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Copernican Revolution

From Wikipedia, the free encyclopedia
16th- to 17th-century intellectual revolution
For other uses, seeThe Copernican Revolution (disambiguation).
Motion of theSun (yellow),Earth (blue), andMars (red). At left, Copernicus'sheliocentric motion. At right, traditionalgeocentric motion, including theretrograde motion of Mars. For simplicity, Mars's period of revolution is depicted as 2 years instead of 1.88, andorbits are depicted as perfectly circular orepitrochoid.

In the 16th century,Nicolaus Copernicus proposed a major shift in the understanding of the cycle of theheavenly spheres. Driven by a desire for a more perfect (i.e. circular) description of the cosmos than the prevailingPtolemaic model - which posited that the Sun circled a stationary Earth - Copernicus instead advanced a heliostatic system where a stationary Sun was located near, though not precisely at, the mathematical center of the heavens. In the 20th century, thescience historianThomas Kuhn characterized the "Copernican Revolution" as the first historical example of aparadigm shift in human knowledge.[1] BothArthur Koestler[2] andDavid Wootton[3], on the other hand, have disagreed with Kuhn about how revolutionary Copernicus' work should be considered.

Heliocentrism

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Before Copernicus

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Main article:Heliocentrism

The "Copernican Revolution" is named forNicolaus Copernicus, whoseCommentariolus, written before 1514, was the first explicit presentation of the heliocentric model in Renaissance scholarship. The idea of heliocentrism is much older; it can be traced toAristarchus of Samos, a Hellenistic author writing in the 3rd century BC, who may in turn have been drawing on even older concepts inPythagoreanism. Ancient heliocentrism was, however, eclipsed by the geocentric model presented byPtolemy in theAlmagest and accepted inAristotelianism.

Martianus Capella (5th century CE) expressed the opinion that the planets Venus and Mercury did not go about the Earth but instead circled the Sun.[4] Capella's model was discussed in theEarly Middle Ages by various anonymous 9th-century commentators[5] and Copernicus mentions him as an influence on his own work.[6]Macrobius (420 CE) described a heliocentric model.[7]John Scotus Eriugena (815-877 CE) proposed a model reminiscent of that from Tycho Brahe.[7]

European scholars were well aware of the problems with Ptolemaic astronomy by the 13th century. The debate was precipitated by thereception byAverroes's criticism of Ptolemy, and it was again revived by the recovery of Ptolemy's text and its translation into Latin in the mid-15th century.[a]Otto E. Neugebauer in 1957 argued that the debate in 15th-century Latin scholarship must also have been informed by the criticism of Ptolemy produced after Averroes, by theIlkhanid-era (13th to 14th centuries) Persian school of astronomy associated with theMaragheh observatory (especially the works ofAl-Urdi,Al-Tusi andIbn al-Shatir).[9]

The state of the question as received by Copernicus is summarized in theTheoricae novae planetarum byGeorg von Peuerbach, compiled from lecture notes by Peuerbach's studentRegiomontanus in 1454 but printed only in 1472.Peuerbach attempts to give a new, mathematically more elegant presentation of Ptolemy's system, but he does not arrive at heliocentrism. Regiomontanus himself was the teacher ofDomenico Maria Novara da Ferrara, who was in turn the teacher of Copernicus.

There is a possibility that Regiomontanus already arrived at a theory of heliocentrism before his death in 1476, as he paid particular attention to the heliocentric theory ofAristarchus in a later work, and mentions the "motion of the Earth" in a letter.[10]

Nicolaus Copernicus

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Main articles:Nicolaus Copernicus andCopernican heliocentrism
Nicolaus Copernicus's heliocentric model

Copernicus studied atBologna University during 1496–1501, where he became the assistant ofDomenico Maria Novara da Ferrara. He is known to have studied theEpitome in Almagestum Ptolemei by Peuerbach and Regiomontanus (printed in Venice in 1496) and to have performed observations of lunar motions on 9 March 1497. Copernicus went on to develop an explicitly heliocentric model[citation needed] of planetary motion, at first written in his short workCommentariolus some time before 1514, circulated in a limited number of copies among his acquaintances. He continued to refine his system until publishing his larger work,De revolutionibus orbium coelestium (1543), which contains detailed diagrams and tables.[11]

The Copernican model makes the claim of describing the physical reality of the cosmos, something which the Ptolemaic model was no longer believed to be able to provide. Copernicus removed Earth from the center of the universe, set the heavenly bodies in rotation around the Sun, and introduced Earth's daily rotation on its axis.[11] While Copernicus's work sparked the "Copernican Revolution", it did not mark its end. In fact, Copernicus's own system had multiple shortcomings that would have to be amended by later astronomers and led to our current understanding of astronomy.

Copernicus did not only come up with a theory regarding the nature of the Sun in relation to the Earth, but thoroughly worked to debunk some of the minor details within the geocentric theory.[12] In his article about heliocentrism as a model, author Owen Gingerich writes that in order to persuade people of the accuracy of his model, Copernicus created a mechanism in order to return the description of celestial motion to a “pure combination of circles.”[13] Copernicus’s theories made a lot of people uncomfortable and somewhat upset. Copernicus was criticised because his theories did not completely align with the teachings of theCatholic Church,[14] leading to the laterGalileo affair. Even with the scrutiny that he faced regarding his conjecture that the universe was not centered around the Earth, he continued to gain support- other scientists and astrologists even posited that his system allowed a better understanding of astronomy concepts than did the geocentric theory.

Reception

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Tycho Brahe

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Main article:Tycho Brahe
Tycho Brahe's geoheliocentric model

Tycho Brahe (1546–1601) was aDanishnobleman who was well known as an astronomer in his time. Further advancement in the understanding of the cosmos would require new, more accurate observations than those thatNicolaus Copernicus relied on and Tycho made great strides in this area. Tycho formulated a geoheliocentrism, meaning the Sun moved around the Earth while the planets orbited the Sun, known as theTychonic system. Although Tycho appreciated the advantages of Copernicus's system, he like many others could not accept the movement of the Earth.[15]

In 1572, Tycho Brahe observed a new star in the constellationCassiopeia. For eighteen months, it shone brightly in the sky with no visibleparallax, indicating it was part of the heavenly region of stars according toAristotle's model. However, according to that model, no change could take place in the heavens so Tycho's observation was a major discredit to Aristotle's theories. In 1577, Tycho observed agreat comet in the sky. Based on his parallax observations, the comet passed through the region of theplanets. According to Aristotelian theory, only uniform circular motion on solid spheres existed in this region, making it impossible for a comet to enter this region. Tycho concluded there were no such spheres, raising the question of what kept a planet inorbit.[15]

With thepatronage of the King of Denmark, Tycho Brahe establishedUraniborg, anobservatory in Hven.[16] For 20 years, Tycho and his team of astronomers compiled astronomical observations that were vastly more accurate than those made before. These observations would prove vital in future astronomical breakthroughs.

Johannes Kepler

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Main article:Johannes Kepler
Kepler'sPlatonic solid model of theSolar System fromMysterium Cosmographicum

Kepler found employment as an assistant to Tycho Brahe and, upon Brahe's unexpected death, replaced him as imperial mathematician ofEmperor Rudolph II. He was then able to use Brahe's extensive observations to make remarkable breakthroughs in astronomy, such as thethree laws of planetary motion. Kepler would not have been able to produce his laws without the observations of Tycho, because they allowed Kepler to prove that planets traveled in ellipses, and that the Sun does not sit directly in the center of an orbit but at a focus.Galileo Galilei came after Kepler and developed his owntelescope with enough magnification to allow him to studyVenus and discover that it hasphases like a moon. The discovery of the phases of Venus was one of the more influential reasons for the transition fromgeocentrism toheliocentrism.[17] Sir Isaac Newton'sPhilosophiæ Naturalis Principia Mathematica concluded the Copernican Revolution. The development of his laws of planetary motion anduniversal gravitation explained the presumed motion related to the heavens by asserting a gravitational force of attraction between two objects.[18]

In 1596, Kepler published his first book, theMysterium Cosmographicum, which was the second (afterThomas Digges, in 1576) to endorse Copernican cosmology by an astronomer since 1540.[15] The book described his model that usedPythagorean mathematics and the fivePlatonic solids to explain the number of planets, their proportions, and their order. The book garnered enough respect from Tycho Brahe to invite Kepler toPrague and serve as his assistant.

In 1600, Kepler set to work on the orbit ofMars, the second most eccentric of the six planets known at that time. This work was the basis of his next book, theAstronomia nova, which he published in 1609. The book argued heliocentrism and ellipses for planetary orbits instead of circles modified by epicycles. This book contains the first two of his eponymous three laws of planetary motion. In 1619, Kepler published his third and final law which determined the relation between orbital period and orbital path of planets.[19]

Kepler's work in astronomy was new in part. Unlike those who came before him, he discarded the assumption that planets moved in a uniform circular motion, replacing it withelliptical motion. Also, like Copernicus, he asserted the physical reality of a heliocentric model as opposed to a geocentric one. Yet, despite all of his breakthroughs, Kepler could not explain the physics that would keep a planet in its elliptical orbit.

Kepler's laws of planetary motion

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Main article:Kepler's laws of planetary motion
1. The Law of Ellipses: All planets move in elliptical orbits, with the Sun at one focus.
2. The Law of Equal Areas in Equal Time: A line that connects a planet to the Sun sweeps out equal areas in equal times.
3. The Law of Harmony: The time required for a planet to orbit the Sun, called its period, is proportional to long axis of the ellipse raised to the 3/2 power. The constant of proportionality is the same for all the planets.

Galileo Galilei

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Main article:Galileo Galilei
In 1610Galileo Galilei observed with his telescope thatVenus showed phases, despite remaining near the Sun in Earth's sky (first image). This proved that it orbits theSun and notEarth, as predicted byCopernicus'sheliocentric model and disproved the then conventionalgeocentric model (second image).

Galileo Galilei was an Italian scientist who is sometimes referred to as the "father of modernobservational astronomy".[20] His improvements to thetelescope, astronomical observations, and support for Copernicanism were all integral to the Copernican Revolution.

Based on the designs ofHans Lippershey, Galileo designed his own telescope which, in the following year, he had improved to 30x magnification.[21] Using this new instrument, Galileo made a number of astronomical observations which he published in theSidereus Nuncius in 1610. In this book, he described the surface of theMoon as rough, uneven, and imperfect. He also noted that "the boundary dividing the bright from the dark part does not form a uniformly oval line, as would happen in a perfectly spherical solid, but is marked by an uneven, rough, and very sinuous line, as the figure shows."[22] These observations challenged Aristotle's claim that the Moon was a perfect sphere and the larger idea that the heavens were perfect and unchanging.

Galileo's next astronomical discovery would prove to be a surprising one. While observingJupiter over the course of several days, he noticed four stars close to Jupiter whose positions were changing in a way that would be impossible if they were fixed stars. After much observation, he concluded these four stars were orbiting the planet Jupiter and were in fact moons, not stars.[23] This was a radical discovery because, according to Aristotelian cosmology, all heavenly bodies revolve around the Earth and a planet with moons obviously contradicted that popular belief.[24] While contradicting Aristotelian belief, it supported Copernican cosmology which stated that Earth is a planet like all others.[25]

In 1610, Galileo observed that Venus had a full set of phases, similar to the phases of the moon we can observe from Earth. This was explainable by the Copernican or Tychonic systems which said that all phases of Venus would be visible due to the nature of its orbit around the Sun, unlike the Ptolemaic system which stated only some of Venus's phases would be visible. Due to Galileo's observations of Venus, Ptolemy's system became highly suspect and the majority of leading astronomers subsequently converted to various heliocentric models, making his discovery one of the most influential in the transition from geocentrism to heliocentrism.[17]

Sphere of the fixed stars

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Main article:Fixed stars

In the sixteenth century, a number of writers inspired by Copernicus, such asThomas Digges,[26]Giordano Bruno[27] andWilliam Gilbert[28] argued for an indefinitely extended or even infinite universe, with other stars as distant suns. This contrasts with the Aristotelian view of asphere of the fixed stars. Although opposed by Copernicus and (initially) Kepler, in 1610 Galileo made his telescopic observation of the faint strip of theMilky Way, which he found it resolves in innumerable white star-like spots, presumably farther stars themselves.[29] By the middle of the 17th century, this new view became widely accepted, partly due to the support ofRené Descartes.

Isaac Newton

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Main article:Isaac Newton
Title page of Newton's 'Philosophiæ Naturalis Principia Mathematica', first edition (1687)

Newton was a well known Englishphysicist andmathematician who was known for his bookPhilosophiæ Naturalis Principia Mathematica.[30] He was a main figure in theScientific Revolution for hislaws of motion anduniversal gravitation. The laws of Newton are said to be the ending point of the Copernican Revolution.[by whom?]

Newton used Kepler's laws of planetary motion to derive his law of universal gravitation. Newton's law of universal gravitation was the first law he developed and proposed in his bookPrincipia. The law states that any two objects exert agravitational force of attraction on each other. The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them.[18] Along with Newton's law of universal gravitation, thePrincipia also presents his three laws of motion. These three laws explain inertia, acceleration, action and reaction when a net force is applied to an object.

Metaphorical usage

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Immanuel Kant

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Immanuel Kant in hisCritique of Pure Reason (1787 edition) drew a parallel between the Copernican hypothesis and theepistemology of his newtranscendental philosophy.[31] Kant's comparison is made in the Preface to the second edition of theCritique of Pure Reason (published in 1787; a heavy revision of the first edition of 1781). Kant argues that, just as Copernicus moved from the supposition of heavenly bodies revolving around a stationary spectator to a moving spectator, so metaphysics, "proceeding precisely on the lines of Copernicus' primary hypothesis", should move from assuming that "knowledge must conform to objects" to the supposition that "objects must conform to our [a priori] knowledge".[b]

Much has been said on what Kant meant by referring to his philosophy as "proceeding precisely on the lines of Copernicus' primary hypothesis". There has been a long-standing discussion on the appropriateness of Kant's analogy because, as most commentators see it, Kant inverted Copernicus's primary move.[33] According toTom Rockmore,[34] Kant himself never used the "Copernican revolution" phrase about himself, though it was "routinely" applied to his work by others.

After Kant

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Further information:Copernican principle

Following Kant, the phrase "Copernican Revolution" in the 20th century came to be used for any (supposed)paradigm shift, for example in reference toFreudianpsychoanalysis[35] orcontinental philosophy andanalyticlinguistic philosophy.[36]

See also

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Notes

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  1. ^"Averroes' criticism of Ptolemaic astronomy precipitated this debate in Europe. [...] The recovery of Ptolemy's texts and their translation from Greek into Latin in the middle of the fifteenth century stimulated further consideration of these issues."[8]
  2. ^In an English translation: "Hitherto it has been assumed that all our knowledge must conform to objects. But all attempts to extend our knowledge of objects by establishing something in regard to thema priori, by means of concepts, have, on this assumption, ended in failure. We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge. This would agree better with what is desired, namely, that it should be possible to have knowledge of objectsa priori, determining something in regard to them prior to their being given. We should then be proceeding precisely on the lines of Copernicus's primary hypothesis. Failing of satisfactory progress in explaining the movements of the heavenly bodies on the supposition that they all revolved round the spectator, he tried whether he might not have better success if he made the spectator to revolve and the stars to remain at rest. A similar experiment can be tried in metaphysics, as regards theintuition of objects."[32]

References

[edit]
  1. ^Kuhn, Thomas (1962). The Structure of Scientific Revolutions.
  2. ^"The figure of Copernicus, seen from the distance, is that of an intrepid, revolutionary hero of thought. As we come closer, it gradually changes into that of a stuffy pendant, without the flair, the sleepwalking intuition of the original genius; who, having got hold of a good idea, expanded it into a bad system, patiently plodding on, piling more epicycles and deferents into the dreariest and most unreadable among the books that made history....The Copernican system is not a discovery...but a last attempt to patch up an out-dated machinery by reversing the arrangement of its wheels. As a modern historian put it, the fact that the earth moves is 'almost an incidental matter in the system of Copernicus which, viewed geometrically, is just the old Ptolemaic pattern of the skies, with one or two wheels interchanged and one or two of them taken out.'" Koestler, Arthur (1959). The Sleepwalkers. The Macmillan Company. p. 205 & p. 214
  3. ^"It used to be thought that Copernicus initiated an intellectual revolution - indeed Thomas Kuhn called his first bookThe Copernican Revolution (1957). But in this Kuhn was mistaken." Wootton, David (2015). The Invention of Science: A New History of the Scientific Revolution. p.145
  4. ^ William Stahl, trans.,Martianus Capella and the Seven Liberal Arts, vol. 2,The Marriage of Philology and Mercury, 854, 857, New York: Columbia Univ. Pr, 1977, pp. 332–333
  5. ^Eastwood, Bruce S. (2007),Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, Leiden: Brill, pp. 244–259,ISBN 978-90-04-16186-3
  6. ^Eastwood, Bruce S. (1982), "Kepler as Historian of Science: Precursors of Copernican Heliocentrism according toDe revolutionibus I, 10",Proceedings of the American Philosophical Society,126:367–394.
  7. ^abCarman, Christián C. (2017-12-23)."The first Copernican was Copernicus: the difference between Pre-Copernican and Copernican heliocentrism".Archive for History of Exact Sciences.72 (1):1–20.doi:10.1007/s00407-017-0198-3.hdl:11336/72174.ISSN 0003-9519.
  8. ^Osler (2010), p. 42
  9. ^George Saliba (1979). "The First Non-Ptolemaic Astronomy at the Maraghah School", Isis 70 (4), pp. 571–576.
  10. ^Arthur Koestler,The Sleepwalkers, Penguin Books, 1959, p. 212.
  11. ^abOsler (2010), p. 44
  12. ^Rushkin, Ilia (6 February 2015). "Optimizing the Ptolemaic Model of Planetary and Solar Motion".History and Philosophy of Physics.1:1–13.arXiv:1502.01967.Bibcode:2015arXiv150201967R.
  13. ^Gingerich, Owen (1973). "From Copernicus to Kepler: Heliocentrism as Model and as Reality".Proceedings of the American Philosophical Society.117 (6):513–522.Bibcode:1973PAPhS.117..513G.ISSN 0003-049X.JSTOR 986462.
  14. ^Maurice A Finocchario. (February 1,2016) 400 Years Ago the Catholic Church Prohibited Copernicanism* Origins.osu.edu
  15. ^abcOsler (2010), p. 53
  16. ^J J O'Connor and E F Robertson. Tycho Brahe biography. April 2003. Retrieved 2008-09-28
  17. ^abThoren (1989), p. 8
  18. ^abNewton, Isaac (1999).The Principia: Mathematical Principles of Natural Philosophy. Translated by I. Bernard Cohen; Anne Whitman; Julia Budenz. Berkeley: University of California Press.ISBN 0-520-08817-4.
  19. ^"Orbits and Kepler's Laws - NASA Science".NASA. 2008-06-26. Retrieved2025-07-07.
  20. ^Singer (1941), p. 217
  21. ^Drake (1990), pp. 133-134
  22. ^Galileo, Helden (1989), p. 40
  23. ^Drake (1978), p. 152
  24. ^Drake (1978), p. 157
  25. ^Osler (2010), p. 63
  26. ^Hellyer, Marcus, ed. (2008).The Scientific Revolution: The Essential Readings. Blackwell Essential Readings in History. Vol. 7.John Wiley & Sons. p. 63.ISBN 9780470754771.The Puritan Thomas Digges (1546–1595?) was the earliest Englishman to offer a defense of the Copernican theory. ... Accompanying Digges's account is a diagram of the universe portraying the heliocentric system surrounded by the orb of fixed stars, described by Digges as infinitely extended in all dimensions.
  27. ^Bruno, Giordano."Third Dialogue".On the infinite universe and worlds. Archived fromthe original on 27 April 2012.
  28. ^Gilbert, William (1893). "Book 6, Chapter III".De Magnete. Translated by Mottelay, P. Fleury. (Facsimile). New York: Dover Publications.ISBN 0-486-26761-X.{{cite book}}:ISBN / Date incompatibility (help)
  29. ^Galileo Galilei,Sidereus Nuncius (Venice, (Italy): Thomas Baglioni, 1610),pages 15 and 16.Archived March 16, 2016, at theWayback Machine
    English translation: Galileo Galilei with Edward Stafford Carlos, trans.,The Sidereal Messenger (London: Rivingtons, 1880),pages 42 and 43.Archived December 2, 2012, at theWayback Machine
  30. ^See thePrincipia online atAndrew Motte Translation
  31. ^Ermanno Bencivenga (1987),Kant's Copernican Revolution.
  32. ^Immanuel Kant (1929) [1787]."Preface".Critique of Pure Reason. Translated byNorman Kemp Smith. Palgrave Macmillan.ISBN 1-4039-1194-0. Archived fromthe original on 2009-04-16.{{cite book}}:ISBN / Date incompatibility (help)
  33. ^For an overview see Engel, M.,Kant’s Copernican Analogy: A Re-examination, Kant-Studien, 54, 1963, p. 243. According toVictor Cousin: "Copernicus, seeing it was impossible to explain the motion of the heavenly bodies on the supposition that these bodies moved around the earth considered as an immovable centre, adopted the alternative, of supposing all to move round the sun. So Kant, instead of supposing man to move around objects, supposed on the contrary, that he himself was the centre, and that all moved round him." Cousin, Victor,The Philosophy of Kant. London: John Chapman, 1854, p. 21
  34. ^Tom Rockmore,Marx After Marxism: The Philosophy of Karl Marx (2002), p. 184.
  35. ^"By defining hysteria as an illness whose symptoms were produced by a person's unconscious ideas, Freud started what can be called a ‘Copernican Revolution’ in the understanding of mental illness — which put him into opposition both to the Parisian Charcot and to the German and Austrian scientific community." José Brunner,Freud and the Politics of Psychoanalysis (2001), p. 32.
  36. ^"Jacques Lacan's formulation that the unconscious, as it reveals itself in analytic phenomena, ‘is structured like a language’, can be seen as a Copernican revolution (of sorts), bringing together Freud and the insights of linguistic philosophers and theorists such asRoman Jakobson." Ben Highmore,Michel de Certeau: Analysing Culture (2006), p. 64.

Works cited

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  • Bala, Arun (2006).The Dialogue of Civilizations in the Birth of Modern Science. New York: Palgrave Macmillan.ISBN 978-0-230-60121-5.OCLC 191662056.
  • Drake, Stillman (1978).Galileo At Work. Chicago: University of Chicago Press.ISBN 0-226-16226-5.
  • Drake, Stillman (1990).Galileo: Pioneer Scientist. Toronto:The University of Toronto Press.ISBN 0-8020-2725-3.
  • Galilei, Galileo (1989).Sidereus Nuncius. Albert Van Helden (trans.). Chicago, Illinois: University of Chicago Press.ISBN 9780226279039.
  • Gillies, Donald. (2019). Why did the Copernican revolution take place in Europe rather than China?.https://www.researchgate.net/publication/332320835_Why_did_the_Copernican_revolution_take_place_in_Europe_rather_than_China
  • Gingerich, Owen. "From Copernicus to Kepler: Heliocentrism as Model and as Reality".Proceedings of the American Philosophical Society 117, no. 6 (December 31, 1973): 513–22.
  • Huff, Toby E. (2017).The Rise of Early Modern Science. Cambridge: Cambridge University Press.ISBN 9781316417805.
  • Huff, Toby E. (Autumn–Winter 2002). "The Rise of Early Modern Science: A Reply to George Sabila".Bulletin of the Royal Institute of Inter-Faith Studies (BRIIFS).4, 2.
  • Kuhn, Thomas S. (1957).The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Cambridge, Massachusetts: Harvard University Press.ISBN 0-674-17103-9.{{cite book}}:ISBN / Date incompatibility (help)
  • Kuhn, Thomas S. (1970).The Structure of Scientific Revolutions. Chicago: Chicago University Press.ISBN 0226458032.
  • Kunitzch, Paul. "The Arabic Translations of Ptolemy's Almagest". Qatar Digital Library, July 31, 2018. https://www.qdl.qa/en/arabic-translations-ptolemys-almagest.
  • Koyré, Alexandre (2008).From the Closed World to the Infinite Universe. Charleston, S.C.: Forgotten Books.ISBN 9781606201435.
  • Lawson, Russell M.Science in the Ancient World: An Encyclopedia. Santa Barbara, CA: ABC-CLIO, 2004.
  • Lin, Justin Y. (1995).The Needham Puzzle: Why the Industrial Revolution Did Not Originate in China.Economic Development and Cultural Change, 43(2), 269–292. Retrieved fromJSTOR 1154499.
  • Metzger, Hélène (1932). Histoire des sciences.Revue Philosophique De La France Et De L'Étranger,114, 143–155. Retrieved fromJSTOR 41086443.
  • Osler, Margaret (2010).Reconfiguring the World. Baltimore, Maryland: The Johns Hopkins University Press. p. 184.ISBN 978-0-8018-9656-9.
  • Redd, Nola (May 2012)."Johannes Kepler Biography". Tech Media Network. RetrievedOctober 23, 2013.
  • Rushkin, Ilia. "Optimizing the Ptolemaic Model of Planetary and Solar Motion".History and Philosophy of Physics 1 (February 6, 2015): 1–13.
  • Saliba, George (1979). "The First Non-Ptolemaic Astronomy at the Maraghah School".Isis.70 (4).ISSN 0021-1753.
  • Sabila, George (Autumn 1999). "Seeking the Origins of Modern Science?".Bulletin of the Royal Institute for Inter-Faith Studies (BRIIFS).1, 2.
  • Sabila, George (Autumn–Winter 2002). "Flying Goats and Other Obsessions: A Response to Toby Huff's "Reply"".Bulletin of the Royal Institute for Inter-Faith Studies (BRIIFS).4, 2.
  • Singer, Charles (2007).A Short History of Science to the Nineteenth Century. Clarendon Press.
  • Swetz, Frank J. "Mathematical Treasure: Ptolemy's Almagest". Mathematical Treasure: Ptolemy's Almagest | Mathematical Association of America, August 2013. https://www.maa.org/press/periodicals/convergence/mathematical-treasure-ptolemy-s-almagest.
  • Thoren, Victor E. (1989).Tycho Brahe. InTaton and Wilson (1989, pp. 3–21). Cambridge University Press.ISBN 0-521-35158-8.

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