Measuring the Heavens: Ten Books of Renaissance Science

How a sixteenth-century reader learned the cosmos, predicted the sky and put astronomy to work

Most of the books on our shelves describe the world. A smaller group explains how people came to know it. Over the past months these science books have quietly grown into a set that hangs together: a schoolbook of the cosmos in Latin and in Italian, the encyclopaedia and the course from which students learned the mathematical arts, the tables with which astronomers predicted the heavens, a cosmography with paper instruments, and the practical manuals that turned all this into telling the time and keeping accounts. This essay walks along that shelf.

The schoolbook of the spheres

Around 1230 Johannes de Sacrobosco, John of Holywood, wrote a short treatise for students in Paris on the sphere of the world: the earth at the centre, the circles of the heavens, the risings and settings of the stars, the climates of the inhabited world. It was not original, but it was clear, and that was enough to make De sphaera the standard introduction to astronomy in European universities for some four hundred years. When printing arrived the text went with it: a modern census of the printed Sphaera tradition counts 359 books between 1472 and 1650 that contain the text or are closely tied to it.

Two such books are on our shelves, and between them they show what the commentators did with Sacrobosco. The Alcalá edition of 1526 presents the text with the Latin commentary of Pedro Ciruelo, a Spaniard trained in Paris, and with the questions on the sphere by Pierre d'Ailly: the university Sacrobosco, surrounded by explanation and disputation. Mauro Fiorentino's Annotationi of 1550 does something different. Mauro, a Servite friar of the Santissima Annunziata in Florence who taught Latin, Greek and Hebrew, gives an Italian commentary and a new word-for-word translation for readers who had no Latin, and then goes beyond Sacrobosco altogether, adding a "theological sphere", a "Platonic sphere" and an instrument of his own for drawing up the twelve houses of a horoscope without tables or calculation. The book was dedicated to Duke Cosimo I de' Medici and printed by Lorenzo Torrentino, the ducal printer, who was a Netherlander: he was born Laurens van den Bleeck at Gemert in Brabant.

The whole curriculum

Sacrobosco was one part of a larger course. The medieval university taught the quadrivium, the four mathematical arts of arithmetic, geometry, music and astronomy, and two books in the collection show how a Renaissance student met the mathematical side of that course.

Gregor Reisch's Margarita philosophica, first printed at Freiburg in 1503 and here in the Strasbourg edition of 1512, packs the whole of learning into one illustrated volume, from grammar and logic through the mathematical arts to natural philosophy, and was used for decades as a textbook. Its woodcuts made abstract subjects visible: Arithmetic presiding over a contest between the counting board and written numbers, Geometry with her instruments, the spheres of the heavens.

Ciruelo's Cursus quattuor mathematicarum artium liberalium carries the mathematical arts into Spain, with one telling change: its four parts are arithmetic, geometry, perspective and music. Astronomy was taught from the Sphere. Ciruelo, who had studied at Salamanca and taught in Paris, brought that learning to the new university of Alcalá de Henares, where the Cursus was first printed by Arnao Guillén de Brocar in 1516 and reissued from the same press under Miguel de Eguía; our copy is a composite of those printings. It is one of the earliest Spanish mathematical textbooks for university use, and the Alcalá Sacrobosco of 1526, from the same press, is its natural companion.

Tables: predicting the sky

Knowing how the heavens were built was one thing; knowing where a planet would stand next Tuesday was another. For that, astronomers relied on tables.

The Alphonsine Tables were compiled at Toledo under King Alfonso X of Castile in the thirteenth century. Recast in Latin at Paris in the early fourteenth century, they became the basis of planetary calculation in Europe for some two and a half centuries, and they were first printed at Venice in 1483 by Erhard Ratdolt. Our copy is the Paris edition of 1553, from the press of Christian Wechel, ten years after Copernicus published De revolutionibus and two years after Erasmus Reinhold's Copernican Prutenic Tables. It is the last of the Renaissance editions, published just as the old tables began to meet competition from the new astronomy.

Tables required calculation. Ephemerides spared the user that labour by printing the results day by day. Regiomontanus published the first great printed ephemerides at Nuremberg in 1474, covering the years up to 1506. Johannes Stöffler and Jacob Pflaum continued them in their Almanach nova, first printed at Ulm in 1499 for the years 1499 to 1531. Our Venice edition of 1504, printed by Petrus Liechtenstein, is the portion for 1516 to 1531: page after page of planetary positions, aspects and eclipses, the raw material for every astronomer, physician and astrologer who needed to know the state of the sky without computing it.

Paper instruments

Between the tables and the user stood the instrument. Peter Apian's Cosmographicus liber first appeared at Landshut in 1524; the revision by Gemma Frisius was first published at Antwerp in 1529. Our copy is the Antwerp edition of 1533, with the first edition of Gemma's Libellus de locorum describendorum ratione, the earliest printed account of triangulation, the method by which surveyors would map whole countries. The book is famous for its volvelles: rotating paper discs, cut out and mounted on the page, with which the reader could find the sun's place in the zodiac, the age of the moon or the hour in another place by turning a wheel instead of working a calculation.

Seen from there, Mauro's instrument of 1550 is part of the same story. His promise on the title page, to construct the twelve celestial houses "subitamente", at once, "senza altri canoni, o, calculo", without further rules or calculation, is the promise of the volvelle: to put astronomy into the hands of someone who was not an astronomer.

Astronomy at work: time and money

The last group of books takes us out of the study altogether. In an age when clocks were few and had to be set by the sun, gnomonics, the science of sundials, was astronomy in daily use. Pedro Roiz's Libro de reloges solares, Valencia 1575, is one of the earliest books on sundials in Spanish, written by a pupil of Jerónimo Muñoz, the Valencian astronomer known for his observations of the new star of 1572. A century later the Traité d'horlogiographie of Dom Pierre de Sainte-Marie-Magdeleine, a Feuillant monk, here in the Paris edition of 1680, taught French craftsmen and gentlemen how to lay out dials on every kind of surface. One detail links it back to Florence: both Mauro in 1550 and Dom Pierre in 1680 show the human hand used as a sundial, the hour read from a shadow falling across the palm.

Mathematics, too, left the university. Juan Gutiérrez de Gualda's Arte breve, first printed at Toledo in 1539 and here in the Zaragoza edition of 1566, taught merchants the rules of arithmetic in both Roman and Arabic numerals, at the moment Spanish commerce was changing from one to the other. Booklets like it were used hard, and few copies survive.

A sphere under suspicion

The collection also shows that this knowledge was not neutral. Mauro's excursions into theology, on the Trinity, the Incarnation, the Eucharist and the immortality of the soul, probably explain why the censors took notice. His Annotationi was placed on the Spanish Index of Cardinal Quiroga in 1583 and on the Roman Indices of 1590 and 1593, before it was left out of the definitive Index of 1596. Our copy carries two early manuscript annotations in Italian, apparently in a hand of the later sixteenth century, commenting on Mauro's arguments about the elements and the faculty of imagination. Someone was reading the book closely, very probably in the decades in which the Church was deciding whether it could be read at all.

Why the shelf hangs together

Taken one by one, these are good books. Taken together, they document a single movement. Between the early sixteenth century and the late seventeenth, the knowledge of the heavens moved from the lecture hall, through tables and paper instruments, into the hands of astrologers and physicians, craftsmen and merchants, and from Latin into Italian, Spanish and French. The same years saw Copernicus publish his new system, yet the astronomy in these books is still that of a central earth, and that is precisely their interest: they show how astronomy was actually taught and used while the new cosmology was still contested. Several of them were printed away from the great centres of the book trade, at Alcalá, Valencia and Zaragoza, and the merchant's arithmetic in particular survives in very few copies, as practical books of this kind tend to.

For a library that already holds one of these texts, the others supply the context: the commentary next to the schoolbook, the tables next to the instrument, the practical manual next to the theory. That, rather than any single rarity, is why we have kept them together.

A note on sources

This is a dealer's essay, written to show how the books in our collection relate to each other, not a work of scholarship. Facts about individual copies come from our own descriptions; facts about the texts and their authors come from the works listed below.

Sources

The schoolbook of the spheres. Lynn Thorndike, The Sphere of Sacrobosco and its Commentators (Chicago, 1949); University of Wisconsin-Madison Special Collections, 'Sacrobosco and His Commentators' (exhibition), citing the Sphaera CorpusTracer of the Max Planck Institute for the History of Science; on Mauro: IdRef authority record 'Mauro de Florence (1493-1556)', Cambridge University Library, Whipple Collection, Sphera volgare (1537), Pietro Riccardi, Biblioteca matematica italiana, I.2, col. 138, and the Annotationi of 1550 itself (Boston Public Library copy, digitised on archive.org); on Torrentino: Dizionario Biografico degli Italiani, s.v. 'Torrentino, Lorenzo' (Treccani).

The whole curriculum. Diocesan library of Plasencia, catalogue record of Ciruelo's Cursus (Alcalá 1516); Columbia University Libraries, 'Our Tools of Learning: George Arthur Plimpton's Gifts to Columbia University' (exhibition), on Reisch; our own catalogue descriptions of FM-0072 and FM-0073.

Tables. Linda Hall Library, 'Scientist of the Day: Alfonso X'; Instituto de Matemáticas de la Universidad de Sevilla, 'The astronomical tables of King Alfonso X'; Gesamtkatalog der Wiegendrucke M44052 (Stoffler and Pflaum, Almanach nova, Ulm 1499); Glasgow Incunabula Project, entry on Stoffler.

Paper instruments. Dictionary of Scientific Biography, 'Gemma Frisius, Reiner' (MacTutor, University of St Andrews); Carleton College Library, on Apian's Cosmographia; Mauro, Annotationi (1550), title page.

Astronomy at work. Our own catalogue descriptions of FM-0096, FM-0210 and FM-0089.

A sphere under suspicion. Christoph Sander, 'Johannes de Sacrobosco und die Sphaera-Tradition in der katholischen Zensur der Frühen Neuzeit', NTM 26 (2018), pp. 437-474.