Christianity and the Mathematical Sciences - the Heliocentric Hypothesis

The mathematician Freeman Dyson writes in [16]:-
... Western science grew out of Christian theology. It is probably not an accident that modern science grew explosively in Christian Europe and left the rest of the world behind. A thousand years of theological disputes nurtured the habit of analytical thinking that could be applied to the analysis of natural phenomena. On the other hand, the close historical relations between theology and science have caused conflicts between science and Christianity that do not exist between science and other religions ...
Christianity has been a major influence on the mathematical sciences, particularly in the 17th and 18th Centuries. There is a widespread belief that Christianity and science, particularly mathematical science, were on opposing sides through this period. However, this oversimplifies the situation to such an extent that it gives a quite false impression of the development of the mathematical sciences through this important time. For example four men who perhaps did as much as any to revolutionise the mathematical sciences in the 16th and 17th Centuries, Copernicus, Kepler, Galileo and Newton, were all deeply religious Christians who in many ways saw their scientific work as a religious undertaking. In this article we look at theories of the structure of the universe and how religion reacted to major advances in the mathematical sciences on this issue.

In order to understand the subtleties of the interaction between Christianity and the mathematical sciences through the 16th and 17th Centuries we need to go back to the Greek philosophers long before the rise of the Christian church. A good starting point is to look briefly at Pythagoras, for he developed a world-view in which mathematics and religion were completely linked. Pythagoras saw the beauty in the theory of numbers and he saw this mathematical beauty translated into musical beauty. From there he developed a view of the world based on numbers and shapes. He believed that the Earth was a sphere, not for any experimental reason, but simply because he believed that the sphere was the most perfect shape, so the Earth had to be a sphere. He also believed that the Earth was not at the centre of the universe but that the Earth moved. Russell notes not only the impact of Pythagoras on science but also on Christian thinking [11]:-
The whole conception of an eternal world, revealed to the intellect but not to the senses, is derived from [Pythagoras]. But for him, Christians would not have thought of Christ as the Word [logos of John's Gospel]; but for him, theologians would not have sought logical proofs of God and immortality.
Carl B Boyer, the famous historian of mathematics, noted the unique interplay of mathematics and religion in the ideas developed by the Pythagoreans:-
Never before or since has mathematics played so large a role in life and religion as it did among the Pythagoreans.
The two ancient Greek philosophers who exerted the most influence on Christianity were Plato and Aristotle. It is impossible to summarise the contributions of these two outstanding philosophers in a few words but we shall give a little information about their ideas which are most relevant to this article.

Plato's theory of ideas makes meaning and concepts as fundamental and real, while the physical realisation of these ideas was not real and of lesser importance. For example the idea of a book is real while the many physical examples of books are only seen as apparent. He saw mathematics as providing the most fundamental of all ideas and the deductive reasoning of mathematics was seen as the ideal way of achieving knowledge. Like Pythagoras, Plato saw the sphere as the ideal shape so argued that the Earth must be a sphere. Similarly circles were the most perfect curves, so planets had to move in circles. He gave a theory of creation based on a good God who created an eternal world by turning disorder into order. God put intelligence into the soul, and the soul into man. However, real knowledge could not be gained through the senses [11]:-
... if we would have true knowledge of anything, we must leave the body. ... While in company with the body, the soul cannot have true knowledge.
Aristotle bases his philosophy on that of Plato but he improved and modified it in various ways. He was an extremely religious man and discussed God at length in his works. He gives a proof of the existence of God in Metaphysics based on a mathematical argument of motion. Every motion has a cause and so there must be a First Cause of motion which is God. Russell [11] gives Aristotle's ideas of God:-
Life also belongs to God; the actuality of thought is life, and God is that actuality; and God's self-dependent actuality is life most good and eternal. We say therefore that God is a living being, eternal, most good, so that life and duration continuous and eternal belong to God; for this is God.
Unlike Plato, Aristotle does not see God as the creator of the world, for the world had always existed. Aristotle's view of the world was based on a spherical Earth round which there were crystalline spheres which carried the Sun, Moon and planets. He attributed 'natural' properties to substances and these dictated their motion. For example a stone is by nature part of the Earth so its nature makes it fall to Earth. This is a physics based on necessity and not on purpose. Aristotle gave a system of logical deduction which was seen as the ultimate form for reasoning for many centuries.

We have discussed Greek philosophers at some length in an article on Christianity and the mathematical sciences. Although their relation to the mathematical sciences is probably well understood by most readers, their relation to Christianity may be less well known. Christianity arose in a number of competing versions and it was not until near the end of the fourth century AD that the Catholic version became dominant throughout the Roman Empire. Shortly after this Augustine, born in 354, developed Christian theology after his conversion to Christianity in 386. He explained in his most important work Confessions how he read the works of Plato and found there ideas which he wove into Christian theology.

One of Augustine's major undertakings was to defend the Catholic faith from what were considered heretical views. He wrote a major work De Genesi ad Litteram , a literal commentary on Genesis, in 401. In this work he takes for granted that the Holy Scriptures are true and that correct descriptions of the world therefore cannot be in conflict with the Holy Scriptures if they are correctly interpreted. He writes (see for example [21]):-
... in Holy Scripture different interpretations are sometimes possible without prejudice to the faith we have received. In such a case we should not rush in headlong and so firmly take our stand on one side that, if further progress in the search for truth justly undermines that position, we too fall with it. That would be to battle not for the teaching of the Holy Scripture but for our own, wishing its teaching to conform to ours, whereas we ought to wish ours to confirm to that of Holy Scripture.
Augustine argued against two types of attack on the truth of the creation story in Genesis. The first of these were arguments based purely on logic, for example that the "day" is defined by the passage of the Sun in the sky so to talk, as in Genesis, of several days passing before the Sun was created makes no sense.

The second type of attack was based on Aristotle's physics. For example in Genesis Chapter 1, Verse 7, it is stated:-
And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so.
Augustine had to answer those who argued that according to Aristotle the "proper place" for water is below so how could water exist "above the firmament".

Augustine argues against a literal interpretation in many cases using the argument (see for example [21]):-
Sacred Scripture in its customary style is speaking with the limitations of human language in addressing men of limited understanding.
If Augustine is the one most responsible for bring Plato's philosophy into Christianity, then Thomas Aquinas in the 13th Century must be considered the one who was most responsible for Aristotle's philosophy and physics becoming absorbed into Christian thinking. The result was his attempt to combine reason and faith, a major contribution to Scholasticism. He encouraged logic, mathematics and science to be seen as contributing to Christianity rather than being opposed to it. Aristotle's universe of circular motion and crystal spheres became part of the Christian view of the world, although of course Aristotle's idea of a universe which had always existed was replaced by the creation of the universe by God, as described in Genesis. The developments of Aristotle's astronomy by Ptolemy became more than a scientific belief; for many Christians it became part of their religious belief.

Copernicus in the 16th century is often seen as providing the revolution which would overturn this ancient Greek world-view. This is not quite accurate for a number of reasons. Firstly Copernicus himself was very much in the mould of the ancient Greek mathematicians, and secondly his book On the Revolutions of the Heavenly Spheres had little impact when fist published. Copernicus used observational data from the Greek astronomers, and stuck rigidly to Aristotle's belief that perfect motion of the heavenly bodies had to be circular. This insistence on circular motion meant that to fit the observations Copernicus had to place the centre of the universe not at the Sun but at a point close to the Sun around which both the Earth and the Sun revolved. It was Ptolemy's mathematical tricks of deferent and epicycle which Copernicus modified to his own mathematical model. His respect for the ancient Greek system is reflected in his own words (see for example [1]):-
It is fitting for us to follow the methods of the ancients strictly and to hold fast to their observations which have been handed down to us like a Testament. And to him who thinks that they are not to be entirely trusted in this respect, the gates of our Science are certainly closed ... he will get what he deserved for believing that he can lend support to his own hallucinations by slandering the ancients.
Certainly Copernicus saw that theologians might attack his work as contrary to the Holy Scriptures. He wrote in the introduction:-
Perhaps there will be prattlers who, although completely ignorant of mathematics, nevertheless take it upon themselves to pass judgement on mathematical questions, and on account of some passage in Scripture, badly distorted to their purpose, will dare to censure and assail what I have presented here.
One might reasonably ask what led a religious man such as he was to even contemplate a vision of the universe which seemed to go against the Holy Scripture. Zimmermann, in [30] suggests the following:-
For Copernicus as for many ancient philosophers the sky is the visible God; therefore the study of the movement of the celestial bodies is the most excellent way to the invisible God. The Creator is the great architect of all things; in the cognition of the mathematically simple structure of the universe man will become united with Him. It is suggested that these theological ideas gave Copernicus the pertinacy to work out his heliocentric system despite the misgivings of contemporary Aristotelian physicists.
Of course Copernicus was correct in assuming that attacks would come. For example, Tolosani, a Dominican who was a contemporary of Copernicus, wrote Heaven and the Elements which was published not long after On the Revolutions of the Heavenly Spheres as an appendix to his book On the Truth of Holy Scripture. Tolosani wrote that Copernicus (see for example [26]):-
... seems to be unfamiliar with Holy Scripture since he contradicts some of its principles, not without the risk to himself and to the readers of his book of straying from the faith ...
The arguments put forward by Tolosani against Copernicus were that, in addition to contradicting Holy Scripture, his ideas contradicted Aristotle's physics (see for example [26]):-
... in his imagination he changes the order of God's creatures in his system when ... he seeks to raise the Earth, heavier than the other elements, from its lower place to the sphere where everybody by common consent correctly locates the Sun's sphere, and to caste the sphere of the Sun down to the place of the Earth, contravening the rational order and Holy Writ, which declares that heaven is up, while the Earth is down ...
Tycho Brahe, who was born three years after the death of Copernicus, made the most accurate observations of the heavenly bodies before the invention of the telescope. He realised the mathematical superiority of Copernicus over Ptolemy but he proposed a modification of Copernicus's system in which the planets revolved around the Sun while the Sun itself moved around the stationary Earth. This retained the mathematical advantages of Copernicus without the problems with contradicting Aristotle or Holy Scripture (see for example [27]):-
What need is there without any justification to imagine the Earth, a dark, dense, and inert mass, to be a heavenly body undergoing even more numerous revolutions than the others, that is to say, subject to a triple motion, in violation not only of all physical truth but also of the authority of Holy Scripture, which ought to be paramount.
In another work Brahe writes (see for example [27]):-
... the Earth, which we inhabit, occupies the centre of the universe and does not perform any annual motion such as Copernicus supposed. These propositions must be upheld without any doubt; so I believe, together with the ancient astronomers and the accepted opinions of the physicists, supported by Holy Scripture.
Kepler, on the other hand, made a bolder step away from the beliefs of Aristotle than had Copernicus. Not only did he accept that the Earth was in orbit round the Sun but he introduced a new brilliant idea, never before postulated, that the heavenly bodies do not travel in circles but in ellipses. Unlike the Catholic mathematicians we have looked at previously in this article, Kepler was a Lutheran. A devout Christian, he wrote in The Mystery of the Cosmos (1596):-
I undertake to prove that God, in creating the universe and regulating the order of the cosmos, had in view the five regular bodies of geometry known since the days of Pythagoras and Plato, and that he has fixed according to those dimensions, the number of heavens, their proportions and the relations of their movements.
He began his book with a discussion of its relevance to the Holy Scripture (see for example [25]):-
It is an act of piety at the very beginning of this discourse about Nature to see whether it says anything contrary to Holy Writ. Nevertheless, I believe that is premature to raise this question here before I am assailed. In general I promise to say nothing harmful to Holy Writ, and if Copernicus is convicted of anything with me, I shall consider him finished. And this was always my intention from the time when I began to examine the six books of Copernicus's Revolutions.
However, he was 'assailed'. The Lutherans were worried that Kepler's theories would cause splits in their own Church at a time filled with difficulties as various different branches of the Christian Church argued with each other. Kepler, however, saw no reason why the Copernican theory should be seen to oppose the Holy Scripture. He tackled the question head-on in the Introduction to Astronomia nova (1609) (see for example [25]):-
To teach mankind about nature is not the purpose of Holy Scripture, which speaks to people about these matters in a human way in order to be understood by them and uses popular concepts. ... Why is it surprising then, that Scripture also talks the language of human senses in situations where the reality of things differs from the perception?

Piety prevents many people from agreeing with Copernicus out of fear that the Holy Ghost speaking in Scripture will be branded as a liar if we say that the Earth moves and the Sun stands still. But these persons should bear in mind that we learn most things and the most important things with the sense of sight, and therefore cannot detach our speech from the visual sense. Thus, very many things happen every day when we talk the language of the sense of sight even though we know for a certainty that the situation is otherwise. ... Thus, when we emerge from a narrow valley, we say that a wide plain opens up before us.
For Kepler, a devout Christian, mathematics was itself a religious undertaking. He wrote in Harmonice Mundi (1619):-
Geometry existed before the creation; is co-eternal with the mind of God; is God himself ... Where there is matter there is geometry. ... geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes. ... It is absolutely necessary that the work of such a Creator be of the greatest beauty...
The Catholic Church, however, in a move against the ideas of Luther, had declared itself the only authority to interpret the Holy Scripture at the Council of Trent in 1546:-
... no one relying on his own judgement and distorting the Sacred Scriptures according to his own conception shall dare to interpret them contrary to that sense which Holy Mother Church, to whom it belongs to judge their true sense and meaning, has held or does hold, or even to interpret them contrary to the unanimous agreement of the Fathers.
Some suffered the ultimate penalty at the hands of the Catholic Church for their beliefs. Giordano Bruno was sentenced to death by the Inquisition and burned alive in February 1600. Certainly in Cena de le Ceneri (1584) Bruno declared his support for the reality of the heliocentric theory and also claimed that the universe is infinite. In this work he also argued that the Holy Scripture was written to teach morals but not to teach astronomy. It is a little difficult to know exactly what he was accused of during his seven year trial. Bruno seems not to have understood himself for when the Inquisition demanded that he retract, he replied that he had nothing to retract and did not understand what he was being asked to retract. Metaphysics and mathematics in Bruno's works are studied in [2].

Galileo had long believed in Copernicus's theory and had corresponded with Kepler on the issue. He explained to him in 1597 that he did not wish to enter the argument because of fear of ridicule. By 1613 Galileo believed that his telescopic observations of the moons of Jupiter proved that the Earth and planets revolved round the Sun. He was drawn into the controversy, however, through Castelli who had been appointed to the chair of mathematics in Pisa in 1613. Castelli had been a student of Galileo and was also a supporter of Copernicus. At a meeting in the Medici palace in Florence in December 1613 with the Grand Duke Cosimo II and his mother the Grand Duchess Christina of Lorraine, Castelli was asked to explain the apparent contradictions between the Copernican theory and Holy Scripture. Castelli defended the Copernican position vigorously and wrote to Galileo afterwards telling him how successful he had been in putting the arguments. Galileo, less convinced that Castelli had won the argument, wrote Letter to Castelli to him examining (see for example [21]):-
... some general questions about the use of Holy Scriptures in disputes involving physical conclusions.
Galileo used arguments similar to those that we have quoted from Kepler's Astronomia nova (1609). By now Galileo had several opponents in Florence and they made sure that a copy of the Letter to Castelli was sent to the Inquisition in Rome. However, after examining its contents they found little to which they could object.

The Catholic Church's most important figure at this time in dealing with interpretations of the Holy Scripture was Cardinal Robert Bellarmine. He seems at this time to have seen little reason for the Church to be concerned regarding the Copernican theory. The point at issue was whether Copernicus had simply put forward a mathematical theory which enabled the calculation of the positions of the heavenly bodies more simply or whether he was proposing a physical reality. At this time Bellarmine viewed the theory as an elegant mathematical one which did not threaten the established Christian belief regarding the structure of the universe.

Various letters were exchanged between theologians, scientists and mathematicians. Both theological and scientific arguments were put by all concerned. Galileo himself began to put forward theological as well as scientific arguments, including use of the Holy Scripture to support the Copernican theory, something he had strongly argued against earlier when he stated that the Holy Scripture was intended only for moral teaching, not to teach physics. Having now discovered arguments by Augustine in De Genesi ad Litteram to support his case, Galileo wrote the Letter to the Grand Duchess which vigorously attacked the followers of Aristotle. In this work, which he addressed to the Grand Duchess Christina of Lorraine, he used some of Augustine's arguments, which he developed much further, to argue strongly for a non-literal interpretation of Holy Scripture when the literal interpretation would contradict facts about the physical world proved by mathematical science.

Galileo certainly started with the assumption that the Holy Scriptures are true so there must be interpretations which agree with all scientifically proved theories. It is important to realise that Galileo was not opposing Christianity, quite the opposite in fact, for he felt that he was a devout Christian doing his very best to save Christianity from serious error. He points out that theologians cannot tell a mathematician what mathematics he must believe to be true (see for example [21]):-
... there is a great difference between giving orders to a mathematician or a natural philosopher and giving them to a merchant or a lawyer; and that proved conclusions about natural and celestial phenomena cannot be changed with the same ease as opinions about what is or is not legitimate in a contract.
There was no holding Galileo back now, and he states quite clearly that for him the Copernican theory is not just a mathematical calculating tool, but is a physical reality:-
I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it. Moreover ... I confirm this view not only by refuting Ptolemy's and Aristotle's arguments, but also by producing many for the other side, especially some pertaining to physical effects whose causes perhaps cannot be determined in any other way, and other astronomical discoveries; these discoveries clearly confute the Ptolemaic system, and they agree admirably with this other position and confirm it.
The Catholic Church was at this time engaged in a vigorous argument with the Protestant Churches. One of the major points of disagreement was whether an individual could form their own interpretation of the Holy Scripture (the Protestant view) or whether, as the Catholic Church argued and had stated clearly after the Council of Trent in 1546, everyone must accept the interpretation of the Holy Scripture made by the Catholic Church. Galileo's arguments came too close to this touchy issue for the Catholic Church to be able to take no action. Pope Paul V ordered Bellarmine to have the Sacred Congregation of the Index decide on the Copernican theory. The cardinals of the Inquisition met on 24 February 1616 and took evidence from theological experts. It may seem strange to readers today to here that an idea was being put on trial, but in the context of the times it was not unusual. It took the theologians only a few of days to reach their decision and, perhaps surprisingly, it seems to have been made more to defend Aristotle's physics than to defend the Holy Scripture. The Inquisition reported:-
.. all said that the proposition of a stationary Sun is foolish and absurd in natural philosophy.
Only as a second reason did they quote that Copernicus's theory was contrary to Holy Scripture and they declared that:-
... the doctrine attributed to Copernicus ... cannot be defended or held.
Bellarmine conveyed the decision of the Inquisition to Galileo who had not been personally involved in the trial. At Galileo's request Bellarmine gave him a written certificate which made clear Galileo's own position. It declared that he was forbidden to hold Copernican views but, strangely, an alternative version would be produced 17 years later which also said that Galileo was forbidden to teach the Copernican theory. Various conjectures about the alternative version have been put forward, many believing that it was a forgery by Galileo's enemies within the Catholic Church. However these matters arose much later and the result of the 1616 decision of the Congregation of the Index was to forbid Catholics to read Copernicus's Revolutions of the Heavenly Spheres until it had been 'corrected'. No works of Galileo were put on the Index, however, and the version of the judgement given by Bellarmine to Galileo appeared to still allow him to discuss the merits of Aristotle's theory and the Copernican theory. It only prevented him from arguing that the Copernican theory was true.

In March 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican. It takes the form of a dialogue between Salviati, who argues for the Copernican system, and Simplicio who is an Aristotelian philosopher. The climax of the book is an argument by Salviati that the Earth moves which was based on Galileo's theory of the tides. Now Galileo's theory of the tides was entirely false despite being postulated after Kepler had already put forward the correct explanation.

One might reasonably ask why Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican after the judgement of 1616. The reasons to write and publish the work were more than simply depending on the certificate that Bellarmine had given him. Rather he felt safe since Maffeo Barberini had been elected as Pope Urban VIII and he was an admirer of Galileo. After being elected Pope he invited Galileo to papal audiences on six occasions and led Galileo to believe that the Catholic Church would not make an issue of the Copernican theory.

Shortly after publication of Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican the Inquisition banned its sale and ordered Galileo to appear in Rome before them. Illness prevented Galileo from travelling to Rome until 1633. When he did so he was confronted with the alternative version of the ruling of 1616, which was an unsigned document. Galileo still had in his possession the certificate Bellarmine had signed and given him in 1616, although Bellarmine had died in 1621 so could not clarify the difference between the two versions. By the legal standards of today one would expect the alternative version stating that Galileo was forbidden to teach the Copernican theory to be overruled. Galileo's accusation at the trial which followed was exactly that he had breached the conditions of this unsigned alternative version. The truth of the Copernican theory was not an issue therefore; it was taken as a fact at the trial that this theory was false. This was logical, of course, since the judgement of 1616 had declared it totally false.

Found guilty, Galileo was condemned to lifelong imprisonment, but the sentence was carried out somewhat sympathetically and it amounted to house arrest rather than a prison sentence. He was able to return to his home but had to spend the rest of his life watched over by officers from the Inquisition.

Galileo may have suffered at the hands of the Church, but he remained totally committed the Christianity. He wrote near the end of his life (see for example [1]):-
I have two sources of perpetual comfort - first, that in my writings there cannot be found the faintest shadow of irreverence towards the Holy Church; and second, the testimony of my own conscience, which only I and God in heaven thoroughly know. And He knows that in this cause in which I suffer, though many might have spoken with more learning, none, not even the ancient Fathers, have spoken with more piety or with greater zeal for the Church than I.

References (show)

  1. D Alexander, Rebuilding the matrix (Oxford, 2001).
  2. A Bönker-Vallon, Metaphysik und Mathematik bei Giordano Bruno (Berlin, 1995).
  3. J Dillenberger, Protestant thought and natural science (London, 1960).
  4. A Funkenstein, Theology and the Scientific Imagination (Princeton, 1986).
  5. R Hooykaas, Religion and the rise of modern science (Edinburgh, 1973),
  6. D C Lindberg and R L Numbers, God and Nature (Berkeley, 1986).
  7. P Machamer (ed.), The Cambridge companion to Galileo (Cambridge, 1998).
  8. J Polkinghorne, One World : the Interaction of Science and Theology (Princeton, 1987).
  9. J Polkinghorne, The Faith of a Physicist : The Gifford Lectures for 1993-4 (Princeton, 1994).
  10. E Rosen, Copernicus and his successors (London, 1995).
  11. B Russell, History of Western Philosophy (London, 1961).
  12. H Shapley, Science Ponders Religion (New York, 1960).
  13. G Simon, Kepler-astronome, astrologue (Paris, 1979).
  14. R Blackwell, Could there be another Galileo case?, in The Cambridge companion to Galileo (Cambridge, 1998), 348-366.
  15. W C Charron and J P Doyle, On the self-refuting statement "There is no truth": a medieval treatment, Vivarium 31 (2) (1993), 241-266.
  16. F Dyson, Review of Feynman and of Polkinghorne "Belief in God in an Age of Science", New York Review of Books (28 May, 1998).
  17. I Grattan-Guinness, Historical notes on the relations between mathematics and the Christianities, Meeting of Austrian Society for the History of Mathematics (Spring, 1999).
  18. S Knuuttila and A I Lehtinen, Change and contradiction: a fourteenth-century controversy, Synthese 40 (1) (1979), 189-207.
  19. F Krafft, Astronomie als Gottesdienst : Die Erneuerung der Astronomie durch Johannes Kepler, in Der Weg der Naturwissenschaft von Johannes von Gmunden zu Johannes Kepler (Vienna, 1988), 182-196.
  20. M Lejbowicz, Logique, mathématiques et contre-acculturation dans l'université médiévale, in La nouvelle physique du XIVe siècle, Nice, 1993 ( Florence, 1997), 203-229.
  21. E McMullin, Galileo on science and Scripture, in The Cambridge companion to Galileo (Cambridge, 1998), 271-347.
  22. M Pera, The god of theologians and the god of astronomers : an apology of Bellarmine, in The Cambridge companion to Galileo (Cambridge, 1998), 367-387.
  23. B Pizzorno, Some logical aspects of the drama of Galileo (Italian), Physis-Riv. Internaz. Storia Sci. 20 (1-4) (1978), 271-283.
  24. E Rosen, Calvin's attitude towards Copernicus, Journal of the History of Ideas 21 (1960), 431-441.
  25. E Rosen, Kepler and the Lutheran attitude towards Copernicus, Vistas in Astronomy 18 (1975), 225-231.
  26. E Rosen, Was Copernicus' Revolutions approved by the Pope, Journal of the History of Ideas 36 (1975), 531-542.
  27. E Rosen, Galileo's misstatements about Copernicus, Isis 32 (1958), 319-330.
  28. J von Plato, Nicole Oresme and the ergodicity of rotations, Acta Philos. Fenn. 32 (1981), 190-197.
  29. R S Westfall, The trial of Galileo: Bellarmino, Galileo, and the clash of two worlds, J. Hist. Astronom. 20 (1) (1989), 1-23.
  30. G Zimmermann, Die Gottesvorstellung des Nicolaus Copernicus, Studia Leibnitiana 20 (1) (1988), 63-79.

Written by J J O'Connor and E F Robertson
Last Update February 2002