Expanding and mapping the disc of the moon.

In February, 1645, the Dutch cartographer and engineer Michael van Langren (1598-1675) printed his Plenilunii lumina Austriaca Philippica, a single engraved lunar map of outstanding detail, and named the various craters Innocenti, Ferdinandi, Caroli, and other Habsburg titles. Like Galileo’s effort to name the Jovian moons after Cosimo de’ Medici, this simply did not last. By 1651, the monumental Almagestum Novum of the Jesuit astronomer Giambattista Riccioli (1598-1671) established our accepted nomenclature, grafted onto the map of his friend, student, and collaborator, Francesco Maria Grimaldi (1618-1663). In the process, most of the names Hevelius had given the craters and seas were quietly ignored. Mons sanctus became Firmicus, Mons Aetna became the crater Copernicus and the Lacus Hercules was replaced by Rheticus and Stadius. Rather loosely, it reads as a parallel to Riccioli’s chronological outline of astronomy: the ancient names of Zoroaster, Endymion and Atlas are in Octant III; Thales, Plato and Eudoxus inhabit Octant II; Hipparchus and Ptolemy are positioned near the center, and the names of Clavius and Tycho Brahe are given to prominent craters in Octant VI. Traces of van Langren remain: the small crater he named after Alessandro Piccolomini (1508-1579) still marks lunar maps today.

Due to libration, the disc has been expanded with craters and seas that cannot always be seen. Really, the names Riccioli gave to the dark plains of basalt are still beautiful, after the passage of centuries: seas of tranquility and nectar, turbulent oceans of storm. Ultimately, Riccioli’s adaptation of a modified Tychonian model for the solar system made his great book less important to the historiography of astronomy after Jean-Étienne Montucla, even though it contained the most detailed treatment of the controversies surrounding heliocentric cosmology written in the seventeenth century.

Hevelius and the selenographic volvelle.

Printed books from the period contained volvelles as well: the image above is from the Selenographia, sive Lunae Descriptio of Johannes Hevelius (1611-1687), which was printed in Gdansk in 1647. It is the first truly systematic description of lunar topography, which had been rendered observationally possible by recent technological refinements of the refracting telescope: indeed, the first five chapters consist of a sustained discussion of the instrument and its astronomical applications. He also used a modified camera obscura in his observations. Importantly, Hevelius discovered longitudinal libration, given that the Moon is in synchronous rotation with the Earth, but with an eccentricity of 0.0549; latitudinal libration is due to the Moon’s mean inclination to the ecliptic by 5.145° and obliquity of 6.68°. Latitudinal libration had been previously described by both Thomas Harriot (arguably on 14 December, 1611) and Galileo (accurately, in 1637). Although the rotating tool allows one to calculate the nodal axis, mapping the Moon in a dynamic system, where slightly more than a single static hemisphere can be glimpsed, would pose its own challenges.

To be sure, the resolution on the image could be much better, but you can easily see the scarlet thread used to wobble the Moon through the snowy paper course of its imagined orbit.

The early modern analog computer

The image above (BSB Cod. icon.182 fol.7r) is from a manuscript composed in Vienna between 1508-1520, and depicts the template for a simplified universal horizon astrolabe. I chose this particular image because the volvelle is intact, allowing the equinoctial ring to be turned to a given set of coordinates, rather like the more sophisticated equatoria published several decades later by Johannes Schöner and Petrus Apianus. The manuscript also contains a template for the so-called Saphea Arzachelis, which was introduced by Ibrahim ibn Yahya al-Zarqali (c.1029-87), which replaced the rete with a graduated alidade, but the paper rule in this manuscript has been ripped from its central pin, and has left nothing but an amber shadow behind. Although extremely simple, this still qualifies as an example of an analog computer, made entirely of paper, and pulled along by a single thread.

Ramus and his woodcut ruler.

So what were rulers good for, then? On leaf i3r of his Arithmaticae Libri duo (Basel, 1569), the French Huguenot logician and scholar Petrus Ramus (1515-1572) uses his gradient-marked regula aurea to show an entirely practical application of Theorem 18 from Euclid’s Optics: the figure in the woodcut measures the elevation of a composite Corinthian pillar from point o in a scenic ruin. But this should be obvious to us. That said, the geometric diagrams superimposed upon the landscapes of Ramus and Niccolo Tartaglia (c.1500-1557), personally echo Igor Stravinsky’s assessment of Beethoven’s Grosse Fuge (Op.133): “an absolutely contemporary piece of music that will be contemporary forever”. In these woodcuts, one thinks of Descartes and the sudden spring of modernity, as startling as birdsong at dawn.

Long after Ramus died in the St. Bartholomew’s Day Massacre (26 August 1572), his practical mathematics would influence the development of Willebrord Snell’s revolutionary development of modern triangulation networks.


On the shadow of Thales of Miletus

Folio 357v of the same manuscript illustrates a much later section in Augustine’s De Civitate Dei (XVIII.2) in which he discusses the origins of the Ionic and Italic schools of Greek Philosophy; Pythagoras of Samos and Thales were respectively credited with the origins of either tradition (cf. Diogenes Laertius, etc.). On Thales, Augustine wrote: …eminuit maximeque admirabilis extitit, quod astrologiae numeris conprehensis defectus solis et lunae etiam praedicere potuit. That is, Thales won the greatest esteem for his ability to use astronomical calculations to predict eclipses of the sun and moon. In the Histories of Herodotus (I.74) Thales is credited with predicting the total solar eclipse (subsequently dated to 28 May 585 BCE), that occurred during a battle between the Lydians and Medes on the banks of the river Halys; to be sure, classical historians dated the eclipse to either Olympiad 49 or 50. Pliny assigned the date of the discovery to Ol. 48.4 (585/4 BCE) in his Naturalis historia II 53, but dates the eclipse itself to year 170 after the foundation of Rome (584/3 BCE). Nevertheless, a copy of Oppolzer’s Canon can confirm the modern date.

We know that the Babylonians were already using a zigzag-function for saros cycle computations (a saros = 223 synodic months or approximately 6585.3213 days) that could have been employed for eclipse predictions, but we cannot quite derive the exact method Thales used to predict the eclipse from a handful of literary references. Presumably, it involved saros calculations. It almost certainly did not involve holding up a ruler to the sun.

In this illumination, Pythagoras teaches a cluster of students from a wooden rostrum placed on the green grass of summer, the morning sun rises over the Gothic spires of Greece, and Thales applies geometry to the source of light and life. Powdered gold in gum arabic and woad or crumbled lapis lazuli, verdigris or malachite, have formed a day on vellum which we can never quite enter, as the sun has run its course far too many times.

Speaking in ribbons: visualizing sound.

In conjunction with the last post, we might wish to remember the famous passage from the Confessions of Augustine (VI.3) on the habit of St. Ambrose, Bishop of Milan, to read in perfect silence: ..oculi ducebantur per paginas et cor intellectum rimabatur, vox autem lingua quiescebat. Of course, a substantial bibliography has emerged over the past several decades on ancient reading techniques, which suggests that Ambrose was far from unique in this ability.

The manuscript illumination above (Den Haag MMW 10A11 fol.13r) is from a French translation of Augustine’s Civitate Dei that was originally made c.1475-80 for Jacques d’Armagnac, duc de Nemours, presumably before his execution for treason in Paris on 4 August 1477. The image itself was composed by the workshop of Maitre Francois, and depicts St. Ambrose, as well as a slender ribbon of Textualis, partially sideways. Although I’m not certain on this, the subject might be derived from the passage in the Legenda Aurea in which Ambrose first arrives in Milan. The previous bishop had perished, and the congregation was divided between heretical adherents to Arianism and orthodox Trinitarians. While they were quarreling, a youth cried out Ambrosius episcopus, or Ambrose ought to be bishop!

The exact details notwithstanding, there is potentially interesting parallel between silent reading and pictorial speech.

Traces of learning and ownership III

Within the same book, on leaf a3v, we can see that text was not only colored with polychrome ink, but was annotated in Latin as well: think of this as a tree diagram depicting the phonetic classification of Greek letters and dipthongs, following a Hellenistic system that can be traced at least to the Poetics of Aristotle (cf.1456b20-38). Plosives were grouped under aphona were faintly commented in the green ellipse on the lower-left; a reader has written longe and breva under vowels marked macra and brachea, and has transcribed the Greek dipla over the doubled letters on the lower right with a Latin equivalent. As there are two distinct hands, we might conclude that at least two readers hovered over this page with a quill, engaged with the task of correlating visual affinities to auditory links. Really, the inventiveness of this visual solution to a novel problem (teaching the pronunciation of a language to readers who’ve never heard it spoken) is rather impressive; that said, variations of the arbor sapientiae diagrams used for didactic purposes were nothing new.

Soon, Erasmus and Johannes Reuchlin would engage in an involved debate on how ancient Greek was once pronounced; in the course of their dialogue, both would use the new technology of print as tools.

Traces of learning and ownership II.


Of course, not every contemporary reader of the second Aldine Greek grammar left it clawed with scrawled notes: this copy of the same text (Bayerische StaatsBibliothek sig.4 Inc.c.a 1451 h), was lavishly decorated by its owner, who used red ink for flourishes and rubrics, and sea-green pigment for a type of Renaissance highlighting. To be sure, these texts were always both scarce and valuable: an extremely well-known anecdote known from Antoine-Augustin Renouard’s Annales de l’imprimerie des Alde suggests that even Erasmus had a difficult time finding a copy in 1499. It seems that to this reader, the book was valuable enough to be embellished.


On traces of learning and ownership I

On 3 January 1499, Bruno and Basilius Amerbach wrote a collaborative letter to their father, the printer and scholar Johannes Amerbach (1440-1513), thanking him for sending a Greek grammar. They also tactfully requested the new edition of the Fundamentum Scholarium attributed to Remigius of Auxerre, as well as the Varia Carmina of Sebastian Brandt as a New Year’s present. Bruno was about fifteen years old, and attending school in the Alsace with his younger brother, separated by miles of winter from their home in Basel. Finally, they sent their greetings to the family, and Johann Froben, Amerbach’s junior partner at the press.

(Die Amerbachkorrespondenz I:89).

Folio 2av of Universitatsbibliothek Basel BC III 112a is above. It is a leaf from the Institutiones Graecae grammatices by Fra Urbano Bolzanio, which was printed in Venice by Aldo Manuzio in January 1497/8, and thus stands as the second Greek grammar he printed. The first was edited by the Byzantine scholar Constantine Lascaris (1434-1501) who had migrated to Italy after the fall of Constantinople. The importance of the second Aldine Greek grammar cannot be underestimated: this was the tool that would give contemporary readers access to his subsequent editions of Sophocles, Euripides and Aeschylus.

Either Bruno or Basilius annotated this leaf in both Latin and rudimentary Greek, surrounding the section on dipthongs, and Greek versions of common prayers, with marks of discovery and use.


 It’s striking to think that a recognizable image of this strange hybrid creature can be observed on a late Kassite boundary stone from the reign of the Babylonian King Marduk-apla-iddina I (c.1171-1159 BCE), was transmitted in the MUL.APIN cuneiform tablets, was chiseled into the Dendera Zodiac, and has survived in our imaginations for over three thousand years, in vellum, copper, paper, tempera and print. This is an image from the fifteenth-century manuscript version of Hyginus in the hand of Francesco Buzzacarini, with certain miniatures by Giovanni Vendramin (NYPL, Ms. Spencer 28 fol.53r). Of course, the depiction of Capricorn is impossible (from certain perspectives, the constellation appears inverted, but never reversed), but when paired with the 1482 Hyginus, it forms a type of mirror. Although a cursory examination revealed discernible textual variations between the two, I wonder if there was a common exemplar. But of course, these questions are easily answered.