Mathematical Astronomy in Copernicus’s De Revolutionibus

Swerdlow, N. M.; Neugebauer, O.

doi:10.1007/978-1-4613-8262-1

Cited by 141 publications

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“…27 The somewhat sinusoidal variations in the deviations (N -Aurifaber), however, suggest that Aurifaber may have used a pre-N version of the solar corrections. In 1541, the corrected solar anomaly (a) at the March and September cardinal points was close to 270° and 90°, respectively (Table 2, col. 7), i.e., places where the solar correction reaches its maximum.…”

Section: Cardinal Pointsmentioning

confidence: 94%

“…82v-83r); however, in M, this table exists in an earlier version derived from a slightly different value for the mean tropical motion (M, f. 93r-v). 26 The earlier version, however, shifts the total motion from Christ to 1541 by about 1;40 hours, and was not used by Aurifaber. My initial recomputation, using N and the tropical mean motions, matches Aurifaber's values fairly well (see Table 2, col. 4).…”

Section: Cardinal Pointsmentioning

confidence: 97%

“…I can remove this correlation by systematically multiplying the value of the solar correction, c 5 (a) + c 4 (θ) · c 6 (a), by 0.95 (best fit). 34 Since in 1541 c 4 (θ) remains very small, essentially I have reduced the values of c 5 (a) by 0.95, which would reduce the maximal solar correction from 1:51° to 1:45° and Copernicus's solar eccentricity in 1541 from 323 to 306 parts. In De revolutionibus III, 17, Copernicus compared values of the solar eccentricity from Ptolemy and al-Battānī, finding that the eccentricity had decreased over time, results mentioned by Rheticus in the Narratio prima.…”

Section: Syzygiesmentioning

confidence: 98%

“…In De revolutionibus III, 14, Copernicus provided two tables for the mean solar motion (tropical and sidereal) with epochs that differ (in both M and N) by 0;01°, a small amount in longitude that shifts the time of the Sun's entry into the cardinal points by about 0;03 hours. 25 My recomputation suggests that Aurifaber used the tropical mean motion table (N, ff. 82v-83r); however, in M, this table exists in an earlier version derived from a slightly different value for the mean tropical motion (M, f. 93r-v).…”

Section: Cardinal Pointsmentioning

confidence: 99%

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Calculating with Andreas Aurifaber: A New Source for Copernican Astronomy in 1540

Kremer

2010

Journal for the History of Astronomy

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In an article recently published in this journal, Jonathan Green announced his discovery of the earliest known printed astrological practica that mentions Copernicus. Apparently extant in a single copy, this Practica auff das Jar M.D.XLI. durch Magistrum Andream Aurifaber gestellet claims to have been computed "from the tables of Nicholas Copernicus" (Figure 1). 1 Although this imprint has been known, bibliographically, since at least 1874, no one before Green, to the best of my knowledge, noticed the remarks about Copernicus in its dedication, although previous historians have documented biographical links between the practica's author, Andreas Aurifaber (1514-59), and several well-known early Copernicans. Was Aurifaber's practica indeed "Copernican"? Might it be possible, from quantitative material therein, to reconstruct the "Copernican tables" from which it claims to have been computed? And might such a reconstruction, based on a source printed three years before the publication of Copernicus's De revolutionibus, shed light on the chronology of the composition of this latter book? Green hinted at these questions but did not pursue them; to do so is the goal of this paper. 2 Consisting of thirteen folios filled with the usual astrological content found in the dozens of German practica editions printed in the 1530s and 1540s, Aurifaber's little pamphlet perhaps not surprisingly escaped notice before Green's discovery. But many threads tie the 1541 practica and its author to Copernicus and the early Copernicans. With its dedicatory letter to the Danzig City Council dated 11 November 1540, this practica probably was printed in late November or December. The colophon identifies the printer as Franz Rhode of Danzig, who had issued Georg Joachim Rheticus's Narratio prima earlier that year. 3 Not a vigorous printing centre, Danzig had only three printshops active in the sixteenth century; Aurifaber's was the only annual calendar, almanac or practica to have been printed in that city before 1580. 4 Against this paucity of astronomical publishing in Danzig, Rhode's two 1540 imprints hence stand out sharply.As Green noted, Aurifaber had met Rheticus in the 1530s at the University of Wittenberg, where both men studied under Philipp Melanchthon. In 1539, as Rheticus headed north to Frauenburg, Aurifaber on Melanchthon's recommendation became first rector of the newly opened St Mary's Latin School in Danzig (about 60 km west of Frauenburg). At Rheticus's request, Aurifaber in February 1540 sent Melanchthon a few sheets from the Narratio prima, then being printed. In April 1540, upon receiving his copy of the Narratio, Duke Albrecht von Hohenzollern described the work as "issued by Magister Joachim Rheticus with his assistant Magister Andreas Aurifaber, schoolmaster in Danzig". Modern editors of the Narratio have suggested

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Section: Cardinal Pointsmentioning

confidence: 94%

Section: Cardinal Pointsmentioning

confidence: 97%

Section: Syzygiesmentioning

confidence: 98%

Section: Cardinal Pointsmentioning

confidence: 99%

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Calculating with Andreas Aurifaber: A New Source for Copernican Astronomy in 1540

Kremer

2010

Journal for the History of Astronomy

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“…title of Copernicus' book De Revolutionibus Orbium Caelestium where the Latin orbis can mean either sphere or circle) from interfering with each other. SeeSwerdlow (1973),Swerdlow and Neugebauer (1984).3 In the traditional view, the anomaly that led Copernicus to reject the geocentric system was the need to add more and more epicycles-even ''epicycles on epicycles''-in order to accommodate more accurate observations. This view is now discredited; seeGingerich (1975).…”

mentioning

confidence: 98%

Mathematics as an Instigator of Scientific Revolutions

Brush¹

2015

Sci & Educ

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In a famous 1960 paper, Wigner discussed ''The Unreasonable Effectiveness of Mathematics in the Natural Sciences.'' I suggest that the effectiveness of mathematics in producing successful new theories and surprising discoveries is even more unreasonable than Wigner claimed. In this paper, I present several historical case studies to support the claim that mathematics is often responsible for instigating scientific revolutions. However, that does not mean that mathematics is always the key to the universe, and other cases where mathematization was not successful are discussed in order to problematize a naïve Platonism.

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Copernicus's Heliograph at Olsztyn: The 500th Anniversary of a Scientific Milestone

Graßhoff

Fischer

2018

Annalen der Physik

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Exactly 500 years ago, Nicolaus Copernicus drew a lattice of lines on a panel above the doorway to his rooms at Olsztyn Castle, then in the Bishopric of Warmia. Although its design has long been regarded as some kind of reflecting vertical sundial, the exact astronomical designation of the lines and related measuring techniques remained unknown. Surprisingly, Copernicus did not refer to his new observational methods in his principal work, De Revolutionibus. A data analysis of a 3D model of the panel has, at last, solved the mystery: Copernicus created a new type of measuring device -a heliograph with a non-local reference meridian -to precisely measure ecliptic longitudes of the Sun around the time of the equinoxes. The data, 3D model and modeling results of our analysis are open access and available in the form of digital (Jupyter) notebooks. Copernicus | heliograph | scientific revolution | astronomical measurement |

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Mathematical Astronomy in Copernicus’s De Revolutionibus

Cited by 141 publications

References 0 publications

Calculating with Andreas Aurifaber: A New Source for Copernican Astronomy in 1540

Calculating with Andreas Aurifaber: A New Source for Copernican Astronomy in 1540

Mathematics as an Instigator of Scientific Revolutions

Copernicus's Heliograph at Olsztyn: The 500th Anniversary of a Scientific Milestone

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