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- Collection: 11. Transmitting Knowledge; The Quadrivium: Arithmetic, Geometry, Astronomy, and Music
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This stout volume is a transcription of two of the astronomer Regiomontanus’s later works, based upon their incunable editions. This manuscript contains Regiomontanus’s highly accurate Calendarium, which provides information on lunar and solar eclipses, daylight hours, and the signs of the zodiac and planetary positions for the years 1475 to 1530 and the Ephemerides, which provides positions for the sun, moon, and planets for each day of each year from 1480 to 1506. Regiomontanus set up his own press in Nuremburg in 1475 in order to ensure sufficient quality in the complex lunar diagrams and tables. Each annual section is indicated by a leather or parchment finding tab. The inclusion of the feast of Saint Kilian and its related Octave in the volume’s liturgical calendar is specific to the Benedictine Abbey of Lambach, in Upper Austria on the Traun River south of Linz.
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While Boethius’s De consolatione philosophiae remained an enduring text beyond the Middle Ages, and his ambitious, unfinished project to translate all Aristotelian and Platonic texts from Greek into Latin resonated with humanist audiences, his treatise on music, De institutione musica, was less frequently copied in the Renaissance. Nevertheless, the De musica was included in the first printed edition of Boethius’s works and remained a fundamental reference work on music theory and harmonics. The work put forward the influential notion of a tripartite division of musical types: the imperceptible music of the spheres, the spiritual and somatic music of the body, and the audible instrumental music of voice and instrument. The present volume, illustrated with diagrams throughout, demonstrates the ongoing utility of the manuscript medium, especially since the complex visual schematics could not readily be printed. The semi-humanist script and watermarks indicate a date of production for this manuscript around 1490.
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Tiny incunables do exist, but the constraints in the production of miniature metal type limited the amount of information they could contain. The finely crafted book, which contains an array of astrological and astronomical charts, as well as other useful information for travel, was produced in 1511 by Imbert Feutrier. Little is known about this individual, who was bailli or bailiff of Crèvecœur-sur-l’Escaut near Cambrai. However, his rank may have given him occasion to travel. Though many of the short texts concern the movements of the celestial bodies, several also touch upon topics as diverse as international commerce, the positions of various European cities, textile production, and remedies for certain ailments. Together, they suggest that the book’s original user, probably Feutrier, intended to bring it along with him on far-flung journeys. Combining science with superstition, the book’s contents represent an updated version of the medieval “bat-book,” or portable medical almanac.
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This booklet consists of extracts, abbreviated and transliterated into Venetian-inflected Italian, drawn from the major texts of Renaissance mathematics and architecture: Luca Pacioli’s Summa de arithmetica, geometria, proportioni et proportionalità and Leon Battista Alberti’s De re aedificatoria. Pacioli’s Summa, which consists of an Italian-language synthesis of mathematical knowledge, was first printed in Venice in 1494 by Paganini. The extracts found in this booklet are taken from the second part of the Summa, which is dedicated to geometry. The second set of extracts concerns the elements of classical architecture. Finally, this book contains three recipes for making ink and two remedies for stomach aches added to its final leaves, proof of ongoing use of the item in a reader’s daily life. Perhaps owned by an architect-in-training, it demonstrates how geometry, as a branch of the quadrivium, came to influence theories of architecture and their real-life application.
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The Austrian astronomer Georg von Peuerbach (1423–61) served as an influential mentor to Regiomontanus and an advisor to such highly placed individuals as cardinal Basilios Bessarion and the polymath theologian Nicholas of Cusa. He was appointed court astrologer to the teenage King Ladislaus V of Hungary and later to his uncle, Emperor Frederick III. Around 1454, Peuerbach composed the Novae theoricae planetarum, which was published posthumously in Nuremberg in 1473. This dependable astronomy manual became the standard reference work on the subject for over 150 years. This volume contains seventy-three full-page diagrams, one double-page diagram, and four half-page diagrams. It is likely that these moveable diagrams originated as teaching aids devised by Peuerbach himself, a skilled instrument maker, in the fifteenth century. He later wrote a treatise entitled Speculum planetarum on the construction of paper manuscript volvelles to demonstrate planetary motions as described in the Novae theoricae planetarum.
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Johannes Müller von Königsberg (1436–76), better known as Regiomontanus, was a Central European astronomer whose peripatetic career brought him into dialogue with some of the key humanist thinkers and patrons. He was one of the founders of modern observational astronomy and exerted a profound influence on Nicolaus Copernicus. His works were even used by Christopher Columbus and Vasco da Gama as navigational aids. Regiomontanus completed his Tabulae directionum et profectionum, a series of tables that allowed for the positions of celestial bodies to be determined mathematically with unprecedented accuracy when compared to the existing Alphonsine Tables that had been developed at the court of Alfonso X of Castile in the mid-thirteenth century. Regiomontanus’s tables, as copied in the present manuscript, continue the Ptolemaic system of their predecessors, but with added tables of tangents and sines that allowed for a much higher degree of predictive accuracy.
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