DOCSLIB.ORG

Renaissance Europe Regiomontanus

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Renaissance Europe Regiomontanus Renaissance Europe Regiomontanus • Born near Königsberg in Lower Franconia in 1436. • Johann Müller • Johannes Germanus • Johannes Francus • Johann von Kunsperk • Regio Monte (“royal mountain”) • Regiomontanus • Johannes de Monte Regio Regiomontanus • Studied under Peurbach, who was writing a corrected translation of Ptolemy’s Almagest. When Peurbach died young, Johann took over this task. • Became friends with Cretan, George of Trebizond, a Ptolemaic scholar, whom he later criticized for errors in interpretation, as “the most impudently perverse blabber‐mouth.” Regiomontanus • Traveled extensively. • Was asked in 1467 to be librarian to the Royal Library of Hungary (the king had just returned triumphant from a war with the Turks, brought back a number of rare books). • Cast the horoscope of the King, predicting that he would not die, and when it turned out that way, was lavishly bestowed with gifts. Regiomontanus • Returned home in 1471. He settled in Nürnberg, which had a printing press. • First publisher of mathematical and astronomical books for commercial use. Also published some very popular calendars. • Was asked by Pope Sixtus IV to come to Rome and help revise the old Julian calendar, which was out of tune with the seasons. • He died there on July 6, 1476. Regiomontanus • We don’t know cause of death, but one tradition is that he was poisoned by the sons of Trebizond, the “most impudently perverse blabber‐mouth.” • Another tradition is that it was a passing comet. Or a plague. Take your pick. Regiomontanus • Wrote De trangulus omnimodis, or On triangles of every kind. It had five parts or books, and was modeled, of course, on the Elements. • Finished in 1464, but not published until 1533. On Triangles of Every Kind • Book 1: Basic definitions of quantity, ratio, equality, circle, arc, chord. • “When the arc and its chord are bisected, we call that half‐chord the right sine of the half‐ arc.” • A list of axioms, followed by 56 theorems, most geometrical, solving plane triangles. Theorem 20 uses the sine to solve a right triangle. On Triangles of Every Kind • Book 2: The Law of Sines, stated literally rather than with symbols. Used to solve SAA and SSA cases (thus dealing with the “ambiguous” case). • Area of triangle in terms of two sides and included angle: • Used sines, cosines (= sine of complement), and versines (1 –cosine). On Triangles of Every Kind • Sines and cosines were still defined not in terms of right angles, but in terms of line segments associated with a given arc in a circle of fixed radius. • The fixed radius was usually a power of 10, or 6 times a power of 10, with the powers getting larger in later books so as to avoid decimal fractions. On Triangles of Every Kind • Books 3‐5 deal with spherical geometry and trigonometry, as a prerequisite to astronomy. • “You, who wish to study great and wondrous things, who wonder about the movements of the stars, must read these theorems about triangles. For no one can bypass the science of triangles and reach a satisfying knowledge of the stars. A new student should neither be frightened nor despair. And where a theorem may present some problem, he may always look down to the numerical examples for help.” Ephemerides • Regiomontanus published his Ephemerides in 1474. • It contained tables listing the position of the sun, moon, and planets for each day from 1474 to 1506. • Columbus took it with him on his fourth voyage, and famously used it to predict the lunar eclipse of February 29, 1504, to the amazement of the hostile natives. Fra Luca Pacioli • 1447‐1517 • Local education, then became a Franciscan Friar. • The “Father of Accounting.” • Introduced for più and meno, or plus and minus. Fra Luca Pacioli • Summa de arithmetica, geometria, proportioni et proportionalita (1494) • Shamelessly borrowed from earlier authors. It laid out the boundaries of contemporary mathematical knowledge. • Ended with the prediction that the solution (by radicals) of the cubic equation was impossible (like the quadrature of the circle). Which leads us to our transitional character, Scipione del Ferro. • Born 1465, but did his important work with the cubic between 1500 and 1515. • Didn’t publish, but closely guarded his work. Depressed Cubic • By making the substitution for an appropriate value of c, any cubic can be reduced to a cubic without a second degree term. Thus it will be of the form: • , with b and c rational numbers. • But in 1500, we only liked positive rational numbers, so there were actually several forms of this “depressed” cubic. Depressed Cubic • • • • • del Ferro solved this depressed cubic in at least one, possibly all, of its forms. Scipione del Ferro • When he died, his papers containing this solution were left to his son‐in‐law Annibale della Nave, and to one of del Ferro’s students, Antonio Maria Fiore. • Fiore intended to use it. <cue ominous music> More on the Cubic Later • But first, some other important mathematics. The Abacists vs Traditionalists • Dear Professor: You keep on using that word. I do not think it means what you think it means. • Abacists were abacists in the sense of Liber Abaci, that is, they used the Islamic tradition of decimal numbers and algorithms, and eschewed counting boards in favor of pencil and paper. The Abacists vs Traditionalists • The Abacists won, but it took a while. • “But what if you were stranded on a desert island without paper? Then you’d wish you’d studied how to use a counting board……” Rafael Bombelli • Rafael Bombelli (1526‐ 1572) • His family had been out of favor with local leaders. • Lived in Bologna and was tutored by an engineer/architect. • Worked as a hydraulic engineer, draining wetlands. Rafael Bombelli • While waiting for a certain project to recommence, decided to write an algebra book. • Published in three volumes (two volumes of geometry that were to follow were not published) Rafael Bombelli • Wrote down rules for negative numbers: • Plus times plus makes plus Minus times minus makes plus Plus times minus makes minus Minus times plus makes minus Plus 8 times plus 8 makes plus 64 Minus 5 times minus 6 makes plus 30 Minus 4 times plus 5 makes minus 20 Plus 5 times minus 4 makes minus 20 Rafael Bombelli • Wrote down rules for computing with complex numbers: • Plus of minus times plus of minus makes minus [+√‐n . +√‐n = ‐n] Plus of minus times minus of minus makes plus [+√‐n . ‐√‐n = +n] Minus of minus times plus of minus makes plus [‐√‐n . +√‐n = +n] Minus of minus times minus of minus makes minus [‐√‐n . ‐√‐n = ‐n] Rafael Bombelli • Notation: Modern Bombelli Printed notation 5x 51 5x2 5 2 46 Rq 4pRq6 3 2 0 121 Rc 2pRq 0m121 François Viète François Viète (1540 – 1603) was a French lawyer who worked for kings Henri III and Henri IV as a cryptanalyst (a breaker of secret codes). François was born a French Protestant (Huguenot), and when Henry of Navarre, also a Protestant, came to power, it alarmed Catholics both inside and outside of France. François Viète • Philip II of Spain rather fancied his own daughter as successor to Henry III (who, by the way, was flamboyantly gay and unlikely to produce a lawful heir) rather than Henry of Navarre. Philip exchanged many letters with members of the French court in support of his daughter, even after Henry of Navarre assumed the throne as Henry IV. François Viète • These letters, written in code, were given to Viète to decode. He was so successful at this that Philip denounced him for being in league with the Devil. François Viète • During a period of exile from Henry III’s court (this was a very unsettled time in French history) he found the time to write several treatises that are collectively known as The Analytic Art, in which he effectively reformulated the study of algebra by replacing the search for solutions with a detailed study of the structure of equations. François Viète • Viète used upper case vowels (A, E, I, O, U, Y) to represent unknowns and upper case consonants to represent given constants. His symbolism was not complete, in the sense that he still used words to indicate powers – A2 is A quadratum, B3 would be B cubus, and C4 is C quadrato‐quadratum. He did at times use abbreviations such as A quad or C quad‐ quad. His rules for combining powers had to be given verbally. François Viète • Our equation , in Viète’s symbolism, would be: • B in A Quadratum, + D plano in A, aequari Z solido. • Here, he uses B, D and Z as known (but unspecified) numbers, and A as the unknown. The word “in” represents multiplication. The “+” sign was used for addition, as was “‐“ for subtraction. There was no “=” but instead some proper conjugation of the Latin verb aequare. François Viète • The words plano and solido demonstrate that Viète was strongly influenced by Greek concepts, since they are there to guarantee that the Z has “cubic” units, and the D has “square” units (resulting in “cubic” units when multiplied by A), thus guaranteeing that quantities of the same kind (cubic) are being added. Viète • On the other hand, he accepted larger powers in equations; he even solved a whopper of a 45th degree equation posed by Adriaan van Roomen. • Viète’s symbolism was to be further refined and superseded by that of René Descartes, who only a few years later gave us what amounts to our modern system of algebraic symbolism. Viète • Provided an approximation of correct to 10 decimals by using Archimedes’ method. • Wrote what seems to be the first infinite product by noting that Viète • What was his most important legacy? • Searching for Analysis • Systematizing algebra – “formulas, rather than rules.” “Focus on the procedures of the solution rather than the solution itself.” • “Replacing the search for solutions to equations by the detailed study of the structure of these equations.” Some Astronomy Nicolaus Copernicus • Mikołaj Kopernik, 19 February 1473 –24 May 1543 • Contributed to mathematics, medicine, astronomy, law, economics.
Load more

Recommended publications
  • Simon Stevin
    II THE PRINCIPAL WORKS OF SIMON STEVIN E D IT E D BY ERNST CRONE, E. J. DIJKSTERHUIS, R. J. FORBES M. G. J. MINNAERT, A. PANNEKOEK A M ST E R D A M C. V. SW ETS & Z E IT L IN G E R J m THE PRINCIPAL WORKS OF SIMON STEVIN VOLUME II MATHEMATICS E D IT E D BY D. J. STRUIK PROFESSOR AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE (MASS.) A M S T E R D A M C. V. SW ETS & Z E IT L IN G E R 1958 The edition of this volume II of the principal works of SIMON STEVIN devoted to his mathematical publications, has been rendered possible through the financial aid of the Koninklijke. Nederlandse Akademie van Wetenschappen (Royal Netherlands Academy of Science) Printed by Jan de Lange, Deventer, Holland The following edition of the Principal Works of SIMON STEVIN has been brought about at the initiative of the Physics Section of the Koninklijke Nederlandse Akademie van Weten­ schappen (Royal Netherlands Academy of Sciences) by a committee consisting of the following members: ERNST CRONE, Chairman of the Netherlands Maritime Museum, Amsterdam E. J. DIJKSTERHUIS, Professor of the History of Science at the Universities of Leiden and Utrecht R. J. FORBES, Professor of the History of Science at the Municipal University of Amsterdam M. G. J. M INNAERT, Professor of Astronomy at the University of Utrecht A. PANNEKOEK, Former Professor of Astronomy at the Municipal University of Amsterdam The Dutch texts of STEVIN as well as the introductions and notes have been translated into English or revised by Miss C.
    [Show full text]
  • Beginnings of Trigonometry
    Beginnings of Trigonometry Trigonometry is an area of mathematics used for determining geometric quantities. Its name, first published in 1595 by B. Pitiscus, means "the study of trigons (triangles)" in Latin. Ancient Greek Mathematicians first used trigonometric functions with the chords of a circle. The first to publish these chords in 140 BC was Hipparchus, who is now called the founder of trigonometry. In AD 100, Menelaus, another Greek mathematician, published six lost books of tables of chords. Ptolemy, a Babylonian, also wrote a book of chords. Using chords, Ptolemy knew that sin(xy+= ) sin x cos y + cos x sin y and abc = = sinABC sin sin In his great astronomical handbook, The Almagest, Ptolemy provided a table of chords for steps of °, from 0° to 180°, that is accurate to 1/3600 of a unit. Ptolemy's degree of accuracy is due in part because the Hellenistic Greeks had adopted the Babylonian base- 60 (sexagesimal) numeration system. He also explained his method for constructing his table of chords, and in the course of the book he gave many examples of how to use the table to find unknown parts of triangles from known parts. Ptolemy provided what is now known as Menelaus's theorem for solving spherical triangles, as well, and for several centuries his trigonometry was the primary introduction to the subject for any astronomer. Sine first appeared in the work of Aryabhata, a Hindu. He used the word jya for sine. He also published the first sine tables. Brahmagupta, in 628, also published a table of sines for any angle.
    [Show full text]
  • Preprint N°494
    2019 Preprint N°494 The Reception of Cosmography in Vienna: Georg von Peuerbach, Johannes Regiomontanus, and Sebastian Binderlius Thomas Horst Published in the context of the project “The Sphere—Knowledge System Evolution and the Shared Scientific Identity of Europe” https://sphaera.mpiwg-berlin.mpg.de The Reception of Cosmography in Vienna: Georg von Peuerbach, Johannes Regiomontanus, and Sebastian Binderlius1 Abstract In this paper, the importance of the cosmographical activities of the Vienna astronomical “school” for the reception of the Tractatus de Sphaera is analyzed. First, the biographies of two main representatives of the Vienna mathematical/astronomical circle are presented: the Austrian astronomers, mathematicians, and instrument makers Georg von Peuerbach (1423– 1461) and his student Johannes Müller von Königsberg (Regiomontanus, 1436–1476). Their studies influenced the cosmographical teaching at the University of Vienna enormously for the next century and are relevant to understanding what followed; therefore, the prosopo- graphical introductions of these Vienna scholars have been included here, even if neither can be considered a real author of the Sphaera. Moreover, taking the examples of an impressive sixteenth-century miscellany (Austrian Na- tional Library, Cod. ser. nov. 4265, including the recently rediscovered cosmography by Sebastian Binderlius, compiled around 1518), the diversity of different cosmographical studies in the capital of the Habsburg Empire at the turning point between the Middle Ages and the early modern period is demonstrated. Handwritten comments in the Vienna edition of De sphaera (1518) also show how big the influence of Sacrobosco’s work remained as a didactical tool at the universities in the first decades of the sixteenth century—and how cosmographical knowledge was transformed and structured in early modern Europe by the editors and readers of the Sphaera.
    [Show full text]
  • The Copernican System
    The Copernican system Jan P. Hogendijk Dept of Mathematics, Utrecht University 8 june 2011 1 Prelude: the 15th century Copernicus: biography Copernicus’ new system: Main Points Copernicus’ new system: Dirty Details The reception of the new system 2 Renaissance Invention of Printing by Johannes Gutenberg (Mainz), ca. 1450: typesetting with movable type, printing press, paper. 3 Most important astronomer of the 15th century Johannes Muller¨ of K¨onigsberg (Bavaria), or Regiomontanus (1436-1476) 4 Biography of Regiomontanus (1436-1476) 1448: Entered University of Leipzig. 1460: Met cardinal Bessarion (from Trebizond), travelled with him to Italy. 1463: completed Epitome of the Almagest (of Ptolemy) [printed 1492]. ca. 1461: made observations of eclipses, etc. which diverged from the predictions by e.g. the Alfonsine tables. 5 Quotation from Regiomontanus (1464) “I cannot [but] wonder at the indolence of common astronomers of our age, who, just as credulous women, receive as something divine and immutable whatever they come upon in books, either of tables of their instructions, for they believe in writers and make no effort to find the truth.” Regiomontanus wanted to restore and “update” Ptolemaic astronomy in order to predict astronomical phenomena accurately. 1471: he founded printing press in Nurnberg,¨ producing mathematical and astronomical works with great accuracy. 6 Product of Regiomontanus’ Press (1472) Novae Theoricae Planetarum, Georg von Peuerbach (1423-1461) 7 Example of Regiomontanus’ own predictions solar and lunar eclipses, 1489, 1490 8 Nicolas Copernicus (1473-1543): biography 1473 Torun (Poland) - 1543 Frauenburg = Frombork (now in Poland, near coast and Russian border) Studied at the University of Krakow. Worked in service of the Catholic Church until his death.
    [Show full text]
  • Regiomontanus and Chinese Mathematics
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Ghent University Academic Bibliography Philosophica 82 (2008), pp. 87-114 REGIOMONTANUS AND CHINESE MATHEMATICS Albrecht Heeffer * ABSTRACT This paper critically assesses the claim by Gavin Menzies that Regiomontanus knew about the Chinese Remainder Theorem ( CRT ) through the Shù sh ū Ji ǔ zh āng (SSJZ ) written in 1247. Menzies uses this among many others arguments for his controversial theory that a large fleet of Chinese vessels visited Italy in the first half of the 15th century. We first refute that Regiomontanus used the method from the SSJZ . CRT problems appear in earlier European arithmetic and can be solved by the method of the Sun Zi , as did Fibonacci. Secondly, we pro- vide evidence that remainder problems were treated within the European abbaco tradition independently of the CRT method. Finally, we discuss the role of recre- ational mathematics for the oral dissemination of sub-scientific knowledge. * Post-doctoral fellow of the Research Foundation Flanders (FWO). An early draft of this paper was presented at the Symposium in Honor of Chikara Sasaki, Mathematical Sciences & Philosophy in the Mediterranean & the East , 4 – 7 August, 2009, Kamena Vourla, Greece, and benefited from constructive com- ments by Roshdi Rashed and Li Wenlin. 88 A. HEEFFER 1 Introduction The title of this paper is inspired by the section heading of Gavin Men- zies’s latest book 1434 (Menzies 2008, p. 147) titled Regiomontanus’s Knowledge of Chinese Mathematics . Menzies already stirred considerable controversy with his first work titled 1421 (Menzies 2002) in which he claims that the Chinese fleet circumnavigated the world during the Ming and travelled to parts of the world yet undiscovered by the Europeans, such as the Americas.
    [Show full text]
  • R Epudiation 2 0
    HUMANIST REPUDIATION OF EASTERN INFLUENCES IN EARLY MODERN MATHEMATICS Albrecht Heeffer1 Centre for Logic and Philosophy of Science Ghent University INTRODUCTION At the beginning of the seventeenth century mathematics in Europe became radically different from mediaeval and Renaissance traditions. Renaissance humanism had a decisive influence on the transition of mediaeval to early modern mathematics. The scholarly tradition of qualitative arithmetic based on Boethian proportion theory passed into oblivion. A systematic program for reforming mathematics was initiated by the end of the fifteenth century by Johannes Regiomontanus and Giorgio Valla and further executed by Petrus Ramus, Jacques Peletier, Francoi Viète and Christopher Clavius. The aim was to provide new grounds for old traditions such as arithmetic and algebra and to set up sixteenth-century mathematics on Greek foundations. Together with their important contribution to the development of modern mathematics, humanists also created the myth that all mathematics, including algebra, descended from the ancient Greeks. Beginning with Regiomontanus’s 1464 lecture at Padua, humanist writers distanced themselves from “barbaric” influences. This paper concerns the humanist repudiation of eastern sources on which the greatest part of mediaeval mathematics depended. The reality was that, with some exceptions, ancient Greek mathematics was more foreign to European mathematics than Eastern influences which were well digested within the vernacular tradition. It was a cultural, not a conceptual distance between European and eastern mathematics that led humanists to repudiate the eastern roots of sixteenth-century mathematics. In a first part we will describe the state of mediaeval mathematics before 1464. We will make the distinction between scholarly and sub-scientific traditions and show that the greater part of the mathematical practice within the vernacular tradition relies on Arabic and Indian sources.
    [Show full text]
  • Regiomontanus and Trigonometry -.: Mathematical Sciences : UTEP
    Regiomontanus and Trigonometry The material presented in this teaching module is appropriate for an advanced high school or college trigonometry course. 1 The Early Years The development of what we now call trigonometry is historically very closely linked to astronomy. From the time of the ancient Greeks and through the Middle Ages astronomers used trigonometric ratios to calculate the positions of stars, planets and other heavenly bodies. It is for this reason that most of the people we associate with the development of trigonometry were astronomers as well as mathematicians. The foundations of modern trigonometry were laid sometime before 300 B.C.E., when the Babylonians divided the circle into 360 degrees. Within the next few centuries the Greeks adopted this measure of the circle, along with the further divisions of the circle into minutes and seconds. While attempting to explain the motions the planets, early astronomers found it necessary to solve for unknown sides and angles of triangles. The Greek astronomer Hipparchus (190-120 B.C.E) began a list of trigonometric ratios to aid in this endeavor. Hipparchus was also able to derive a half-angle formula for the sine [1]. The most influential book on ancient astronomy was the Mathematiki Syntaxis (Mathematical Collection), otherwise known as The Almagest, by Claudius Ptolemy (c. 100-178 C.E.). This masterwork contains a complete description of the Greek model of the universe, and is considered by many to be the culmination of Greek astronomy [1]. It is interesting to note that The Almagest is the only completely comprehensive work on Greek astronomy to survive to the modern era.
    [Show full text]
  • The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries Jean-Pierre Luminet
    The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries Jean-Pierre Luminet To cite this version: Jean-Pierre Luminet. The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries. International Review of Science, 2017. hal-01777594 HAL Id: hal-01777594 https://hal.archives-ouvertes.fr/hal-01777594 Submitted on 25 Apr 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries* Jean-Pierre Luminet Laboratoire d'Astrophysique de Marseille (LAM) CNRS-UMR 7326 & Centre de Physique Théorique de Marseille (CPT) CNRS-UMR 7332 & Observatoire de Paris (LUTH) CNRS-UMR 8102 France E-mail: [email protected] Abstract We discuss the reception of Copernican astronomy by the Provençal humanists of the XVIth- XVIIth centuries, beginning with Michel de Montaigne who was the first to recognize the potential scientific and philosophical revolution represented by heliocentrism. Then we describe how, after Kepler’s Astronomia Nova of 1609 and the first telescopic observations by Galileo, it was in the south of France that the New Astronomy found its main promotors with humanists and « amateurs écairés », Nicolas-Claude Fabri de Peiresc and Pierre Gassendi.
    [Show full text]
  • The Astronomy and Cosmology of Copernicus
    The Astronomy and Cosmology of Copernicus t was close to the northernmost coast of Europe, in the city of Torun, that the King of Poland and the Teutonic Knights signed I and sealed the Peace of 1466, which made West Prussia part of Polish territory. And it was in that city, just seven years later and precisely 500 years ago, in 1473, that Nicholas Copernicus was born. We know relatively few biographical facts about Copernicus and vir- tually nothing of his childhood. He grew up far from the centers of Renaissance innovation, in a world sti11largely dominated by medieval patterns of thought. But Copernicus and his contemporaries lived in an age of exploration and of change, and in their lifetimes they put to- gether a renewed picture of astronomy and geography, of mathematics and perspective, of anatomy, and of theology. I When Copernicus was ten years old, his father died, but fortunately his maternal uncle stepped into the breach. Uncle Lucas Watzenrode was then pursuing a successful career in ecclesiastical politics, and in 1489 he became Bishop of Varmia. Thus Uncle Lucas could easily send Copernicus and his younger brother to the old and distinguished University of Cracow. The Collegium Maius was then richly and un- usually endowed with specialists in mathematics and astronomy; Hart- mann Schedel, in his Nuremberg Chronicle of 1493, remarked that "Next to St. Anne's church stands a university, which boasts many Selection 9 reprinted from Highlights in Astronomy of the International Astronomical Union, ed. by G. Contopoulos, vol. 3 (1974), pp. 67-85. 162 ASTRONOMY AND COSMOLOGY OF COPERNICUS eminent and learned men, and where numerous arts are taught; the study of astronomy stands highest there.
    [Show full text]
  • Narratio Prima Or First Account of the Books on the Revolution by Nicolaus Copernicus
    Introduction There are few, if at all, examples of scientific books which successfully preceded the publication of a groundbreaking work, announcing it with considerable success which can be additionally measured by, for instance, the number of successive editions. There are no traces of such a vanguard enterprise announcing the Almagest by Ptolemy who in the middle of the 2nd century, in Alexandria, presented to the world his opus magnum of Hel- lenistic mathematical astronomy. Similarly unaided was Johannes Kepler’s Astronomia nova, propagating the idea of elliptic orbits. In 1687, Isaac Newton published the Principia, a work that was fundamental for contemporary celestial mechanics, and yet without any earlier lite version. Typically, it is the explicit acknowledgement of the scientific significance of a given work 9 which triggers elucidating commentaries, synopses and summaries aimed at readers of varying competence. It is also in this respect that the history of this book appears extraordinary, or in fact, unique. De revolutionibus by Nicolaus Copernicus is one of the most famous sci- entific works of all time. The book was published by a Nuremberg printer, Johannes Petreius, in spring 1543. Paradoxically enough, however, De revo- lutionibus was not the first to introduce heliocentric astronomy to Latin Eu- rope. For the three preceding years the geocentric world model had already been challenged by the Narratio prima. The book entitled the First Account of the Books «On the Revolutions» by Nicolaus Copernicus appeared in 1540 Narratio prima or First Account of the Books “On the Revolutions”… in Danzig (Gdańsk), and was reprinted in Basel the following year.
    [Show full text]
  • Where Did Copernicus Obtain the Tools to Build His Heliocentric
    Where Did Copernicus Obtain the Tools to Build His Heliocentric Model? Historical Considerations and a Guiding Translation of Valentin Rose’s “Ptolemaeus und die Schule von Toledo” (1874) Kevin Krisciunas Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843 USA and Bel´en Bistu´e CONICET, Universidad Nacional de Cuyo, Mendoza, Argentina Abstract We present a translation of the German text of an 1874 article by Valentin Rose that concerns the possible school of translators that worked in Toledo, Spain, from about 1150 to 1250. Rose’s article relies significantly on the first-hand account of the activities in Toledo by the Englishman Daniel of Morley. The most prolific translator in Toledo was Gerard of Cremona, who translated Ptolemy’s Almagest from Arabic into Latin with the help of Galib the Mozarab; this translation was significant to Copernicus’s work. Georg Peurbach and Regiomontanus based their Epitome of the Almagest (1463) on Gerard’s translation, which in turn introduced Greek astronomy to astronomers in Italy and throughout Europe. Copernicus studied in Padua in the first few years of the sixteenth century, where he learned about Ptolemy’s Almagest. Copernicus’s book De Revolutionibus (1543) also contains two geometrical tools of astronomers from thirteenth century Maragha, and his model of the arXiv:1712.05437v1 [physics.hist-ph] 14 Dec 2017 − motion of the Moon is mathematically identical to that of Ibn al-Shat.ir (fourteenth century Damascus). A Greek language manuscript written prior to 1308, and the residence in Padua of Moses Galeano, a Jewish scholar from Constantinople and Crete, who was familiar with − the work of Ibn al-Shat.ir, provide evidence of the transmission of Arabic astronomical ideas to Copernicus.
    [Show full text]
  • The Humanistic, Fideistic Philosophy of Philip Melanchthon (1497-1560)
    Marquette University e-Publications@Marquette Dissertations (2009 -) Dissertations, Theses, and Professional Projects The umH anistic, Fideistic Philosophy of Philip Melanchthon (1497-1560) Charles William Peterson Marquette University Recommended Citation Peterson, Charles William, "The umH anistic, Fideistic Philosophy of Philip Melanchthon (1497-1560)" (2012). Dissertations (2009 -). Paper 237. http://epublications.marquette.edu/dissertations_mu/237 THE HUMANISTIC, FIDEISTIC PHILOSOPHY OF PHILIP MELANCHTHON (1497-1560) by Charles W. Peterson, B.A., M.A., M. Div., S.T.M. A Dissertation Submitted to the Faculty of the Graduate School, Marquette University, in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Milwaukee, Wisconsin December 2012 ABSTRACT THE HUMANISTIC, FIDEISTIC PHILOSOPHY OF PHILIP MELANCHTHON (1497-1560): Charles W. Peterson, B.A., M.A., M.Div., S.T.M. Marquette University, 2012 This dissertation examines the way Philip Melanchthon, author of the Augsburg Confession and Martin Luther’s closest co-worker, sought to establish the relationship between faith and reason in the cradle of the Lutheran tradition, Wittenberg University. While Melanchthon is widely recognized to have played a crucial role in the Reformation of the Church in the sixteenth century as well as in the Renaissance in Northern Europe, he has in general received relatively little scholarly attention, few have attempted to explore his philosophy in depth, and those who have examined his philosophical work have come to contradictory or less than helpful conclusions about it. He has been regarded as an Aristotelian, a Platonist, a philosophical eclectic, and as having been torn between Renaissance humanism and Evangelical theology. An understanding of the way Melanchthon related faith and reason awaits a well-founded and accurate account of his philosophy.
    [Show full text]