The contribution of Giordano Bruno to the principle of relativity
TThe contribution of Giordano Brunoto the principle of relativity
Alessandro De AngelisINFN - Istituto Nazionale di Fisica Nucleare, sezione di Padova and INAF PadovaCatarina Espirito SantoLIP - Laborat´orio de Instrumenta¸c˜ao e F´ısica Experimental de Part´ıculas, LisboaOctober 6, 2016
Abstract
The trial and condemnation of Giordano Bruno was mainly based on arguments of philosoph-ical and theological nature, and therefore different from Galilei’s. Such elements contribute tounfairly devalue the scientific contribution of Bruno and do not properly account in particularfor his contribution to physics. This paper discusses the contribution of Bruno to the principleof relativity. According to common knowledge, the special principle of relativity was first enun-ciated in 1632 by Galileo Galilei in his
Dialogo sopra i due massimi sistemi del mondo (Dialogueconcerning the two chief world systems), using the metaphor today known as “Galileo’s ship”:in a boat moving at constant speed, the mechanical phenomena can be described by the samelaws holding on Earth. We shall show that the same metaphor and some of the examples inGalilei’s book were already contained in the dialogue
La cena de le Ceneri (The Ash WednesdaySupper) published by Giordano Bruno in 1584. In fact, Giordano Bruno largely anticipated thearguments of Galilei on the relativity principle, in particular to support the Copernican view. Itis likely that Galilei was aware of Bruno’s work, and it is possible that the young Galilei discussedwith Bruno, since they both stayed in Venezia for long periods in 1592.Keywords: Giordano Bruno, principle of relativity, Galileo Galilei, Heliocentric system, NicolausCopernicus, Doctores Parisienses, Jean Buridan, Nicole Oresme.PACS01.65.+g (To be published in Journal of Astronomical History and Heritage)1 a r X i v : . [ phy s i c s . h i s t - ph ] N ov Introduction
The principle of relativity states that it is impossible to determine whether a system is at rest ormoving at constant speed with respect to an inertial system by experiments internal to the system,i.e., there is no internal observation by which one can distinguish a system moving uniformly fromone at rest. This principle played a key role in the defence of the heliocentric system, as it made themovement of the Earth compatible with everyday experience.According to common knowledge, the principle of relativity was first enunciated by Galileo Galilei(1564 – 1642) in 1632 in his
Dialogo sopra i due massimi sistemi del mondo ( Dialogue concerningthe two chief world systems ) [1], using the metaphor known as “Galileo’s ship”: in a boat moving atconstant speed, the mechanical phenomena can be described by the same laws holding on Earth.Many historical aspects of the birth of the relativity principle have received little or scatteredattention. In this short note, we put together some elements showing that Giordano Bruno largelyanticipated [2] the arguments of Galilei on the relativity principle. In addition, we briefly discuss thesilence of Galilei on Bruno and the relation between the lives and careers of the two scientists.
The
Dialogo sopra i due massimi sistemi del mondo is the source usually quoted for the enunciationof the principle of relativity by Galilei. However, its publication in 1632 was certainly not a surprise,as Galilei had expressed his views much before, in particular when lecturing at the University ofPadova from 1592 to 1610. Some aspects of the evolution of Galilei’s ideas, from the
Trattato dellasfera (1592) [3] in which the Earth is still placed at the centre of the Universe, towards the
Dialogo ,passing through his heliocentric correspondence with Kepler from 1597 onwards [4], are examined forexample in [5–11].In February 1616, the Roman Inquisition condemned the theory by Nicolaus Copernicus (1473 –1543) [12] as being “foolish and absurd in philosophy”. The month before, the inquisitor MonsignorFrancesco Ingoli addressed Galilei with the essay
Disputation concerning the location and rest of Earthagainst the system of Copernicus [13]. The letter listed both scientific and theological argumentsagainst Copernicanism. Galilei replied only in 1624. In his lengthy reply, he introduced an earlyversion of “Galileo’s ship” metaphor, and discussed the experiment of dropping a stone from the topof the mast. Both arguments, as we shall see, had been previously raised by Bruno, and will be laterused again by Galilei, although with small differences, in the
Dialogo .In the
Dialogo sopra i due massimi sistemi del mondo , Galilei discusses the arguments then currentagainst the idea that the Earth moves. The book is a fictional dialogue between three characters. Twoof these, Salviati and Sagredo, refer to real figures disappeared since a few years at the publication ofthe book. The first plays the role of the defender of the Copernican theory, putting forward Galilei’spoint of view; the second, a Venetian aristocrat, educated and liberal, willing to accept new ideas, actsas a moderator placed between Salviati and the third character, a certain Simplicio, fierce supporterof Aristotle. The name of the latter (reminiscent of “simple-minded” in Italian) is in itself a clearindication of the Galilean dialectics, designed to destroy the opponents. Simplicio, despite being oneof the most famous commentators of Aristotle, manifests himself with an embarrassing simplicity ofspirit. Galilei uses Salviati and Simplicio as spokespersons of the two clashing chief world systems;Sagredo represents the discreet reader, the steward of science, the one to whom the book is addressed:he intervenes in the discussions asking for clarifications, contributing conversational topics, acting likea science enthusiast.In the second day, Galilei’s dialogue considered Ingoli’s arguments against the idea that the Earthmoves. One of these is that if the Earth were spinning on its axis, then we would all be movingeastward at hundreds of miles per hour, so a ball dropped down from a tower would land west of the2ower that would have in the meantime moved a certain distance eastwards. Similarly, the argumentwent, a cannonball shot eastwards would fall closer to the cannon compared to a ball shot westwards,since the cannon moving East would partly catch up with the ball.To counter such arguments Galilei proposes through the words of Salviati a gedankenexperiment :examine the laws of mechanics in a ship moving at a constant speed. Salviati claims that there is nointernal observation which allows to distinguish between a system smoothly moving and one at rest.So two systems moving without acceleration are equivalent, and non-accelerated motion is relative: “Salviati – Shut yourself up with some friend in the main cabin below decks on some large ship,and have with you there some flies, butterflies, and other small flying animals. Have a large bowl ofwater with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it.With the ship standing still, observe carefully how the little animals fly with equal speed to all sides ofthe cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, inthrowing something to your friend, you need throw it no more strongly in one direction than another,the distances being equal; jumping with your feet together, you pass equal spaces in every direction.When you have observed all these things carefully (though doubtless when the ship is standing stilleverything must happen in this way), have the ship proceed with any speed you like, so long as themotion is uniform and not fluctuating this way and that. You will discover not the least change inall the effects named, nor could you tell from any of them whether the ship was moving or standingstill. In jumping, you will pass on the floor the same spaces as before, nor will you make larger jumpstoward the stern than toward the prow even though the ship is moving quite rapidly, despite the factthat during the time that you are in the air the floor under you will be going in a direction oppositeto your jump. In throwing something to your companion, you will need no more force to get it to himwhether he is in the direction of the bow or the stern, with yourself situated opposite. The dropletswill fall as before into the vessel beneath without dropping toward the stern, although while the dropsare in the air the ship runs many spans. The fish in their water will swim toward the front of theirbowl with no more effort than toward the back, and will go with equal ease to bait placed anywherearound the edges of the bowl. Finally the butterflies and flies will continue their flights indifferentlytoward every side, nor will it ever happen that they are concentrated toward the stern, as if tired outfrom keeping up with the course of the ship, from which they will have been separated during longintervals by keeping themselves in the air. And if smoke is made by burning some incense, it willbe seen going up in the form of a little cloud, remaining still and moving no more toward one sidethan the other. The cause of all these correspondences of effects is the fact that the ship’s motion iscommon to all the things contained in it, and to the air also. That is why I said you should be belowdecks; for if this took place above in the open air, which would not follow the course of the ship, moreor less noticeable differences would be seen in some of the effects noted.”
Note that Galilei does not state that the Earth is moving, but that the motion of the Earth andthe motion of the Sun cannot be distinguished (hence the name of relativity): “There is one motion which is most general and supreme over all, and it is that by which the Sun,Moon, and all other planets and fixed stars – in a word, the whole universe, the Earth alone excepted– appear to be moved as a unit from East to West in the space of twenty-four hours. This, in so faras first appearances are concerned, may just as logically belong to the Earth alone as to the rest of theUniverse, since the same appearances would prevail as much in the one situation as in the other.”
The possibility that the Earth moves had been discussed several times in particular by the Greeks,mostly as a hypothesis to be rejected. Also an annual motion of the Earth around the Sun hadbeen considered, by Aristarchus of Samos (c. 310 – c. 230 BC). Unfortunately, very little is known3bout Greek astronomy as a science, being many of our reconstructions a speculation. Later, somemedieval authors discussed the possibility of the Earth’s daily rotation. The first notable example isprobably Jean Buridan (c. 1300 – 1361), one of the “doctores parisienses” – a group of professors atthe University of Paris in the fourteenth century, including notably Nicole Oresme.In Buridan the example of the ship, later used in particular by Oresme, Bruno, and Galilei, iscontained in the Book 2 of his commentary [14] to Aristotle’s
On the heavens [15]: “It should be knownthat many people have held as probable that it is not contradictory to appearances for the Earth tobe moved circularly in the aforesaid manner, and that on any given natural day it makes a completerotation from west to east by returning again to the west - that is, if some part of the Earth weredesignated [as the part to observe]. Then it is necessary to posit that the stellar sphere would be atrest, and then night and day would result through such a motion of the Earth, so that motion of theEarth would be a diurnal motion. The following is an example of this: if anyone is moved in a shipand imagines that he is at rest, then, should he see another ship which is truly at rest, it will appearto him that the other ship is moved. This is so because his eye would be completely in the samerelationship to the other ship regardless of whether his own ship is at rest and the other moved, or thecontrary situation prevailed. And so we also posit that the sphere of the Sun is totally at rest and theEarth in carrying us would be rotated. Since, however, we imagine we are at rest, just as the man onthe ship moving swiftly does not perceive his own motion nor that of the ship, then it is certain thatthe Sun would appear to us to rise and set, just as it does when it is moved and we are at rest.”
It appears to us, in agreement with Barbour [10], that the relativity invoked by Buridan is in thefirst place kinematic. In the words of Barbour, “we have [here] a clear statement of the principleof relativity, certainly not the first in the history of the natural philosophy of motion but perhapsexpressed with more cogency than ever before. The problem of motion is beginning to become acute.We must ask ourselves: is the relativity to which Buridan refers kinematic relativity or Galileanrelativity? There is no doubt that it is in the first place kinematic; for Buridan is clearly concernedwith the conditions under which motion of one particular body can be deduced by observation of otherbodies.”
Buridan writes later on, still in [14]: “But the last appearance which Aristotle notes is moredemonstrative in the question at hand. This is that an arrow projected from a bow directly upwardfalls to the same spot on the Earth from which it was projected. This would not be so if the Earth weremoved with such velocity. Rather, before the arrow falls, the part of the Earth from which the arrowwas projected would be a league’s distance away. But still supporters would respond that it happensso because the air that is moved with the Earth carries the arrow, although the arrow appears to us tobe moved simply in a straight line motion because it is being carried along with us. Therefore, we donot perceive that motion by which it is carried with the air.”
Some worry about dynamics is, thus,already in Buridan. But the conclusion is that “the violent impetus of the arrow in ascending wouldresist the lateral motion of the air so that it would not be moved as much as the air. This is similarto the occasion when the air is moved by a high wind. For then an arrow projected upward is notmoved as much laterally as the wind is moved, although it would be moved somewhat.”
The theoryof impetus is thus not pushed to the limit in which one could identify it with the principle of inertia,nor with a dynamical concept of relativity.A further step is implicitly made, few years later, by Nicole Oresme (c. 1320 – 1382) in [16].Oresme first states that no observation can disprove that the Earth is moving: “[O]ne could notdemonstrate the contrary by any experience. [...] I assume that local motion can be sensibly perceivedonly if one body appears to have a different position with respect to another. And thus, if a man is ina ship called a which moves very smoothly, irrespective if rapidly or slowly, and this man sees nothingexcept another ship called b, moving exactly in the same way as the boat a in which he is, I say thatit will seem to this person that neither ship is moving.”
Oresme also provides an argument against Buridan’s interpretation of the example of the arrow(or stone in the original by Aristotle) thrown upwards, introducing the principle of composition of4ovements: “[O]ne might say that the arrow thrown upwards is moved eastward very swiftly with theair through which it passes, with all the mass of the lower part of the world mentioned above, whichmoves with a diurnal movement; and for this reason the arrow falls back to the place on the Earth fromwhich it left. And this appears possible by analogy, since if a man were on a ship moving eastwardsvery swiftly without being aware of his movement, and he drew his hand downwards, describing astraight line along the mast of the ship, it would seem to him that his hand was moved straight down.Following this opinion, it seems to us that the same applies to the arrow moving straight down orstraight up. Inside the ship moving in this way, one can have horizontal, oblique, straight up, straightdown, and any kind of movement, and all look like if the ship were at rest. And if a man walkswestwards in the boat slower than the boat is moving eastwards, it will seem to him that he is movingwest while he is going east.”
Also Nicolaus Cusanus (1401 – 1461) stated later, without going into detail, that the motion ofa ship could not be distinguished from rest on the basis of experience, but some different argumentsneed to be invoked – and the same applies “to the Earth, the Sun, or another star” [17].All this happens before Copernicus: we still discuss how things could be, not much how things“are”. This view will change after Copernicus.
In April 1583, forty years after the publication of the book by Copernicus and nine years beforethe then 28-years old Galilei was called to the University of Padova, Bruno went to England andlectured in Oxford, unsuccessfully looking for a teaching position there. Still, the English periodwas a fruitful one. During that time Bruno completed and published some of his most importantworks, the six “Italian Dialogues”, including the cosmological work
La cena de le Ceneri ( The AshWednesday Supper , 1584) [2].This book consists of five dialogues between Theophilus, a disciple that exposes the theories ofBruno; Smitho, a character probably real but difficult to identify, possibly an English friend of Bruno(perhaps John Smith or the poet William Smith) – the Englishmen has simple arguments, but hehas good common sense and is free of prejudice; Prudencio, a pedantic character, and Frulla, alsoa fictional character who, as the name in Italian suggests, embodies a comic figure, provocative andsomewhat tedious with the proposition of stupid arguments.In the third dialogue, the four mostly comment discussions heard at a supper attended byTheophilus in which Bruno – called in the text “il Nolano” (the Nolan), because he was born inNola near Naples – was arguing in particular with Dr. Torquato and Dr. Nundinio, representing theOxonian faculty. Bruno starts by discussing the argument related to the air, winds and the movementof clouds. He largely uses the fact that the air is dragged by the Earth: “Theophilus – [...] If the Earth were carried in the direction called East, it would be necessary thatthe clouds in the air should always appear moving toward west, because of the extremely rapid and fastmotion of that globe, which in the span of twenty-four hours must complete such a great revolution.To that the Nolan replied that this air through which the clouds and winds move are parts of theEarth, because he wants (as the proposition demands) to mean under the name of Earth the wholemachinery and the entire animated part, which consists of dissimilar parts; so that the rivers, therocks, the seas, the whole vaporous and turbulent air, which is enclosed within the highest mountains,should belong to the Earth as its members, just as the air does in the lungs and in other cavities ofanimals by which they breathe, widen their arteries, and other similar effects necessary for life areperformed. The clouds, too, move through happenings in the body of the Earth and are based in itsbowels as are the waters. [...] Perhaps this is what Plato meant when he said that we inhabit theconcavities and obscure parts of the Earth, and that we have the same relation with respect to animalsthat live above the Earth, as do in respect to us the fish that live in thicker humidity. This means that in a way the vaporous air is water, and that the pure air which contains the happier animals is abovethe Earth, where, just as this Amphitrit [ocean] is water for us, this air of ours is water for them.This is how one may respond to the argument referred to by Nundinio; just as the sea is not on thesurface, but in the bowels of the Earth, and just as the liver, this source of fluids, is within us, thatturbulent air is not outside, but is as if it were in the lungs of animals.” The Dialogue than moves to discussing the argument of projectiles. He starts by explaining theAristotelian objection of the stone sent upwards: “Smitho – You have satisfied me most sufficiently, and you have excellently opened many secretsof nature which lay hidden under that key. Thus, you have replied to the argument taken from windsand clouds; there remains yet the reply to the other argument which Aristotle submitted in the secondbook of
On the Heavens where he states that it would be impossible that a stone thrown high upcould come down along the same perpendicular straight line, but that it would be necessary that theexceedingly fast motion of the Earth should leave it far behind toward the West. Therefore, given thisprojection back onto the Earth, it is necessary that with its motion there should come a change in allrelations of straightness and obliquity; just as there is a difference between the motion of the ship andthe motion of those things that arc on the ship which if not true it would follow that when the shipmoves across the sea one could never draw something along a straight line from one of its corners tothe other, and that it would not be possible for one to make a jump and return with his feet to thepoint from where he took off.” Bruno then gives, in Theophilus’s speech, the following reply (referring to Figure 1 in the text): “Theophilus – With the Earth move [...] all things that are on the Earth. If, therefore, from apoint outside the Earth something were thrown upon the Earth, it would lose, because of the latter’s Amphitrite was in Greek mythology the wife of Poseidon and, therefore, the goddess of sea. See [15], Section 296b. otion, its straightness as would be seen on the ship AB moving along a river, if someone on pointC of the riverbank were to throw a stone along a straight line, and would see the stone miss its targetby the amount of the velocity of the ship’s motion. But if someone were placed high on the mast ofthat ship, move as it may however fast, he would not miss his target at all, so that the stone or someother heavy thing thrown downward would not come along a straight line from the point E which isat the top of the mast, or cage, to the point D which is at the bottom of the mast, or at some pointin the bowels and body of the ship. Thus, if from the point D to the point E someone who is insidethe ship would throw a stone straight up, it would return to the bottom along the same line howeverfar the ship moved, provided it was not subject to any pitch and roll.” He then continues with the statement that the movement of the ship is irrelevant for the eventsoccurring within the ship and explains the reasons for that: “[...] If there are two, of which one is inside the ship that moves and the other outside it, of whichboth one and the other have their hands at the same point of the air, and if at the same place and timeone and the other let a stone fall without giving it any push, the stone of the former would, withouta moment’s loss and without deviating from its path, go to the prefixed place, and that of the secondwould find itself carried backward. This is due to nothing else except to the fact that the stone whichleaves the hand of the one supported by the ship, and consequently moves with its motion, has suchan impressed virtue, which is not had by the other who is outside the ship, because the stones havethe same gravity, the same intervening air, if they depart (if this is possible) from the same point,and arc given the same thrust.From that difference we cannot draw any other explanation except that the things which are affixedto the ship, and belong to it in some such way, move with it: and the stone carries with itself the virtue[impetus] of the mover which moves with the ship. The other does not have the said participation.From this it can evidently be seen that the ability to go straight comes not from the point of motionwhere one starts, nor from the point where one ends, nor from the medium through which one moves,but from the efficiency of the originally impressed virtue, on which depends the whole difference. Andit seems to me that enough consideration was given to the propositions of Nundinio.”
The experiments carried out in a ship are thus not influenced by its movement because all thebodies in the ship take part in that movement, regardless of whether they are in contact with theship or not. This is due to the “virtue” they have, which remains during the motion, after the carrierabandons them. Bruno thus clearly expresses the concept of inertia, using the word “virt`u”, in Italianmeaning “quality”, which is carried by the bodies moving with the ship – and with the Earth. Thearguments of Bruno certainly constitute a significant step towards the principle of inertia.
We have seen that Bruno in La cena de le Ceneri anticipates to a great extent the arguments of Galileion the principle of relativity. In fact, his explanation does contain all the fundamental elements ofthe principle. The idea that the only movement observable by the subject is the one in which he doesnot take part, was present before in the works of Buridan, and later by Nicole Oresme together withthe notion of the composition of movements, alien to Aristotelian mechanics [9]. Similar argumentswere used by Copernicus [12]. The main missing ingredient was the idea of inertia, which explainsthe fact that projectiles move along with Earth. In fact, while there is a continuous line betweenBuridan, Oresme, Copernicus, Bruno, and Galilei, the arguments of Bruno on the impossibility todetect absolute motion by phenomena in the ship constitute a significant step towards the principleof inertia and to a dynamical context for relativity. What is new in Bruno, and what brings himalmost exactly to where Galilei stood, is thus a clear concept on inertia.The arguments and metaphors used in discussions concerning the world systems were common to7ifferent authors. They were largely derived from Aristotle, Ptolemy and their commentators, oftenused without referencing and sometimes attributed to the wrong source. For example, Aristotle inhis On the heavens uses as experimental argument the one of the stone sent upwards. Buridan andOresme, in their comment to this work, used a modified version of this experiment in which an arrowis sent upwards in a ship - probably introduced by an earlier commentator/translator. Nevertheless,the description by Galilei of exactly the same ship experiment that Bruno used in the Cena makesit very likely that Galilei knew this work. The use of the dialogue form with a similar choice ofcharacters can also be seen as a possible sign of the influence of Bruno in Galilei.On the other hand, Galilei never mentioned Bruno in his works, and in particular there is noreference to him in Galilei’s large corpus of letters, while he referenced the “doctores parisienses” inhis MS 46 [18], a 110 pages long manuscript, containing physical speculations based on Aristotle’s
Onthe Heavens . Some authors have commented on Galilei’s silence about Bruno putting forward reasonsof prudence [11]. As pointed out in [5], this can hardly explain the absence of any mention also in hispersonal correspondence. Furthermore, although Galilei himself never mentions the name of Bruno inhis personal notes and letters, several of his correspondents do mention the Nolan. Martin Hasdale,in a letter to Galilei from 1610, tells him that Kepler expressed his admiration for Galilei, althoughhe regretted his failure to mention in his works Copernicus, Giordano Bruno and several Germanswho had anticipated such discoveries – in particular Kepler himself . “This morning I had the opportunity to make friends with Kepler [...] I asked what he likes aboutthat book of yourself and he replied that since many years he exchanges letters with you, and thathe is really convinced that he does not know anybody better than you in this profession. [...] As forthis book, he says that you really showed the divinity of your genius; but he was somehow uneasy,not only for the German nation, but also for your own, since you did not mention those authorswho introduced the subject and gave you the opportunity to investigate what you found now, namingamong these Giordano Bruno among the Italians, and Copernicus, and himself.” We can thus say that Galileo Galilei was probably aware of the work by Giordano Bruno on theCopernican system. When Galilei arrived in Padova, in 1592, it is also possible that the two scientistsmet: Bruno was guest of the noble Giovanni Mocenigo in Venezia, and Galilei was living betweenPadova and Venezia. In 1591, Bruno had unsuccessfully applied for the chair of Mathematics thatwas assigned to Galilei one year later. Although a confirmation that such a meeting occurred mightbe difficult to find, it remains hard to believe, given the motivations and characters of the two menand the circumstances of their lives during those years, as well as the size of the literate and scientificcommunity in those days, that they failed to discuss on the arguments concerning the defence of theCopernican system.
Acknowledgenents –
We thank Luisa Bonolis, Alessandro Bettini, Alessandro Pascolini, GiulioPeruzzi and Antonio Saggion for useful suggestions. We thank the anonymous referee for indicatingus some important aspects that we neglected in the first draft.
References [1] Galileo Galilei, “Dialogo sopra i due massimi sistemi del mondo”, Firenze 1632; translation istaken from S. Drake, University of California Press 1953.[2] Giordano Bruno, “La cena de le Ceneri”, London 1584; translation is taken from S.L. Jaki,Mouton, The Hague/Paris 1975.[3] Galileo Galilei, “Trattato della sfera”, Roma 1656 (apparently written in Padova in 1606). Letter from M. Hasdale to G. Galilei [4].
84] Galileo Galilei, Carteggio, Edizione Nazionale delle opere di Galileo Galilei, voll. 10-18, TipografiaG. Barbera, Firenze 1890-1907.[5] R. de Andrade Martins, “Galileo e o princ´ıpio da relatividade”, Cadernos de Hist´oria e Filosofiada Ciˆencia (9):69-86, 1986.[6] E. Giannetto, “Da Bruno ad Einstein”, Nuova Civilt`a delle Macchine 24 n.3 (2006), pp. 107-137.[7] A.G. Crombie, “The History of Science from Augustine to Galileo”, Dover 1996.[8] W.A. Wallace, “Galileo and His Sources: Heritage of the Collegio Romano in Galileo’s Science”,Princeton University Press 1984.[9] W.A. Wallace, “Prelude to Galileo”, Reidel, Dordrecht 1981.[10] J. Barbour, “The Discovery of Dynamics”, Oxford University Press 2001.[11] M. Clavelin, “La philosophie naturelle de Galil´ee”, Colin, Paris 1968.[12] Nicolaus Copernicus, “De revolutionibus orbium celestium”, Nuremberg 1543.[13] Monsignor Francesco Ingoli, “De situ et quiete terrae contra Copernici systema disputatio”(Disputation concerning the location and rest of Earth against the system of Copernicus), Roma1616; translated in http://arxiv.org/abs/1211.4244[14] Jean Buridan, “Quaestiones super libris quattuor de caelo et mundo”, c. 1340, Book 2, Question22, translated by M. Clagett in “The science of mechanics in the middle ages”, University ofWisconsin press, Madison 1959.[15] Aristoteles, “Peri ouranou” (On the heavens)(On the heavens)