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THE RENAISSANCE

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Bianca
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« Reply #60 on: October 17, 2008, 07:03:53 pm »









The early-modern historian of mathematics and the sciences, however, generally had to intervene more dramatically in the narrative. For reasons that will become clear from the papers below, almost all rejected a static conception of the arts. A few (like Regiomontanus and Savile) embraced a narrative of progress, in which the Greeks surpassed the biblical or mythical ancients, and moderns might hope to do the same. Others (such as Ramus and Raleigh) constructed a cycle of degeneration and recovery. But whichever model they adopted, they used their history to address the current state of their discipline. Unlike magic, mathematics was part of the medieval arts curriculum; most of the authors considered in these essays were, in one way or another, concerned with the reform of the syllabus and the introduction of newly discovered texts or techniques into the schools (or into popular currency). The mismatch between their ideals and the actual condition of the sciences all but demanded a historiographical model built upon change, whether for the better or the worse.

Regiomontanus, for instance, saw a break in the history of astronomy, but not between classical and medieval authors—as one might expect a humanist author to do. Instead, the divide occurs between the semi-mythical origins of the sciences, and their practice by historical human beings. He accepts that Abraham and Prometheus had some extraordinary knowledge of astronomy and were instrumental in its foundation as a science; on the other hand, historical records show that Hipparchus first discovered the precession of the equinoxes, a prerequisite to any adequate astronomy or accurate calendar. While Regiomontanus's own astronomy could claim continuity with that of the most ancient human beings, he found room for technical innovation and the increase of the art itself both in history and in its contemporary practice. 
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« Reply #61 on: October 17, 2008, 07:12:33 pm »










Many of the authors here connected their reforms of their arts with other movements of reform, especially religious reform. Ramus teasingly hinted at the irenic outcome of a reform of the sciences, completing the process begun in the religious sphere while reconciling Catholics and Protestants through a new, common epistemological clarity. His history itself, [End Page 39] in its repeated redraftings, took on more and more the pattern of Protestant accounts of primitive Christianity and its subsequent effacement by non-Scriptural innovation. Reginald Scot attributes the rise of false charges of magic and witchcraft to the baneful and superstitious influence of Catholicism. A true understanding of nature and rejection of superstition were marks both of the earliest times (before the rise of "witchcraft") and the latest, in which the Protestant churches had done away with Roman excesses, returning Christians to a more primitive—and hence more authentic—relationship both with God and with the world.

As Nicholas Popper writes in the conclusion to his paper, the histories of science he surveys posed a problem of recovery, rather than invention—a narrative which might seem at odds with the progressive optimism of the authors of the "new science," from Bacon and Descartes through to Boyle. But, within their grand narratives, Renaissance historians seemed to uncover a profusion of mathematical practice, not at all made explicit in the ancient sources they drew upon. They legitimized expertise (another focus of modern histories of early-modern science)20 for the wider intellectual culture, a crucial step in the epistemological transformations which led to the Scientific Revolution. 
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« Reply #62 on: October 17, 2008, 07:13:48 pm »











Footnotes
I am grateful to Lauren Kassell for comments and substantial advice on this introduction; to Nicholas Popper and James Byrne, who organized a panel at the 2004 History of Science Society annual meeting at which these papers were first presented; and to Anthony Grafton, who encouraged their publication and offered extensive criticisms on all of the papers presented here.

1. Jeanne Peiffer, "France" in Writing the History of Mathematics: Its Historical Development, ed. Joseph W. Dauben and Christoph J. Scriba (Basel: Birkhäuser, 2002), 3–43, at 6.

2. On Montucla, see Noel M. Swerdlow, "Montucla's Legacy: The History of the Exact Sciences," JHI 54 (1993): 299–328.

3. Cited by Christoph J. Scriba, Menso Folkerts, and Hans Wussing, "Germany," in Writing the History of Mathematics, 109–49 at 112. Note also the brief treatment and dismissal of Renaissance histories at 110.

4. Peiffer, "France," 10.

5. For instance, Serafina Cuomo, Ancient mathematics (London and New York: Routledge, 2001).

6. Anthony Grafton, "From Apotheosis to Analysis: Some Late Renaissance Histories of Classical Astronomy," in History and the Disciplines: The Reclassification of Knowledge in Early Modern Europe, ed. Donald R. Kelley (Rochester, N.Y.: University of Rochester Press, 1997), 261–76 (especially 262).

7. Owen Hannaway, "Georgius Agricola as Humanist," JHI 53 (1992): 553–60, at 553.

8. For a survey of this literature, see H. Floris Cohen, The scientific revolution: a historiographical inquiry (Chicago: University of Chicago Press, 1994), 271–303. On humanists as translators and commentators, see Paul L. Rose, The Italian Renaissance of Mathematics: Studies on Humanists and Mathematicians from Petrarch to Galileo (Geneva: Librairie Droz, 1975); Noel M. Swerdlow, "The Recovery of the Exact Sciences of Antiquity: Mathematics, Astronomy,Geography," in Rome Reborn: The Vatican Library and Renaissance Culture, ed. Anthony Grafton (Washington D.C.: Library of Congress, 1993), 125–67.

9. See Brian W. Ogilvie, "Science," in Renaissance Historiography, ed. Jonathan Woolfson (Basingstoke: Palgrave Macmillan, 2005), 241–69, for a comprehensive survey of scholarship in the history of Renaissance science.

10. See especially Anthony Grafton, "The New Science and the Traditions of Humanism," in The Cambridge Companion to Renaissance Humanism, ed. Jill Kraye (Cambridge: Cambridge University Press, 1996), 203–23.
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« Reply #63 on: October 17, 2008, 07:14:56 pm »










11. Anthony Grafton and Lisa Jardine, From Humanism to the Humanities: Education and the Liberal Arts in Fifteenth- and Sixteenth-Century Europe (Cambridge Mass.: Harvard University Press, 1986).

12. Lisa Jardine and Anthony Grafton, "'Studied for Action': How Gabriel Harvey Read his Livy," Past and Present 129 (1990): 3–51.

13. See, for instance, Ann Blair, "Annotating and Indexing Natural Philosophy," in Books and the Sciences in History, ed. Marina Frasca-Spada and Nick Jardine (Cambridge: Cambridge University Press, 2000), 69–89.

14. Lauren Kassell, "Reading for the Philosophers' Stone," in Books and the Sciences in History, 132–50; Anthony Grafton, "John Dee Reads Books of Magic," in The Reader Revealed, ed. Sabrina Alcorn Baron (Seattle: University of Washington Press, 2001), 31–37.

15. Ann Blair and Anthony Grafton, "Reassessing Humanism and Science," JHI 53 (1992): 535–40.

16. Johannes Stadius, Tabulae Bergenses (Cologne, 1560). The preface, entitled "Astronomiae aetas, usus, peregrinatio, incrementum, utilitas," and occupying the first 25 pages of the work, seems to have been an important source for elements of Ramus's historical narrative.

17. See Grafton, "From Apotheosis to Analysis."

18. Allen G. Debus, "An Elizabethan History of Medical Chemistry," Annals of Science 18 (1962): 1–29.

19. Nancy Siraisi, "Anatomizing the Past: Physicians and History in Renaissance Culture," Renaissance Quarterly 53 (2000): 1–30.

20. See, most recently, Eric Ash, Power, knowledge, and expertise in Elizabethan England (Baltimore: Johns Hopkins University Press, 2004).



http://muse.jhu.edu/journals/journal_of_the_history_of_ideas/v067/67.1goulding01.html
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« Reply #64 on: October 17, 2008, 07:18:37 pm »





               









                                                   R E G I O M O N T A N U S





Johannes Müller von Königsberg (June 6, 1436 – July 6, 1476), known by his Latin pseudonym Regiomontanus,
was an important German mathematician, astronomer and astrologer.

He was born in the Franconian village of Unfinden near Königsberg, Bavaria, not in the more famous Königsberg
in East Prussia.

Thus, he is also called Johannes Müller, der Königsberger (Johannes Müller of Königsberg). His full Latin name
was Joannes de Regio monte, which abbreviated to Regiomontanus

(from the Latin for "Königsberg"—"King's Mountain").
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« Reply #65 on: October 17, 2008, 07:21:15 pm »










Born June

6, 1436



Died

July 6, 1476
 


Nationality

German



Fields

Mathematics



Doctoral advisor

Georg von Peuerbach





At eleven years of age, he became a student at the university in Leipzig, Saxony.

Three years later he continued his studies at Alma Mater Rudolfina, the university in Vienna, Austria. There he became a pupil and friend of Georg von Peurbach.

In 1457 he graduated with a degree of "magister artium" (Master of Arts) and held lectures in optics and ancient literature.

He built astrolabes for Matthias Corvinus of Hungary and Cardinal Bessarion, and in 1465 a portable sundial for Pope Paul II.

His work with Peurbach brought him to the writings of Nicholas of Cusa (Cusanus), who held a heliocentric view. Regiomontanus, however, remained a geocentrist after Ptolemy.

Following Peurbach's death, he continued the translation of Ptolemy's Almagest which Peurbach
had begun at the initiative of Basilios Bessarion.

From 1461 to 1465 Regiomontanus lived and worked at Cardinal Bessarion's house in Rome.

He wrote De Triangulis omnimodus (1464) and Epytoma in almagesti Ptolemei. De Triangulis
(On Triangles) was one of the first textbooks presenting the current state of trigonometry and
included lists of questions for review of individual chapters. In it he wrote:



"You who wish to study great and wonderful things, who wonder about the movement of the stars, must read these theorems about triangles.

Knowing these ideas will open the door to all of astronomy and to certain geometric problems."



In the Epytoma he critiqued the translation, pointing out inaccuracies.

Later Nicolaus Copernicus would refer to this book as an influence on his own work.

In 1467 Regiomontanus left Rome to work at the court of Matthias Corvinus of Hungary. There he calculated extensive astronomical tables and built astronomical instruments.
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« Reply #66 on: October 17, 2008, 07:33:02 pm »










In 1471 he moved to the Free City of Nuremberg, in Franconia, then one of the Empire's important seats of learning, publication, commerce and art. He associated with the humanist and merchant Bernhard Walther who sponsored the observatory and the printing press. Regiomontanus remains famous for having built at Nuremberg the first astronomical observatory in Germany. In 1472 he published the first printed astronomical textbook, the "Theoricae novae Planetarum" of his teacher Georg von Peurbach. Peurbach worked at the Observatory of Großwardein (Oradea) in Transylvania, the first in Europe, and established in his "Tabula Varadiensis" this Transylvanian town's observatory as lying on the prime meridian of Earth.

In 1475 he went to Rome to work with Pope Sixtus IV on calendar reform. On the way he could publish his "Ephemeris" in Venice. Regiomontanus died mysteriously in Rome, July 6, 1476, a month after his fortieth birthday. Some say he died of plague, others by (more likely) assassination.

A prolific author, Regiomontanus was internationally famous already in his lifetime. Despite having completed only a quarter of what he had intended to write, he left a substantial body of work. Domenico Maria Novara da Ferrara, the teacher of Nicolaus Copernicus, referred to Regiomontanus as having been his own teacher.

It is not true that he came to be called posthumously after the place of his birth, Königsberg/Bavaria (in Latin, Regiomontanus). In Regiomontanus' day it was common for scholars to Latinize their names when publishing.

He is known for having built one of the most famous automata, the wooden eagle of Regiomontanus, which flew from the city of Königsberg to meet the emperor, saluted him, and returned. He also built an iron fly of which it is said it flew out of Regiomontanus's hands at a feast, and taking a round, returned to him.

In 1561, Daniel Santbech compiled a collected edition of the works of Regiomontanus, De triangulis planis et sphaericis libri quinque (first published in 1533) and Compositio tabularum sinum recto, as well as Santbech's own Problematum astronomicorum et geometricorum sectiones septem. It was published in Basel by Henrich Petri and Petrus Perna.

 
Regiomontanus crater, on the Moon, is named after him.
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« Reply #67 on: October 17, 2008, 07:35:13 pm »



REGIOMONTANUS' TOMB
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« Reply #68 on: October 17, 2008, 07:36:27 pm »









One biographer has claimed to have detected a decline in Regiomontanus' interest in astrology over his life, and came close to asserting that Regiomontanus had rejected it altogether. But more recent commentators have suggested that the occasional expression of skepticism about astrological prognostication reflected a disquiet about the procedural rigour of the art, not about its underlying principles. It seems plausible that, like some other astronomers, Regiomontanus concentrated his efforts on mathematical astronomy because he felt that astrology could not be placed on a sound footing until the celestial motions had been modeled accurately.

In his youth, Regiomontanus had cast horoscopes (natal charts) for famous patrons. His Tabulae directionum, completed in Hungary, were designed for astrological use and contained a discussion of different ways of determining astrological houses. The calendars for 1475-1531 which he printed at Nuremberg contained only limited astrological information—a method of finding times for bloodletting according to the position of the moon; subsequent editors added material.

But perhaps the works most indicative of Regiomontanus' hopes for an empirically sound astrology were his almanacs or ephemerides, produced first in Vienna for his own benefit, and printed in Nuremberg for the years 1475-1506. Weather predictions and observations were juxtaposed by Regiomontanus in his manuscript almanacs, and the form of the printed text enabled scholars to enter their own weather observations in order to likewise check astrological predictions; extant copies reveal that several did so. Regiomontanus' Ephemeris would be used in 1504, by a Christopher Columbus stranded on Jamaica, to intimidate the natives into continuing to provision him and his crew from their scanty food stocks, when he successfully predicted a lunar eclipse for February 29, 1504.[1]

Regiomontanus did not live to produce the special commentary to the ephemerides that he had promised would reveal the advantages the almanacs held for the multifarious activities of physicians, for human births and the telling of the future, for weather forecasting, for the inauguration of employment, and for a host of other activities, although this lack was again made good by subsequent editors. Nevertheless Regiomontanus' promise suggests that he either was as convinced of the validity and utility of astrology as his contemporaries, or was willing to set aside his misgivings for the sake of commercial success.
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« Reply #69 on: October 17, 2008, 07:38:08 pm »










Notes



^ Samuel Eliot Morison, Christopher Columbus, Mariner, 1955, pp. 184–92.

^ Victor J. Katz-Princeton University Press





[edit] Literature



Irmela Bues, Johannes Regiomontanus (1436-1476). In: Fränkische Lebensbilder 11.
Neustadt/Aisch 1984, S. 28 - 43

Rudolf Mett: Regiomontanus. Wegbereiter des neuen Weltbildes.
Teubner / Vieweg, Stuttgart / Leipzig 1996, ISBN 3-8154-2510-7

Helmuth Gericke: Mathematik im Abendland: Von den römischen Feldmessern bis zu Descartes.
Springer Verlag, Berlin 1990, ISBN 3-540-51206-3

Günther Harmann (Hrsg.): Regiomontanus-Studien. (= Österreichische Akademie der Wissenschaften, Philosophisch-historische Klasse, Sitzungsberichte, Bd. 364; Veröffentlichungen der Kommission für Geschichte der Mathematik, Naturwissenschaften und Medizin, Heft 28-30), Wien 1980. ISBN 3-7001-0339-5

Samuel Eliot Morison, Christopher Columbus, Mariner, Boston, Little, Brown and Company, 1955
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« Reply #70 on: October 17, 2008, 07:39:48 pm »









                                              Regiomontanus and Astrology






One biographer detected a decline in Regiomontanus' interest in astrology over the course of his life, and came close to asserting that he rejected it altogether.

But more recent commentators have suggested that occasional expressions of scepticism about astrological prognostications reflect a disquiet about the procedural rigour of the art, not its underlying principles.

It seems plausible that, like certain other astronomers, Regiomontanus concentrated his efforts on mathematical astronomy because he felt that astrology could not be placed on a sound footing until the celestial motions could be modelled accurately. 
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« Reply #71 on: October 17, 2008, 07:41:05 pm »





             

              A Horoscope "He will be a Doctor"

             from the Astrolabium planum (Augsburg, 1488)
             of Johannes Engel (c.1453-1512),
             who is said to have been a student of Regiomontanus.
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« Reply #72 on: October 17, 2008, 07:42:22 pm »










In his youth, Regiomontanus cast horoscopes for famous patrons.

His Tabulae directionum, completed during his time in Hungary, were designed for astrological use,
and contained a discussion of the different ways of determining the astrological houses.

The calendars for 1475-1531 which he printed at Nuremberg contained only a limited quantity of astrological information, namely the method of finding times for blood-letting according to the
position of the moon; subsequent editors added a quantity of additional material.

But perhaps the works most indicative of Regiomontanus' hopes for an empirically-sound astrology
were his almanacs or ephemerides, produced first in Vienna for his own benefit, and printed for the years 1475-1506 in Nuremberg.

Weather forecasts and observations were juxtaposed by Regiomontanus in his manuscript almanacs, and the form of the printed text enabled scholars to enter their own weather observations in order
to likewise check astrological predictions; extant copies reveal that several did so.

Regiomontanus did not live to produce the special commentary to the ephemerides which he promised would reveal what advantages these almanacs hold for the multifaceted activities of physicians, for human births and telling the future, for weather forecasting, for the start of employment, and for a host of other activities, although this lack was again rectified by subsequent editors.

Nevertheless this announcement suggests that Regiomontanus was either as convinced of the validity and utility of astrology as his contemporaries, or willing to put aside his misgivings to achieve commercial success.
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« Reply #73 on: October 17, 2008, 07:43:56 pm »



A page from Regiomontanus's Tabulae Primi Mobilis.
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« Reply #74 on: October 17, 2008, 07:45:02 pm »










Regiomontanus' Astronomical Tables
 





One scholar has remarked that Regiomontanus was a "lightning calculator, and a very accurate one too." Certainly, he was a prolific compiler of tables and ephemerides.

He produced tables of sines at intervals of sixths of a degree in which the value of sin 90° was set
at 6 000 000 and 10 000 000; these were printed by Johann Schöner in 1541.

His Tabulae primi mobilis, completed in Hungary and dedicated to King Matthias, were first published
in 1514. They gave values of a, an unknown side of a right-spherical triangle, in accordance with the relationship a = sin-1 (sin a sin c) for values of a and c from 1 to 90° at one degree intervals.

Never widely used, they were rendered obsolete by the advent of logarithmic calculating techniques.

The Tabulae directionum, produced with the assistance of Martin Bylica, were primarily for astrological use and seem to have been correspondingly more popular: they were first printed in 1490, and went through eleven editions up to 1626.

In addition to tables for calculating horoscopes, the collection included a table of the declination of
the sun for every degree of longitude in the ecliptic, and introduced, probably for the first time in
the Latin West, a table of tangents.

Tan 45° was set to 100 000, in accordance with Regiomontanus' developing and influential preference for a decimal system over a sexagesimal one for performing such calculations.




With respect to astronomical tables proper, Regiomontanus expressed misgivings about both the Alfonsine and the Toledan Tables.

He did not live to produce tables of his own, but did issue almanacs and calendars from his press in Nuremberg.

The calendars included the times of new and full moons and eclipses for the years 1475-1531;
the almanacs gave mean planetary positions, true positions for the sun and moon, and eclipse times
for 1475-1506.

Both were extremely popular, and an edition of the almanacs was used by Christopher Columbus. 
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