Textmanuscripts - Les Enluminures
161 folios on paper, two water marks, on f. 2 the bottom of a heraldic design with the name COTODI underneath, the remaining folios contain an anchor in a circle topped by a six pointed star (similar to Piccard, DE5580-Codgraec271_116/117), foliation in modern pencil in top right recto, two previous foliations incomplete through folio 7, complete, collation, (i8-1 [-8, cancelled], ii8, iii14+1 [+7, added singleton], iv14+1 [+15, added singleton], v12, vi10-1 [-6, cancelled], vii12, viii8, ix14, x-xi16, xii14-1 [-13, cancelled], xiii16), quire marks added in modern hand in bottom left recto of first folio in quire, starting with "C" at f. 16, catchwords at bottom right on ff. 87-121, text of ff. 85v-121v written in small Italian humanist cursive, single column, unruled, 22-99 lines per page, justification 115 x 65 mm, text in illustrations (ff. 5-62) written in a squat German cursive belonging to Johann Halter, and an Italian cursive with tall ascenders, twenty-eight geometric diagrams constructed with compass and straight-edge (found in ff. 87-121), five rough pencil sketches of architecture and armaments (ff. 157v, 158v, 159v, 160v, 161v), geographical sketch in pencil (f. 37), two astronomical tables (ff. 15 and 16), eleven cosmological and astronomical diagrams painted with gouache and gold (ff. 8, 9, 10, 11, 13, 14, 23, 26, 27 [in outline], 30, 85v [in ink]), seven illustrations of quadrants and other surveying tools in gouache and gold (ff. 17, 18, 19, 20, 21 [in outline], 22 [pencil sketch], 28), eight full page landscapes in watercolor (ff. 29, 36, 48, 51, 56, 60, 61, 62), five full-page paintings in gouache and gold of the seven wonders of the ancient world (ff. 31-35), twenty full-page paintings of landscapes, buildings, and towns in Switzerland and Italy in gouache and gold (found in ff. 31-59), three-full page paintings in gouache and gold depicting the Virgin and Child, a crest with a cherub head, and the family crest of Johann Rudolf Halter, all surrounded with floral motifs and mathematical instruments (ff. 5, 6, 7), minor smudging throughout, gouache and gold slightly worn from illustrations, ink has corroded the through the page at f. 28 and started to corrode at ff. 97-121, paper chipped at ff. 18, 38, 42, 43, 52, 58 due to the aging of the paint, otherwise good condition. Contemporary vellum wrap binding over cardboard, some chipping on front cover and spine, somewhat loose from the gatherings, slightly scuffed and stained, "Mathematica" written on the spine in a later hand, otherwise good condition. Dimensions 192 x 132 mm.
Showcasing the intersection of the visual arts, mathematics, and military strategy, this manuscript contains over thirty full-page illustrations in gouache, watercolor, and gold of landscapes, measuring tools, and architecture. Its artist, the mathematician, Johann Rudolf Halter, may have been a recent graduate of the University of Basel who traveled through Italy in search of leisure and education. Many of his paintings of landscapes include sightlines for the accurate measurement of distances. Of special note is the inclusion of the extremely rare text of Galileo's Operations of the Geometric and Military Compass, attesting to an interest in state-of-the-art equipment for both surveying and ballistics.
1. Produced by Johann Rudolf Halter of Basel, a mathematician and land surveyor, between 1625 and 1628. Halter gives his name and credentials on f. 6: "D.O.M. Kunst Bauch. Iohann Ruodolph Halter von Bassell dorin allerley Geometerise auch Astonomise Vie auch Aritmetig begriffen Kreißsachen exercicium mi allerlei Instermenten zu Gebrachen Augenscheinlich auf gerisen datum den 20 feb 1628. Ceua" (To God best and greatest. An Art Book. Johann Rudolph Halter of Basel educated in all kinds of Geometry and Astronomy as well as Arithmetic, trained in property appraisal with several instruments, manifestly expert in their use. Given on 20 February 1628). The "Ceua" mention on f. 6 is probably modern Ceva in Piedmont. On f. 5 Halter signs the illustration in Rome in 1627, so he may have been returning northward to his native Basel. Besides being a successful mathematician, he was also an artist who painted over thirty full-page images of astronomical equipment and landscapes in this manuscript. Very little is known about Halter, but he may possibly be identified with a Hans Rudolf Halter, who matriculated from the University of Basel in May 1624 (Wackernagel, 1962, p. 265, no. 50).
2. The treatise of Galileo on the Geometric and Military Compass is written in an Italian humanist hand, perhaps contemporaneous, perhaps slightly later than Halter. There are also watercolor paintings, which could be contemporary with Halter or later, with captions in an Italian humanist cursive.
3. A note in pencil on the back pastedown reads "Acquistato 8/VII/37." Probably purchased by an Italian bookseller 8 July 1937. The same owner perhaps added collation marks in pencil to the manuscript.
ff. 1-85, [blank], some rectos bear illustrations (See ILLUSTRATION below);
ff. 86, Instrumentorum Mechanicorum liber. Demonstratio noui Geometrici Instrumenti, incipit, "Ad metiendum altitudinis latus…3. Distantia stationis";
This table of operations in Latin seems to refer to Galileo's treatise Il Compasso that follows. The table does not appear in the plagiarized Latin version of Baldessar Capra (1607), or the authorized Latin translation of Galileo's work published by Mathias Bernegger in 1613 and 1635. It may be original to the scribe who wrote the text that follows.
ff. 87-121v, L'Operacion del Compasso Geometrico et Militare di Galileo Galilei Nobil Fiorentino Lettor delle Matematiche nello Studio di Padoua, incipit, "Al Serenissimo D. Cosmo Medici Prinicipe di Toscana. Se io volessi…quanta a punto è la distanza cercata da principis E.D.C. etc";
The text of Galileo's Operations of the Geometric and Military Compass in this manuscript is a direct copy of the first edition of the text published in 1606 at Galileo's home in Padua. Galileo only printed 50 copies of the text, which were to be sold along with the instrument they explained. Only six copies of the 1606 edition survive today (USTC, 4033777). The text in this manuscript reproduces the text of the 1606 edition faithfully but ends a page short of the printed text at p. 422.26 in the Edizione Nazionale (1891). If this copy is nearly contemporaneous with the paintings made by Halter, it is an important witness to the transmission of the Operazioni, since the next known edition dates to 1640.
Galileo began experimenting with the idea of producing a rudimentary computer capable of solving arithmetic and geometric problems quickly and efficiently 1597. By 1599 he had developed a working version of his compass (better known in English as a sector) "a general-purpose mechanical calculator capable of solving any practical mathematical problem that was likely to arise" (Drake, 1978, p. 9). The usefulness of the tool quickly spawned imitators and plagiarists, who claimed the instrument as their own invention. In 1607 Baldessar Capra published a faulty Latin paraphrase of Galileo's Operazioni with an illustration of the compass. Hoping to retain a monopoly on his invention, Galileo brought Capra to court and roundly demonstrated the fraudster's ignorance and ineptitude. Nevertheless, a steady stream of translations and adaptations of the Operazioni appeared in the seventeenth century (see Drake, 1978, pp. 25-35). The copy of Galileo's text in this manuscript with its meticulous reproduction of the diagrams represents the unsanctioned dissemination of a text closely guarded by its author.
Operations of the Geometric and Military Compass provided instructions for calculations essential to arithmetic, currency exchange, geometry, land surveying, ballistics, and more. More importantly, however, it allowed engineers, cartographers, and artillerymen without formal training in mathematics to perform complex calculations such as root derivation mechanically.
ff. 122-161, [blank] few versos bear illustrations (See ILLUSTRATION below).
ff. 5, 6, 7, three full-page illustrations advertising the learning and piety of Johann Rudolf Halter.
On f. 5 Halter has painted in gouache the Virgin and Christ Child in majesty surrounded by a wreath and vines bearing fruit and flowers, while at the intercardinal points of the wreath are surveying instruments like an alidade and a globe. Two winding ribbons in blue and orange descend from the wreath and a cannon and mill are painted within the folds. "S.D.G." (soli Deo gloria, "glory to God alone") is written in prominent majuscules. Dated 11 May 1627 at Rome.
On f. 6 Halter painted a coat of arms in red and gold surmounted by a cherub's head and wings in blue, red, and green. Bunches of fruits and flowers hang down from the left and right supporters. Above the shield is a set of surveying tools and globe, and above those a ribbon painted in gold with text that has faded. At the center of the shield "D.O.M" (Deo Optimo Maximo, "To God Best and Greatest") appears prominently at the top. Below Johann Halter calls this manuscript his "Kunst Bauch" (Craft Book) and notes that he is proficient in Geometry, Astronomy, and Arithmetic, as well as the use of the tools associated with each of the disciplines. Dated 20 February 1628.
On f. 7 Halter painted his own coat of arms, containing three mountains in gold over red, a tree in brown, and an arrow and two stars in brown ink over green. Red and green foliage surround the coat of arms and a helmet of blue and gold is the crest. A figure surmounts the coat of arms wearing red, green, and gold robes, holding a globe in its right hand and a star in its left. The coat of arms is set in an oval filled with vegetation and fruit in green, blue, red, and gold, as well as astronomical and mathematical instruments. A ribbon over the coat of arms reads "Scio saluatorem meum venire et me. / Suo tempore certo certius exaudi tuum. / Iohan. Ruodolph Halter" (I know I and my savior come. / At the fixed time hear your [servant] more certainly.);
ff. 8, 9, 10, 11, 13, 14, 23, 26, 27, 30, Cosmological diagrams:
This set of illustrations depict the earth and its place in the cosmos. On f. 8 Halter paints a globe on a table with the longitudinal and latitudinal marks along with a note commenting on the size of the earth's circumference. (252,000 stadia, the traditional measure given by Eratosthenes and other ancient commentators.) f. 23 contains a diagram of the earth moon and sun in green, blue, and brown gouache and gold, demonstrating the phases of the moon and the date 1 March 1628. Other diagrams contain astronomical data on the position of planets within the zodiac and the spheres of the universe containing earth at the center (f. 13);
ff. 17, 18, 19, 20, 21, 22, 28, 85v, Depictions of Astronomical and Surveying Instruments:
This set of illustrations present astronomers' and surveyors' tools in great detail. On f. 17 a quadrant is painted in green, red, and blue gouache and gold. Within the instrument are vegetal patterns and fruit, a coat of arms, and a rural scene. A sector with plumb bob is painted in gold on f. 19 with a rural scene in green and red gouache at the center, dated 16 June 1627;
ff. 31, 32, 33, 34, 35, Sequence of the Seven Wonders of the World:
Halter paints the Great Pyramid of Giza (f. 31), the Colosseum (f. 32), the Hanging Gardens of Babylon and the Tower of Babel (f. 33), an obelisk from Babylon (f. 34), and the Colossus of Rhodes (f. 35). The foregrounded wonders are painted in green, red, brown, and purple gouache and gold, while the landscapes in the background are painted in soft blues and greens in watercolor. In the painting of the pyramid on f. 31 two alidades are depicted which provide sight lines pointing to the top of the pyramid. The Colossus of Rhodes is dated 26 April 1627;
ff. 29, 36, 48, 51, 56, 60, 61, 62, A series of watercolor paintings:
These paintings primarily depict rural landscapes, except for a painting of a nude female figure on f. 29, a peacock on f. 48, and a lionlike figure on f. 60. All of these watercolors have been painted by the same artist and bear some similarity to Halter's treatment of landscapes in the background of his gouache paintings. These paintings use green, blue, ochre, red, and brown watercolors and bold black strokes for the outlines. On f. 56, a heading in Italian states that the painting demonstrates the method of pulling a canon through mountains;
ff. 31, 38-47, 49-50, 52-55, 57-59, A series of gouache paintings of the Italian countryside and Rome:
Halter filled his Kunst Bauch primarily with gouache paintings (with some watercolor backgrounds) done in green, red, pink, purple, brown, and orange with gold highlights. Many of the paintings contain sight lines related to surveying and some include unit measures and marked points (A, B, C, etc.). On f. 57, Halter writes that the sight lines and points in the diagram are used to measure a castle in the painting. There are some named places in the paintings, such as Saint Onofrio at Rome, dated to 24 April 1627. Another painting (f. 44) is placed in Aquino. The earliest date given in the paintings is 23 February 1625 (f. 50).
ff. 87-121, 28 Geometric diagrams:
These diagrams are found within Galileo's treatise on Operations of the Geometric and Military Compass. They are draw in ink and constructed with straight edge and compass. The diagrams faithfully reproduce the sequence of diagrams found in Galileo's 1606 edition of the text.
ff. 157v, 158v, 159v, 160v, 161v, Rough sketches of architecture and armature:
A series of rough pencil sketches of architecture and armature appear upside down on the versos of the final folios. This suggests that Halter or another artist reoriented the book and started using this manuscript in reverse for simple sketches.
The illustrations and texts in this manuscript highlight the special intersection of art and mathematics required in engineering, and in land surveying and ballistics specifically, a combination of skills still actively employed by engineers and surveyors into the twentieth century. While the use of illustrations and diagrams was common in seventeenth-century printed texts which advertised novel instruments for measurement, the evidence of hand-painted renderings by a traveling mathematician is much rarer (see Vollrath, 2014). Halter seems to have studied mathematics for its practical applications, both military and geometric. His Kunst Bauch provides a glimpse into both the mathematical and artistic perception of space in the early seventeenth century.
Drake, Stillman. "An Unrecorded Manuscript Copy of Galileo's Use of the Compass," Physis 2 (1960), pp. 281-90.
Galileo Galilei. "Il Compasso Geometrico e Militare," in Edizione Nazionale delle Opere di Galileo Galilei, vol. 2, Florence, 1891, pp. 335-424.
--. Operations of the Geometric and Military Compass, 1606, trans. Stillman Drake, Washington D.C., 1978.
Lindgren, Uta. "Land Surveys, Instruments, and Practitioners in the Renaissance," in The History of Cartography, Volume 3: Cartography in the European Renaissance, Part 1, ed. David Woodward, Chicago, 2007, pp. 477-508.
Vollrath, Hans-Joachim. "The Didactic Function of Illustrations in Historical Surveying Books," trans. Allison Moseley, in Mapping Spaces: Networks of Knowledge in 17th Century Landscape Painting, ed. Ulrike Gehring and Peter Weibel, Munich, 2014, pp. 355-65.
Wackernagel, Hans Georg. Die Matrikel der Universität Basel. III. Band 1601/02-1665/66, Basel, 1962.
"Galileo's Compass - History of an Invention," Museo Galileo, 2008, https://brunelleschi.imss.fi.it/esplora/compasso/dswmedia/storia/estoria1_st.html
TM 1395
