time showed the distance between magnetic and true north (five examples of this sundial survive).
A second edition of De radio astronomico was published by Cavellat at Paris in 1557 (and was reissued the following year).
Gemma Frisius was born in Dokkum in Friesland (now in the Netherlands) in 1508. From humble origins, Gemma studied medicine in the Collegium Trilingue at Louvain (modern Belgium) from 1525, achieving an M.D. in 1536. Although Gemma is most remembered for his contributions to instrument making and cosmography, his formal training and occupation in medicine shows that most mathematical cosmography was then practiced outside universities. At 21 and while still a student, Gemma published his corrected edition of Apian’s Cosmographia (to be followed by several subsequent enlarged editions), and in the following year Deprincipiis astronomiae et cosmographiae. The latter included ‘De novo modo inveniendi longitudinem’, the first description of how an accurate clock could be used to determine longitude. In the ‘Libellus de locorum describendorum ratione’, annexed to the 1533 edition of the Cosmographia, Gemma first described the principle of triangulation for use in surveying. During these years and after, Gemma produced a great number of mathematical instruments, maps and globes. His new designs included the astronomical rings described in Cosmographia and the new kind of cross-staff described in the present work. During and after his schooling, Gemma ran an instrument-making workshop that achieved great renown. As late as the end of the century, Tycho commented on the quality and accuracy of Gemma’s instruments. Among his students were Gerard Mercator, John Dee, his nephew Arsenius and possibly the early English instrument maker Gemini. Like Apian, Gemma was patronized by the Emperor Charles V. Gemma Frisius died in 1555 at the age of 47 in Louvain.
Adams G390; Horblit 454 (“Description of an improved cross-staff; the woodcuts show its construction and use … Tycho Brahe states in his Astronomiae instauratae mechanica (1602) that his observations relied on the instrument beginning in 1564”); Houzeau & Lancaster I, 2428; STC 83; Van Ortroy 123; Zinner, Astronomische Instrumente, 321. Goldstein, ‘Remarks on Gemma Frisius’s De Radio astronomico et geometrico,’ pp. 167-180 in: From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe, Berggren & Goldstein (eds.), 1987. Goldstein, The Astronomy of Levi ben Gerson (1288-1344), 2012. Mosley, Bearing the Heavens: Tycho Brahe and the Astronomical Community of the Late Sixteenth Century, 2007. Omodeo, Copernicus in the Cultural Debates of the Renaissance, 2014. Tredwell & Barker, ‘Copernicus’ first friends: physical Copernicanism from 1543 to 1610,’ Filosofski Vestnik 25 (2004), pp. 143-166. Vanden Broeke, The Limits of Influence: Pico, Louvain, and the Crisis of Renaissance Astrology, 2003. Van Nouhuys, The Age of Two-Faced Janus: The Comets of 1577 and 1618 and the Decline of the Aristotelian World View in the Netherlands, 1998. Veltman, Military Surveying and Topography: The Practical Dimension of Renaissance Linear Perspective, 1979. Wlodarczyk, ‘Solar eclipse observations in the time of Copernicus,’ pp. 297-298 in: The History of Science and the Cultural Integration of Europe. Proceedings of the 2nd ICESHS (Cracow, Poland, September 6-9, 2006), M. Kokowski (ed.). The most detailed account of Gemma’s life can be found in De Vocht, History of the Foundation and the Rise of the Collegium Trilingue Lovaniense 1517-1550, vol. 2, 1953 (pp. 542-565).
Small 4to (200 x 140mm), ff. , 4-59,  (Tabula gnomonica Georgij Peurbachij, ff. 59v-r), woodcut arms of the dedicatee, Pedro Fernandez de Cordoba, Count de Feria (1518-52) on title, numerous woodcut diagrams in text, woodcut initials, final leaf with errata and colophon on recto and printer’s device on verso with motto: ‘Graviora legis misericordia, fidesm iudicium. Mat, XXIII’ (occasional light browning, worming to upper inner gutter and to lower outer margin, neither affecting text, two pin-sized wormholes affecting about 10 leaves of text, hardly noticeable and not affecting legibility, woodcut on fol. 31v slightly cropped at fore-edge, affecting extreme western side of the Sun’s disc, old ink underlining to approximately 6 pages). Contemporary vellum with manuscript lettering to spine, early manuscript material used in the binding (cover with old soiling, some chipping along margin). A genuine copy in original condition.