Table Of ContentPOLISH ACADEMY OF SCIENCES* INTERNATIONAL ASTRONOMICAL I NION -
INTERNATIONAL I NION OP THE HISTORY AND PHILOSOPHY OF SCIENCE
INTERNATIONAL ACADEMY OF HISTORY OF SCIENCE
COLLOQITA COPERMCANA
III
Prncecdingti of the Joint Symposium of the
IA I! and the IlHPS. cosponsored by the IA US
ASTRONOMY OK COPERNICUS AND ITS BACKGROUND
Torun 19??
WROCLAW • WARSZAWA * KRAKOW * <;1>ANSK
lAKLAD NARODOWY 1 MIEN IA OSSOIJNSKICH
WYRAWNICTWO POLSKIEJ AKADEMlI NALK
1975
o
EDITORIAL COMMITTEE
MARIAN B1SKUP, JLRZY BUKOWSKJ,
I'AWEL CZARTORYSKI (chief editor), JERZY DOBRZYCKI,
KAROL G0RSK1, BOGUSLAW LESNODORSKI, BOGDAN SUCHODOLSKI
Editors for ttsb volume
OWEN GINGER1CH, JERZY DOBRZYCKI
Asaisuitt editor
BOLES*. AW OfttOWSKI
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PREFACE
The third joint symposium of the International Astronomical Union '1'TQ
(IAU) and the International Union of the History and Philosophy of
Science (IUHPS) cosponsored by the International Academy of the His
tory of Science (IAHS), wan held at the Nicholas Copernicus University
Library, Toruri, Poland, on 6—7 September 1973, both as part of the
Colloquia Copernicana organized by the IUHPS and as one of six sym
posia arranged by the IAU in connection with their Extraordinary General
Assembly. The symposium was opened by the Rector of the University,
Professor Witold Lukaszewicz, and the three sessions proceeded under
the successive chairmanships of Owen Gingerich, (President, IAU Com
mission 4.1 oil the History of Astronomy), Eugeniusz Bybka (Past-pres
ident, Commission 41) and Willy Hartner (President of the IAH8 and
pastviee-president, Commission 41).
Members of IAU Commission 41 have increasingly appreciated the
importance of understanding Copernicus’ astronomical work within a broad
er background of medieval science, and to underscore this significant
as|»ect, the symposium was from its conception planned to include sessions
on the background as well as the Copernican astronomy itself. Certainly
the immediate benefit of the symposium was to bring together Copernican
experts for an exchange of ideas and a sharing of their research rc.sults
with a larger circle of astronomers and historians. A long-range contri
bution, however, was to stimulate a deeper and continuing examination
of the Copernican astronomy and especially its background.
We wish to thank the invited speakers for the enthusiasm and co-
o]>eration with which they approached the topics assigned to them by
the organizers, and we must express our regret that Tadeusz Przypkowski,
for reasons of health, was unable to accept our invitation.
The papers presented in this volume differ somewhat in order and
content from the actual symposium. Some authors, with the encourage
ment of the organizers, considerably expanded or revised their contri
butions. The discussion included after certain papers has been highly
selected and abridged by the editors.
6 Prttfticr
Preliminary planning for the Colloquia Copcrnicana programme was
carried out by a Bub-committee of the Comity Mcolas Coperaie of the
IUHPS consisting of Jerzy Bukowaki (chairman), Owen Gingerich and
Ren6 Tatont and with the close assistance of Jerzy Dobrzycki. The appro
priateness of IAU sponsorship for the particularly astronomical part was
promptly recognized and supported by the IAU Executive Committee.
Details of the joint symposium were then organized by the undersigned.
The symposium was greatly assisted by travel grants from both the
IAU and the IAHS, and by additional financial aid from the local orga
nizing committee. We also wish to thank Boleslaw Orlowski for his effi
cient services both as symposium secretary and as assistant editor of
this volume.
Owen Gingerich
Smithsonian Astrophysical Observatory
and Harvard College Observatory
Jerzy Dobrzyclti
Institute of the History of Science and Technology
Polish Academy of Sciences
Warsaw, July 1974
WILLY HARTNER
Johann Wolfgang Goethe University,
Frankfurt /Main
THE ISLAMIC ASTRONOMICAL BACKGROUND
TO NICHOLAS COPERNICUS
“It results from the preceding proof that the Sun and the Moon move
in circular orbits. Now if this is true of the motion of the two luminaries,
it will of necessity be true also of the motions of the other planets for
the simple reason that there is a natural concord between them and the
fixed stars. However, there might be somebody saying that, perhaps,
the planets move along elliptical orbits, but that the difference of the
two axes of the ellipse does not beeome manifest because to the observer
this difference is too small to be perceived by the senses ... To him it
must be said that, etc.” There follows a refutation culminating: in the
well-known statement that locomotion must be either rectilinear or cir
cular, whence the whole argument may be disposed of.
This passage wa« written in the early 11th century by Abu Nasr Man
sur b. rAl! b. 'Iraq, the great al-Blrunifs great teacher; it is found in his
missive “On the Sphericity of the Heavens” (Hisftla fl kwiyyat al-sama*)1
addressed to the same BlrBm, who was born in 973, exactly a thousand
yeiirfi ago, and thus 500 years before Nicholas Copernicus.
The fact alone that Abu Nasr ventilates the possibility of non-circular
motion deserves attention, ife speaks of ellipses in the mathematical
sense, using the unambiguous technical term qaF naqis, which is nothing
but a literal translation of the Greek In other words, he does
not have in mind oval curves that have a more or less close similarity
to ellipses without, mathematically speaking, being such. In point of
fact, the distinction between oval or elliptiform motion on the one hand,
and true elliptic on the other, is of essential importance, at least at this
stage of the historical evolution.
1 Arabic texl in 1tasdii Abi Nasr Ua'l-Birtmi {2'ke Dairalu’b Mcfarifi l-Otmania,
Hyderabad-Deccan, 1048), 9th Risala, p. 11.
8 Willy llartner
To demonstrate this, may I summarize as briefly an possible the prin- »
ciples governing ancient astronomy and those cases in which them; prin
ciples, owing to a necessity imposed hy observat ional facts, are silently
violated.
Aristotle (Be oaelo, I, 2) postulates that there can be only two kinds
of natural motion: rectilinear, which is necessarily finite, as an essential
quality of the four terrestrial elements, and circular, necessarily infinite,
exemplified by the everlasting uniform revolution of the starry heavens.
Then the definition of motion as an essential quality makes it a logical
necessity that the matter constituting the celestial bodies must be dif
ferent from the four elements. It is the fifth element, to which Aristotle
applies the old word ether, from then 011 used as a technical term. It. is
devoid of gravity, i.e., neither heavy nor light, and it is characterized,
in strict analogy to the terrestrial element#, by eternal circular motion.
And it is to these two kinds of natural locomotion that Abu Nasr refers
in his refutation of elliptic motion.
In consequence of this distinction according to natural motion, cel.
estial and terrestrial kinematics have nothing in common. They are
governed by different laws, and any attempt to combine the two into
one is a primi doomed to fail, whence no such endeavour seems to have
been made until late scholasticism when, among others, Uobert Kilwardby,
probably under the influence of Averroes, extended the notion of natural
tendency {inclinaUo, Ar. xhahwa), otherwise applied only to the terres
trial elements, also to account for the ethereal bodies’ circular motion2.
The only place where a direct action of the celestial on the terrestrial
worlds has to be postulated is the spherical shell comprising the upjxtr
layer of air and the whole of the sphere of fire. IHte to its contact with
the inferior limit of the lunar sphere it revolves with approximately the
same velocity as the fixed stars, which explains that the comets, which
originate in the highest terrestrial regions, partake yrosao motlv of the
daily revolution (Meteor. I, 7).
It is astounding that Aristotle’s argumentation, on which rests the
whole of his mechanics, was hardly ever called into question. Above alt,
the flimsiness of his assertion that the light elements, air and fire, have
a natural rectilinear motion contrary to that- of gravity could hardly
escape the attention even of an unskilled observer. Indeed, how could it
be overlooked that the velocity of particles ascending from a fire decreas
es rapidly and, how ever great the heat, comes to a standstill at a very
* See O. Pedersen, Nicole Oresme og ham naturfiloaofiske system, [in:j “Acta
Histories Scientiarum Naturalium «t Medicinaliuin ”, vol. 13, Copeuhageo, 1956,
pp. 218 and 267, n. 16.
The Islamic Astronomical Background 9
moderate height. H m we have a striking example of the hampering
influence exerted by the authority of a great, man.
In astronomy it is a well-known fact that the axiom of uniform cir
cular motion was accepted as unshakeable from the very beginning and,
with few exceptions, an in Abu JN aBr’s case, was never calked seriously
into question nor even subjected to discussion. The circumstance that
Ptolemy saw himself forced to abandon the principle of uniformity by
introducing the equmti in ins planetary theory and the center of prosneu-
sit! in his lunar theory remained undiscussed ami uncontented for more
than a thousand years. It was only in the period immediately following
the downfall of the Caliphate and, 200 years later, at Copernicus’ time*
that astronomers centered their interest about this crucial question* But
the efforts then made aimed not at getting rid of the straight-jacket of
Aristotelian dogmatism but, on the contrary, at purifying the Ptolemaic
system of philosophical inconsistencies and thus at devising models of
motion strietly in accordance with the Aristotelian postulates,
(If Ptolemy’s modelh the least problematic is the one devised for the
Sun because it consists of one sole eccentric circle representing the orbit
of the Bun itself, while in all other cases the planet travels in, or rather,
is carried about by, an epicycle whose center moves either in a fixed
or in a movable eccentric deferent. IHolemy himself has shown in his
Hypotheseis3 that the plane geometrical models can be understood as
equatorial sections of solid spheres, all of which, with the two significant
exceptions already mentioned, revolve uniformly about their respective
axes. But there remain those two exceptions: the eccentrics in the case
of the live planets, and the epicycle in that of the Moon. In the former,
a sphere revolving non-uniformly about its axis such that the revolution
appears uniform with regard to another axis parallel to the former and
fixed in space, ie a mechanical monstrosity even if one claims that the
rules valid for terrestrial mechanics are not applicable to celestial kine
mattes* The expedient resorted to by Aristotle’s Byzantine commenta
tors and later philosophers down to Kepler’s time, to explain celestial
motion as due to the spheres’ and planets’ animation by souls or angels4,
could not possibly satisfy a mathematician, physicist, or astronomer.
* Book 2; see AV, Hartner, Mediaeval Viewt on Cosmic Dimensions and lHo-
lemy'e Eitdb ai-Mamhunll, [in:] MMtmges Alexandre Koyr£t I; L'Aventure de la Science,
Paris, 1964 (reprint in W. Hartner, Often* Occidem, Hildeabeitn, 1668) and B. E.
Goldstein, The Arabic Yernion of Ptolemy'# Planetary Hy'potlieseet [ic:] “TranBRctioiiu
of the American Philosophical Society”, vol. 57, Pt. 4, Philadelphia, 1967-
* See H.A. Wolfson, The Problem of the Soule of the Spheres from the Byzan
tine Commentaries on Aristotle through the Arabs and St. Thomas to Kepler, Jin:}
*4I> tun barton Oaks Papons”, vul. 16, 1962, pp. 67-93-
10 W illy Hartner
And no more satisfactory is the expedient devised to account for the
Moon’s evectioni the introduction of the mentioned center of promeusia,
by which the mean apogee of the lunar epicycle is determined in a mecha
nically inconceivable way.
Although the principle of uniformity thus was violated on several
occasions, that of circular motion was strictly maintained. The models
are always described in the same way. A point X is carried about, in a cir
cle concentric or eccentric to the Earth. X in turn is the center of a second
circle in which a point Y revolves, etc. finally, the planet itself moves
in its epicycle, being the last of this sequence. Thus the consecutive steps
and the respective parameters deduced from observation are indicated
and form the basis of tables serving to compute the geocentric co-ordi-'
nates of the planets at any time desired. It is only these co-ordinates:
the planets* longitudes and latitudes, which are of interest, whence astro
nomers during many centuries seemed to pay no attention to logical
inconsistencies or consequences at variance with observation, such aft
the intolerable variation of the Moon’s apparent diameter as it would
result from Ptolemy’s model.
However, even more surprising is the fact that neither Ptolemy nor
any of the great astronomers down to the time of ai-BIrum, Ibn al-Hay-
tham, and Ibn Yunis seems to have given thought to the question as to
the curves resulting from the combined motions of those circles. In the
case of two circles, an eccentric and an epicycle, there could not of course
rule any doubt as to t he resultant being what we call today an epicycloid.
But even in that of the Moon and of Mercury no sophisticated reasoning
was required to understand that the deferent itself carrying the epicycle
munt have an oval shape, with two axes of symmetry for the Moon, and
one for Mercury. And this being an established fact, one might have been
induced to wonder about the validity of the postulate of circular motion,
in view of the circumstance that other, mathematically simpler, curves —
among them first and foremost the ellipse—could serve as welt to render
the motion of the center of the epicycle within the limits of observational
accuracy.
A first step in this direction was taken, indeed, one or two generations
after al-BIi'fim, by Azarquiel of Toledo who to our knowledge was the
first to construct geometrically the oval deferent of Mercury, which I
have shown in an earlier paper6 is an algebraic curve eommg so very
close to an ellipse that the two are interchangeable. Actually the difference
of the radii vectored of the two curves amounts at a maximum to 0.3%.
However, Azarquiel carried out his construction only in order to manu-
* See W. Hartner, The Mercury Horoscope of Marc Antonio Michiel of Venice,
[in:] Vistas in Aetronomy, e<3. A. Bear, vol. 1, London and New York, 1055, pp. 109 —
122 (also in Orfam Occident, Bee it. 3, pp. -HS5— 478).
The Islamic Aetrojwmieat Background 11
facture an instrument permitting him to find without computation the
longitude of the planets, and nothing is known that would point to hia
theoretical interest in the matter.
In this light Abu Nasr Mansflr’s theoretical considerations cited at
the outset of the present lecture assume considerable weight because,
in spite of the fact that he withdraws instantly behind the safe fence of
Aristofcelianism, they put in evidence that he or some of his contempora
ries (we don’t know whether the locution “there might be somebody
saying”, indicates a dialogue or a monologue) had the daring of envisa
ging a possibility capable of shaking the foundations laid by the “Master
of those who know11 — the maestro di color che sanno, as Dante calls him.
Evidently, the idea of accepting elliptic motion without leaving behind
Aristotelianism did not occur to him, and this seems astonishing. As
the excellent mathematician he was he could not but be aware of the
elementary fact that an ellipse can be produced by making a point re
volve in an epicycle whose center in turn revolves in a circle in the op*
poeite direction and with half the angular velocity of the former. In astro
nomy this definition was not taken up until Kepler’s time {first by David
Fabrieiusj then by Kepler himself, later by Boulliau®), when it served
partly as a means to facilitate computation, partly as a tranquillizer
to those who were afraid of accepting Kepler’s heresy. With Islamic
authors I have not so far discovered any trace of it.
Al'Bitriidji’s (Lat. Alpetragins) attempt, carried out with insufficient
means, to abandon Ptolemaic astronomy altogether and to replace it
by reviving Eudoxus1 and Aristotle’s homocentric spheres7 is of interest
only because his work was early translated into Latin (Michael Scot,
1217) and much discussed in the late Middle Ages down to Regiomon
tanus, What the great Eastern Islamic astronomers who lived after the
conquest of Bagdad (1258), despite their wholly different approach, had
in common with him and ttthe commentator", Averroes, was the con
viction that only an astronomy based strictly on Aristotelian principles
can be regarded as satisfactory. The idea of relying more on empirical
facts and of using new observations — a great many such had been made
during tlie preceding centuries—seems not to have crossed Alpetragius*
mind, and the same is true, at least to a large extent, of the Easterners,
the men of the Maragha School, as they are usually called, namely, Ua§Ir
al-DIn of Tus, Qutb al-Din of Shiraz, and Ibn al Shutir of Damascus,
• See Y. Mae.yam a, Hypothesen zar PlaiuttetUhevrie des 17. JahthundtrU. Pub
lication of Institut fur Grachichto der Naturwisseiischafton, Johann Wolfgang Goe
the-UniverBitat, Frankfurt am Main, 1971, Ch. 3, pp. 13 17: Analysis ffllipseoa
in dues CircutoB.
1 See B. K. Goldstein, At-BUruji: On the Frinci-pUs of Astronomy* 1/2, New
Havea and London, 1971.
12 Willy Hartner
Nevertheless these latter are of the very greatest interest Iw1 cause their
aims aii<l method*, aw K. W. Kennedy with his collaborators a« well as
others among them myself -have shown, bear witness to a so very
great similarity to those of Nicholas Copernicus that the possibility of
a mere accident must be ruled out6. But even without this they would
be of great interest to the historian of mathematics because, to the best
of my knowledge, Nairn* al-Din was the first to substitute, in his lunar
theory, a curve better in accordance with the Aristotelian postulates
for the one given by the Ptolemaic theory and to define very exactly
the maximum deviation occurring between the two9. A new theorem
lined in this connexion has a twofold interest. It showR on the one hand
that rectilinear motion can be produced by the combined action of two
circles and demonstrates (although Na^Ir does not mention it) the unten-
ability of the dogmatic view that celestial and terrestrial motions are
essentially different. On the other, it is one out of many examples testi
fying to Copernicus’ dependency on his Islamic predecessors since, as
1 have shown in a recent paper10, even Copernicus’ lettering is the same
as Naslr’s. I say this against one critic11 after having carefully weighed
the pros and cons of my assertion. Actually, in the light of the many
other similarities and identities iso far discovered this one cannot possibly
be accidental. But this and all other similarities in the methods and objec
tives certainly do not impair Copernicus’ greatness, were it only for the
reason that he, and nobody before him, revived the Aristarchiun idea
of a heliostatic universe and thus Ojtened the way to modern astronomy,
above all, to Kepler’8 third law, based on the planets’ heliocentric dis
tances as resulting from the Copernican hypothesis.
Of the many concords between Copernicus and the Maragha Hchool
I enumerate the TusI device mentioned of the two circles producing
rectilinear motion, and its variant, a linkage of two equal vectors employed
in the theory of Mercury to produce a periodical variation of the epicycle
radius; furthermore, their replacement of the equant by a second epicycle,
n the lunar theory the int roduction of a second epicycle serving to reduce
• See V. Roberts, The Solar and Lunar Theory of Ibn ash-Shatir, "Isis” 48,
1957, pp. 428 — 32; E. S. Kennedy and V. Roberts, The Planetary Theory of Ibn
at-Shatir, “Isis” 50, 1056, pp. 227 — 36; Fuad Abbud, The Planetary Theory of Ibn
al-Shatir: Reduction of the Geometric Mod-els to Numerical Tables, “Isis” 63, 1062, pp.
492 — 00; W. Hartner, Nasir al-Din al-Turi's Z'unur Theory, “Physis" U, I9«0;
W. Hartner, Trepidation and Planetary Theories, Accadeinia Nazionale dei Lined,
13° Convegno Volta, Roma, 1971.
• See W. Hartner, Amir al-Dili's Lunar Theory (see u. 8), pp. 297 — 9U.
10 See W. Hartner, Trepidation (wee n. 8), pp. 614 — 19 (Figs. 5 — 7).
11 I, N. Veselovsky, Copernicus and Nasir al~I)in alTusi, “Journul for the
History of Astronomy” 4. 1073, pp. 128 — 30.
