Talk:History of astronomy/Common misconceptions

Discussion

In the course of editing various articles on the history of astronomy, I have come across a number of claims that various non-western astronomers had anticipated certain modern discoveries. These claims arise in a broader context of editors who present historical articles as lists of the "first person to discover X". Well written history of science is not concerned with listing discoverers to give them credit, rather it is concerned with discussing how a particular intellectual, institutional, and social context contributed to a person coming to specific scientific ideas.

The specific myths I am concerned with here arise from an understandable desire to make Islamic and Indian scholars more "modern" than they were, as if giving them points for beating European scholars to specific discoveries is a way to increase their stature, and from a sense that European scholars have been wrongfully given credit for non-western achievements.

Unfortunately, these claims have the opposite effect:

• In so far as they reflect misunderstandings of what these astronomers were actually doing, they lead the reader away from an understanding of their actual achievements.
• To the extent that they are demonstrably false, they discredit both Wikipedia and the genuine achievements of Islamic and Indian astronomers.

I have spent some time tracing down the apparent sources of some of these claims, as best as I can, and have found several points.

1. Most of them appear only in tertiary literature, based on (erroneous or selective) reading of the secondary literature.
2. The tertiary sources cited often do not provide proper citations to their sources (which makes tracing the ultimate sources of their claims difficult).
3. They are securely rebutted in the text-based secondary literature (or in the case of al-Biruni, in the texts themselves).

I have presented the sources of these claims, followed by critical material that can be used to evaluate them. I would welcome additional quotations of any sources on either side of these issues.

Unless sources are forthcoming, I will begin to remove these unsupported claims from the articles where they appear.--SteveMcCluskey 19:52, 9 June 2007 (UTC)

---

well done. this is a well known problem, of course. The internet is rife with websites full of hype along these lines, and we get many simple-minded patriots interested in seeing their nation as the "first" of no matter what without any deeper interest in the field. But I took the liberty to re-title this to "common misconceptions", since I was confused as to what you mean by "myth". An astronomical myth in my book is something entirely different (solar deities or dragons eating the moon, not shoddy research). dab (𒁳) 07:28, 11 June 2007 (UTC)

I agree with most of the points you've raised, and the sources and quotes you've gathered here do look very useful. I'll try to add them into some of those articles later. Jagged 85 05:27, 15 June 2007 (UTC)

I've just added a quote from Hugh Thurston (to keep the argument a bit more balanced). Jagged 85 09:58, 15 June 2007 (UTC)

Thanks for the comments. In view of the research I've done into the sources on the elliptical orbits issue and the Islamic heliocentric claims, I'm removing the former and toning down the latter. Most "heliocentric" discussions are actually discussions of the earth's possible rotation in the context of a geocentric planetary system.

I hope we can clean up this area. There are really so many poorly documented sources out there that shouldn't be accepted as reliable historical sources. The worst example I see is the undocumented historical introduction to Asghar Qadar's Textbook on relativity, but some of the web pages are awfully shaky.

What seems to be happening is that there are a sequence of authors, all of whom are enthusiastic advocates of particular national views of science succumbing to what I call the "How The Irish Saved Civilization" syndrome. Each succesive advocate selects out and interprets material from previous advocates and at each stage in the process, the presentations get more and more enthusiastic, and farther away from the content of the historical texts. We should try to go back to the secondary texts which directly cite and interpret the primary documents.

Relevant to all this, you might want to look at the discussion of Whig history, below --SteveMcCluskey 16:49, 15 June 2007 (UTC)

Whig history in Wikipedia

Beginning students in the history of science are commonly warned of the danger of writing Whig history; that is, the danger of writing about the past from a present perspective. One problem with Whig history is that it becomes a principle of selection, which is especially dangerous in writing a summary like an encyclopedia. As Herbert Butterfield said:

If we can exclude certain things on the ground that they have no direct bearing on the present, we have removed the most troublesome elements in the complexity [of history] and the crooked is made straight.

This principle of selection dominates Wikipedia's history of astronomy articles, as editors choose to discuss those elements where past authors anticipated modern ideas, and ignore the rest. As an example, compare the discussion of al-Biruni's astronomy with the source on which it is chiefly based. In the Wikipedia article, more than half of the section on astronomy (12 out or 21 lines) deals with heliocentrism or gravity; in the principle source 11 out of 36 lines deal with his discussion of the possible rotation of the earth; there are no further discussions of heliocentrism or gravity.

Further examples could be made by comparing Wikipedia's presentations with those of other scholarly encyclopedias, such as the Dictionary of Scientific Biography or the Encyclopedia of Islam. A survey of the essays in Walker's Astronomy Before the Telescope by David Pingree, "Astronomy in India" and David A. King, "Islamic Astronomy" shows that the question of heliocentrism is only briefly mentioned in one page (p. 150) that discusses the work of al-Tusi and his followers and its possible influence on Copernicus while elliptical orbits are briefly mentioned on another (p. 128) to contrast Indian dual-epicycle models with modern ones.

Yet in Wikipedia, due to this presentist principle of selection, we find discussions of certain modern topics dominating articles on the history of ancient and medieval astronomy:

• Anticipations of heliocentrism
• Anticipations of the rotation of the Earth
• Anticipations of elliptical orbits
• Anticipations of the concept of gravitation

These anticipations are selected to such an extent that the reader of these articles could come away almost totally unaware of the questions and methods governing early investigations of celestial phenomena.

• That their inquiry followed the model of geometrical astronomy, based on combinations of uniform circular motions, that is first documented in the writings of Hipparchus and Ptolemy.
• That the criticisms they levelled at their predecessors (such as Ptolemy) were framed within that model of geometrical astronomy.

In sum, by selecting material from the perspective of the present, we are in danger of writing a history, which, while accurate in detail, presents a false overall picture. --SteveMcCluskey 14:09, 14 June 2007 (UTC) (edited 15:03, 14 June 2007 (UTC))

Indian heliocentrism

The general consensus among mainstream historians of Indian astronomy is that Indian astronomical systems were fundamentally geocentric, using a non-Ptolemaic double-epicycle model (see, for example, Swerdlow 1973).

The strongest statement among mainstream historians of astronomy supporting the concept of heliocentricity is that of van der Waerden (1987) who maintains the generally accepted view that Āryabhata considered the Earth to rotate on its axis and draws from this the further inference that his system may have derived from an earlier Greek heliocentric theory. Most historians of Indian astronomy either ignore (Pingree 1973) or reject (Swerdlow 1973) claims for Indian heliocentricity. Less specialized historians of astronomy cautiously present the claim of a possible underlying heliocentric theory (Thurston 1994) "of which the Indians were unaware" (Duke 2005).

There is a consenus that Indian astronomers never explicitly presented a heliocentric system, although there is some belief that traces of a prior heliocentric system may be found in their work.

The uncertainty of the evidence for Indian heliocentrism makes it extremely unlikely, if not impossible, that this heliocentrism could have influenced later Islamic or European astronomers. --SteveMcCluskey 14:52, 21 June 2007 (UTC)

B. L. van der Waerden (1987)

The astronomical system of Āryabhata was composed about A.D. 510 or a little later. It is based on the assumption of epicycles and eccenters, so it is not heliocentric, but my hypothesis is that it was based on an originally heliocentric theory....

Most Hindu astronomers did not assume a rotation of the earth, but Āryabhata did assume it. We can explain this by supposing that his theory was derived from a heliocentric theory.

Of course, this is not a conclusive proof: it is only an indication of a possible explanation of a curious fact....

The relation between [Āryabhata's] Midnight System and the more sophisiticated Sunrise System underlying the Ārhabhatiya have been carefully investigated by P.C. Sengupta. In the Midnight System the apogees of the sun and Venus are both at 80°; and their eccentricities are also equal. This fact can be explained by assuming that the Midnight System was originally derived from a heliocentric system....

I think it is highly probable that the system of Āryabhata was derived from a heliocentric theory by setting the center of the earth at rest.

Noel Swerdlow (1973)

The revolutions of the planets in a Mahāyuga are given in two parts, the first corresponding to the planet's mean motion in longitude, the second to its mean motion on the epicycle, just as Ptolemy specifies mean motions in longitude and anomaly. For example, Jupiter completes 364,224 revolutions in longitude and 4,320,000 revolutions on its epicycle. When the motions are reduced to single revolutions, it turns out that the periods of the epicycles of the superior planets are one year, and the periods of the epicycles of Mercury and Venus are respectively about 88 and 225 days; that is, the periods of the inferior planets correspond to what we now call their heliocentric longitudinal periods, while the periods of the superior planets correspond to the annual motion of the earth. For this reason van der Waerden concludes that the models must be heliocentric.

Such an interpretation, however, shows a complete misunderstanding of Indian planetary theory and is flatly contradicted by every word of Aryabhata's description. Therefore, that mithyājñāna may not prosper, we shall explain the method of measuring motions in Indian planetary theory....

David Pingree (1973)

The reader should note that, in writing this survey, I have disregarded the rather divergent views of B. L. van der Waerden; these have been most recently expounded in his Das heliozentrische System in der griechischen, persischen und indischen Astronomie, Zürich 1970.

Hugh Thurston (1994)

Not only did Aryabhata believe that the earth rotates, but there are glimmerings in his system (and other similar systems) of a possible underlying theory in which the earth (and the planets) orbits the sun, rather than the sun orbiting the earth. The evidence is that the basic planetary periods are relative to the sun.

Dennis Duke (2005)

For the inner planets, the sighra argument uses not the mean longitude of the planet, which would be just the mean longitude of the Sun, but instead the absolute longitude λ_P′of the sighra epicycle radius,⁴...

4. Thus for both outer and inner planets, the mean motion given is the heliocentric mean motion of the planet. There is no textual evidence that the Indians knew anything about this, and there is an overwhelming amount of textual evidence confirming their geocentric point of view. Some commentators, most notably van der Waerden, have however argued in favor of an underlying ancient Greek heliocentric basis, of which the Indians were unaware. See, e.g. B. L. van der Waerden, “The heliocentric system in greek, persian, and indian astronomy”, in From deferent to equant: a volume of studies in the history of science in the ancient and medieval near east in honor of E. S. Kennedy, Annals of the New York Academy of Sciences, 500 (1987), 525-546. More recently this idea is developed in about as much detail as the scant evidence allows in L. Russo, The Forgotten Revolution (2004).

Islamic heliocentrism

The following three sections, dealing with general claims for Islamic heliocentrism and with specific claims that al-Zarqali, al-Biruni, and even al-Tusi had proposed elliptical orbits can be answered on two general points.

• First, it should be noted that these claims appear primarily in the historical introduction to Asghar Qadir's textbook on special relativity and in a popular article on Islamic Science appearing in an on-line version of a magazine published by a petroleum company.
• Secondly, there is a consensus among the principal historians of Islamic astronomy (Ragep 1987; Sabra 1998; Saliba 1996) that all Arabic / Islamic astronomy is based on the combination of the uniform circular motions of geocentric spheres; there is no question of either heliocentrism or elliptical orbits.

Specific comments are provided below. --SteveMcCluskey 14:02, 21 June 2007 (UTC)

Asghar Qadir (1989)

These estimates [of the size and distance of the Sun and Moon] were available to Ibn-al-Haytham, over a thousand years later. He revived the view of Aristarchus. If on no other count, then just the sheer size of the Sun would have convinced him that the Earth went round the Sun. He showed that the planets / moved in circles round the Sun. Two centuries later, Al Zarkali modified these results... (pp. 5-6)

There were also major advances made in the study of celestial motion. Nicolai Copernicus, a Polish monk, had revived the views of Ibn-al-Haytham. According to this view, Mercury, Venus, Earth, Mars, Jupiter and Saturn followed concentric, circular orbits of increasing radius about the Sun. The Moon followed a circular path about the Earth. Beyond Saturn were the fixed stars. (This picture is nowadays known as the Copernican system instead of Aristarchus' or Ibn-al-Haytham's system.) (p. 10)

Ibn al-Haytham (ca. 1000 [1990])

[22] The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its [the world's] middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest....

[35] The part which is neither heavy nor light surrounds the two remaining parts and moves around them with an unceasing motion. This part is that which is called the orb, and it is that which contains all the stars. [36] Its shape in its entirety is a spherical shape. It is surrounded and bounded by two spherical surfaces, whose center is the center of the world.... [37] This body in its entirety moves with a swift motion from the direction that is called east to the direction that is called west. It sets in motion by means of its own motion all the heavenly bodies which are contained within it with a circular motion.

A. I. Sabra (1972)

[On the Configuration of the World] In his careful description of all movements involved, Ibn al-Haytham provided, in fact, a full, clear, and untechnical account of Ptolemaic planetary theory....

Perhaps most important historically was ibn al-Haytham's objection against the device introduced by Ptolemy which later became known as the equant".

F. Jamil Ragep (1987)

In fact, the aim of virtually every theoretical astronomer in the Arab/Islamic tradition was to provide a physical structure, or Hay'a,^* for the universe in which each of Ptolemy's motions in the Almagest would be the result of a uniformly rotating solid body called an orb (falak). This process, of course, had been initiated by Ptolemy himself in Book II of his Planetary Hypotheses....

* Whence the name of the enterprise, 'ilm al-hay'a, i.e., the "science of hay'a." Eventually this came to denote astronomy in a general sense though the more specialized meaning was still understood....

A. I. Sabra (1998)

All Islamic astronomers from Thabit ibn Qurra in the ninth century to Ibn al-Shatir in the fourteenth, and all natural philosophers from al-Kindi to Averroes and later, are known to have accepted what Kuhn has called the "two-sphere universe" (Kuhn 1962, chap. 3)--the Greek picture of the [End Page 317] world as consisting of two spheres of which one, the celestial sphere made up of a special element called aether, concentrically envelops the other, where the four elements of earth, water, air, and fire reside, all ideally so ordered in their rounded regions as one proceeds from the common center to the circumference....

The work done on planetary theory in thirteenth century Syria and northwest Iran and subsequently resumed in fourteenth century Damascus did not constitute a "revolution," as Saliba suggests (Saliba 1994, pp. 245ff., 258ff.), but a remarkably successful reform that exposed possibilities of achieving greater theoretical consistency within the Ptolemaic system, and, in [End Page 321] some cases, a better fit with observation. There was no attempt or desire to break away from the Ptolemaic paradigm as such. It would be odd to call "revolutionary" a reformist project intended to consolidate Ptolemaic astronomy by bringing it into line with its own principles. True, the new configurations embodied a number of "non-Ptolemaic" models, "non-Ptolemaic" in that they freed themselves from embarrassing features that appeared to mar the Ptolemaic constructions (Roberts 1966, p. 208), but, in their attempt to save the Ptolemaic principles (circularity, uniformity, and the use of eccenters and/or epicycles), the new configurations may equally well be regarded as more Ptolemaic than Ptolemy's. To look on these pre-Copernican endeavors as a reform, the result of a problem- or puzzle-solving program, is not to divest them of their obvious value, but to stress their adherence to the principles and the methodology of a hugely successful enterprise--principles and methodology which, understandably, had to be fully explored before they could be overthrown. Problem-solving, in this sense, is not a useless or second-rate effort but an exercise of the type that often functions in the history of scientific thought as a necessary prelude to "revolution." But, as is well known, when "the revolution" began to take shape, on the way from Copernicus to Kepler, an entirely new set of astronomical observations and a new flight of imaginative theorizing happened to be crucially involved.

George Saliba (1999)

There is no talk at this point of heliocentrism, the concept commonly stressed in Copernican astronomy. But one should also equally hasten to say that Copernican heliocentrism is itself stressed (in a hindsight fashion) at the expense of the mathematical foundations of Copernican astronomy, foundations that Copernicus developed and used before he took the last step of displacing the center of the universe from the earth to the sun. One should also add at this point that in mathematical terms heliocentrism can be accomplished just by reversing the direction of the last vector connecting the earth to the sun. The rest of the mathematics involved in both types of astronomical systems could then remain the same. That fact was well known to pre-Copernican astronomers, and notably to someone like the polymath Biruni (d. c. 1049), and was dismissed as a philosophical problem and not an astronomical / mathematical one per se....

With the same mathematics, the same observations, more or less, astronomers working within the Islamic world could account for the planetary positions just as well as Copernicus could do, or even Ptolemy for that matter, despite the fact that the astronomers of the Islamic world continued to work within the cosmologically earth-centered Aristotelian system which was perfectly defensible for their time. The central problem for them had nothing to do with the issue of heliocentrism, rather it had to do with issues related to the lack of the inner consistency of Greek astronomy. By that I mean that they were seeking mathematical constructions that did not exhibit by their very definition a contradiction with the physical realities they were supposed to represent, as was clearly done in the defunct Ptolemaic astronomy.

al-Zarqali's elliptical orbits

The notion that al-Zarqali posited an elliptical orbit for Mercury has been in the literature since (Ball, ca. 1908), (Briffault, 1919), (Rufus, 1939), and (Qadir 1989). More recent historians of astronomy (Hartner 1955) and (Aiton 1987) correct the claim in several ways.

• The path being described is not the path of the planet but the path of the center of the epicycle of the planet Mercury.
• The path is not centered on the Sun but is centered on a moving point near the Earth.
• The path is not a mathematical ellipse, but an ellipsoidal shape defined by combinations of uniform circular rotations as defined by Ptolemy.
• This path is not found for all the planets, but only to the unusual case of the planet Mercury.

Hartner, who presented the most detailed description of al-Zarqali's ellipse-like figures, identifies the details in the diagram that led some interpreters to misinterpret it as a heliocentric ellipse. Recent studies by Samsó and Mielgo (1994), indicate that the path of the center of Mercury's epicycle as described in al-Zarqali's text describe this path as having the shape of an ellipse. The consensus among historians of science shows no evidence for an elliptical orbit of Mercury in al-Zarqali. --SteveMcCluskey 14:30, 21 June 2007 (UTC); edited 16:41, 29 April 2010 (UTC)

Al-Zarqali also presented a similar, but unrelated, model to account for the slow motion of the Solar apogee (1° in 279 years) in which the center of the Sun's deferent moved on a slowly-moving small circle. This was first reported by Regiomontanus and Peurbach and has since been discussed by such historians as (Delambre, 1819), (Sédillot, 1847), and (Toomer, 1969 and 1987). --SteveMcCluskey (talk) 16:41, 29 April 2010 (UTC)

Asghar Qadir (1989)

Two centuries later [after Alhacen], Al Zarkali modified these results, in the light of better data, to state that they [the planets] moved in ellipses with the Sun at one focus. (p. 6)

Kepler revived Al Zarkali's law of planetary motion, which states that planets move in ellipses with the Sun at one focus. (This is now known as Kepler's first law rather than Al Zarkali's law.) He went on, however, to state two more laws which were quantitatiive. (p.11)

J. B. J. Delambre (1819)

Pour accorder ses observations à celles d'Albategni, et rendre raison de la diminution qu'il remarquait dans l'excentricité du soleil. Arzachel faisait tourner, dans un petit cercle, le centre de l'excentrique, ainsi que Ptolémée en avait donné l'exemple pour la Lune.

L. P. E. A. Sédillot (1847)

Aben-Esra professait une haute considération pour Arzachel; il nous fait connaitre son hypothèse relative à l'excentricité du soleil, hypothèse qui consistait à faire tourner dans un petit cercle le centre de l'excentrique, ainsi que Ptolémée en avait donné l'exemple pour la lune(3).

(3) Regiomontan, [probably In Ptolemæi magnam compositionem, quam Almagestum vocant Libri XIII], éd. 1550, III, 13, dit: Velut in mercurio habetur— V. sur Aben-Esra les not de Scaliger in Manil., et Snellius in addit. obs. Hass., p. 103, 106, etc.

W. W. R. Ball (1908 or earlier)

Arzachel.² Another Arab of about the same date was Arzachel, who was living in Toledo in 1080. He suggested that the planets moved in ellipses, but his contemporaries with scientific intolerance declined to argue about a statement which was contrary to Ptolemy's conclusions in the Almagest.

2. See a memoir by M. Steinschneider in Boncompagni's Bulletino di Bibliografia, 1887, vol. xx.

Robert Briffault (1919)

...although Al-Zarkyal declared the planetary orbits to be ellipses and not circles, although the orbit of Mercury is in / Al-Farâni's tables actually represented as elliptical,...

W. Carl Rufus (1939)

A direct effect was the work in Spain under Alphonso X, who brought together a staff of astronomers and prepared the Alphonsine Tables published [not so, S.Mc.] on the day of his accession in 1252. He also compiled an extensive astronomical encyclopedia chiefly from Arabic sources. In this work Mercury's orbit is represented as an ellipse; geocentric of course, but interesting as the first representation of the mo-/tion of a heavenly body that departed from the Greek idea of uniform circular motions.

Willy Hartner (1955)

The Curve Described by the Centre of the Epicycle.... (p. 109)

The table [1] demonstrates with sufficient clarity that the "Ptolemaic curve" (about which no word is found in Ptolemy's Almagest) is practically interchangeable with the ellipse.... (p. 114)

As mentioned before, the first European author I know of who expressly stated the similarity of the curve described by the centre of the epicycle with an ellipse was Peurbach, and even he contents himself with saying that it is a "kind of oval". In the Islamic world, however, as will be seen, the discovery is of a much earlier date.... (p. 118)

The text of Chapter IX [of Azarquiel's treatise] however, which will be summarized here, leaves no doubt that it is nothing but the curve resulting from Ptolemy's theory, which we discussed above in detail:

"Finally, join every three of the points thus marked, by an arc, and there will result a curve similar to a pignon. And when you have made the circles of Mercury as I have shown in this chapter, its postion will result from them very accurately, more so than in any other way".

Thus the first explicit description of the curve of Mercury's true deferent, as well as its practical application, is undoubtedly Arabic....

Concerning the plate illustrating Azarquiel's text, it may be well to note that it was obviously not carried out in accordance with the author's prescription. The small circle inthe middle (which looks like the Sun and therefore has deceived many interpreters) is nothing but the small circle with radius ε round F.(pp. 120-121).]

G. J. Toomer (1969)

The second source is the work of Regiomontanus and Peurbach, usually known as the Epitome of the Almagest, Book III Prop. 13.... I quote it verbatim:

So he [al-Battānī] set the maximum solar equation as 1;59,10°. Az-Zarqāl, 193 years after al-Battānī, made four observations round about four points between the positions of equinox and solstice and found BH ro be 12;10°. Therefore he was forced to say that the center of the sun's eccentric moves in a small circle, as is the case with Mercury.

G. J. Toomer (1987)

One of the two major sources for knowledge of az-Zarqāl's solar theory in the West was the Epitome of the Almagest by Peurbach and Regiomontanus.³ Although this is mostly a tissue of errors and misinterpretations, it does contain some true and important information, notably that az-Zarqāl said that the center of the sun's eccenter moves on a small circle. On the basis of sources which had only recently become available, I was able to show that this was indeed a feature of az-Zarqāl's solar model, although its purpose was misunderstood in the Epitome.

3. Regiomontanus Bk. III Prop. 13, quoted and translated in Toomer, 307. As N. Swerdlow pointed out to me, the fourth sentence in my quotation is misprinted in the Venice edition, and should be emended to read "Vide [for "Inde"] igitur cuius obseruationi fidem habeas."Translation: "Consider then whose observation [az-Zarqāl's or al-Battānī's] you should trust."

E. J. Aiton (1987)

Sixth, from what has been said it appears clearly that the center of the epicycle of Mercury, on account of the motions stated above, does not, as in the cases of the other planets, describe the circular circumference of the deferent but rather the periphery of a figure that resembles a plane oval.⁷¹

71. A modern analysis of the motion of the epicycle in the theory of Ptolemy described by Peurbach may be found in Hartner, Oriens-occidens, (cit. n. 65), pp. 465-478. Peurbach was the first European to describe the curve as similar to an ellipse, though it had been so described by al-Zarqali in the eleventh century. According to Hartner's analysis, the curve implied by Ptolemy's theory is practically an ellipse. On al-Zarqali see Heinrich Suter, Die Mathematiker und Astronomen der Araber und ihre Werke (Leipzig: Teubner, 1900; rpt. New York: Johnson, 1972), pp. 109-11.

Julio Samsó and Honorino Mielgo (1994)

One item in Ibn al-Zarqālluh's book [the Libro de las láminas de los siete planetas] is its description of the method used to draw Mercury's deferent which, in this instrument, is a non-circular curve.... The curve drawn following this procedure is described, in the Alfonsine translationof Ibn al-Zarqālluh's words, as follows: "et sera el çerco del leuador figura de taiadura menguada de las taiaduras que uienien en la figura pinnonata."... The translation of the aforementioned Alfonsine Castilian text is, then: "The deferent circle will have the shape of the deficient section [ellipse], of those sections which appear in the pineal figure [cone]."

Now we also know that Ibn al-Zarqālluh identified this curve as an ellipse and this is the first instance, to the best of our knowledge, of the use of such a conic section in astronomy, even if the eleventh-century Toledan astronomer had no theoretical pretensions in his use of an ellipse and employed it only to simplify his design of an equatorium.

A systematic attempt has been made, however, to see if a model based on elliptic deferent could have been used to calculate the tables of equations for Mercury in Andalusian, medieval Spanish, and Maghribi astronomical tables.... The results obtained have been negative: all the tables considered derive their Mercury equation tables from [Ptolemy's] Handy tables. --SteveMcCluskey (talk) 21:48, 10 April 2010 (UTC)

J. L. Bergren (1997)

In view of the theoretical importance ellipses assumed in astronomy as a result of the work of Kepler it is interesting to note that the 11th-century, Spanish astronomer Azarquiel (Ibn al-Zarqaālluh) used them to approximate the path of the center of Mercury’s epicycle in his design of an equatorium. Mercè Comes [31] has published the treatise in which this occurs, along with another by Ibn al-Samḥ.²² As Julio Samsó and Honorino Mielgo [140, 292] point out, in using the ellipse Azarquiel / had no "theoretical pretentions," and indeed they establish that none of the writers of Spanish or northwest African zijes used the elliptical approximation as a basis for the difficult task of computing the positions of Mercury.

22. Both treatises concern the equatorium, a medieval instrument for analogue computation of the position of the planets. The fact that the only known application of conics prior to the time of Kepler occurs in a treatise on an astronomical instrument is just one instance of many that could be adduced of the importance of the history of instruments for the history of mathematics.

al-Biruni's elliptical orbits

In addition to the general comments above, the specific claim that al-Biruni maintained that the planets moved in elliptical shapes in his Canon Mas`udi is not supported by Kennedy's (1971) detailed summary of that work nor by the figure reproduced by Hartner (1955) from the Canon.

Biruni (11th c. [2004]) does speak of possible ellipsoidal or lenticular shapes for the celestial orbs in another work (correspondence with Ibn-Sina on Aristotle's cosmology), where he finds fault with validity of Aristotle's proof that the heaven's are spherical, but

• He maintains that these ellipsoidal or lenticular shapes are consistent with circular motion and
• He nonetheless considers that the celestial orbs are spherical.

One historian of Islamic science, (Nasr 1964), quotes this passage in his Introduction to Islamic Cosmological Doctrines and maintains that Biruni implies "that the heavens could have an elliptical motion", despite Biruni's assertion that they actually do not.

The consensus view is that Biruni maintained a traditional Ptolemaic model of circular eccentrics and epicycles; the minority view maintains that Biruni considered "that the heavens could have an elliptical motion," although this is not supported by Biruni's discussion of the possible circular rotation of ellipsoidal or lenticular shapes. --SteveMcCluskey 14:14, 21 June 2007 (UTC)

Richard Covington (2007)

In his comprehensive encyclopedia of astronomy, Kitab al-qanun al-Mas’udi, or the Canon Mas’udicus, dedicated in 1031 to Mahmud’s son and successor, Mas’ud, al-Biruni also observed that the planets revolved in apparent elliptical orbits, instead of the circular orbits of the Greeks, although he failed to explain how they functioned. It was not until the 13th century that al-Tusi conceived a plausible model for elliptical orbits.

Willy Hartner (1955)

n. 87. For Al-Biruni's (973-1048) purely mathematical treatment, see Fig. 15, showing a page from one of the earliest manuscripts known of his Mas`udic Canon (al-Qanun al-Mas`udi), written less than a century after the author's death. [The Figure cited shows two conventional figures, one for the motion of Venus and the superior planets, the other for the motion of mercury. Both employ traditional Ptolemaic geocentric models of circular deferents and epicycles.]

S. H. Nasr (1964)

[al-Biruni] goes as far as to imply that the heavens could have an elliptical motion without contradicting the tenets of medieval physics. Again, criticizing Aristotle on this point he writes [Nasr then quotes a different translation of the discussion with ibn-Sina quoted below at al-Biruni (11th c. [2004]), italicizing the significant conclusion]:

Aristotle has mentioned in his second article that the elliptical an lentil-shaped figures need a vacuuum in order to have circular motion, and a sphere has no need of a vacuum.... For ir we make the axis of rotation of the ellipse the major axis and the axis of rotation of the lentil-shaped figure the minor axis, they will revolve like a sphere and have no need of a void. The objedction of Aristotle and his statement become true in the case where we make the minor axis of the ellipse and the axis of fotation of the lentil-shaped figure... I am not saying according to my belief that the shape of the great heavens is not spherical, but elliptical or lentil-shaped. I have made copious studies to reject this view, but I wonder at the logicians.

[It is noteable that Nasr's discussion speaks of elliptical motion, while the text he quotes speaks only of the circular motion of an elliptical body. SteveMcCluskey 15:33, 15 June 2007 (UTC)]

[For a presentation of some of the "factual errors and misinterpretations" in Nasr's work see David King's scathing review of the chapters on mathematics and astronomy of Nasr's Islamic Science: An Illustrated History. --SteveMcCluskey 15:16, 21 June 2007 (UTC)]

E. S. Kennedy (1970)

[The Canon] Treatises 1 and 2 set forth and discuss general cosmological principles (that the earth and heavens are spherical, that the earth is stationary, etc.)....

Treatises 6 and 7 are on the sun and moon respectively. Here (and with planetary theory further on) the abstract models are essentially Ptolemaic.

E. S. Kennedy (1971)

"Al-Bīrūnī's Masudic Canon"

Treatise I ... Chapter 2. Brief explanation of the bases of the art (of astronomy), containing six principles (ūsūl):

First Principle: that the heavens are spherical in shape and motion.

Second Principle: that the earth is spherical.

Third Principle: that the earth is at the center of the heavens.

Fourth Principle: that its size is negligible with respect to that of the heavens.

Fifth Principle: that the earth has no motion.

Sixth Principle: that the primary motions are of two sorts.

...

Treatise VI ... Chapter 4. On the necessity of the eccentric orbit [of the sun] and how to picture it in the heaven of the sun.

...

Treatise X ... Chapter 2. On the method Ptolemy came upon for (determining) the conditions, apogees, epicycles, and motions of the two inferior planets.

Section 1. On the apogee and its motion.

Section 2. On the amount of the eccentricity.

Section 3. On the determination of the epicycle radius and the verification of the anomaly by it.

Chapter 3. On the method Ptolemy arrived at for the superior (planets) like that he came upon for the inferior ones....

[At no point in his summary of the Masudic Canon does Kennedy indicate the possibility of an ellptic orbit, yet his discussion begins with the traditional Ptolemaic axioms of circular motion and he dedicates sections to the discussion of the traditional Ptolemaic model based on eccentric circles and epicycles.]

al-Biruni (11th c. [2004])

33) The Sixth Question: [Aristotle] has mentioned in Book II that [the shape of the heaven is of necessity spherical because] the oval and the lenticular shapes would require space and void whereas the sphere does not, but the matter is not so. In fact, the oval [shape] is generated by the rotation of ellipse around its major axis and the lenticular by its rotation around its minor axis. As there is no difference concerning the rotation around the axes by which they are generated, therefore none of what Aristotle mentions would occur and only the essential attributes of the spheres would follow necessarily. If the axis of rotation of the oval is its major axis and if the axis of rotation of the lenticular is its minor axis, they would revolve like the sphere, without needing an empty space (makan khal). This could happen, however, if the axis of [rotation of] the oval is its minor axis and the axis of [rotation of] the lenticular is its major axis. In spite of this, it is possible that the oval can rotate around its minor axis and the lenticular around its major axis, both moving consecutively without needing an empty space, like the movement of bodies inside the celestial sphere, according to the opinion of most people. And I am not saying this with the belief that the celestial sphere is not spherical, but oval or lenticular; I have tried hard to refute this theory but I am amazed at the reasons offered by the man of logic.

al-Tusi's elliptical orbits

As in the cases of Al-Zarqali and al-Biruni, this claim appears to be based on a simplified identification of an ellipse with an oval curve. Hartner's detailed mathematical analysis shows that al-Tusi's curve differs both from an ellipse and from the Ptolemaic path. In this case again, the ellipsoidal path is the path of the center of the epicycle, not the path (or orbit) of the planet. --SteveMcCluskey 22:58, 21 June 2007 (UTC)

Richard Covington (2007)

It was not until the 13th century that al-Tusi conceived a plausible model for elliptical orbits.

Willy Hartner (1969)

The curve described by the centre of the [Moon's] epicycle according to Ptolemy, when referred to the mean Sun (see Fig. 4) has an oval shape with two axes of symmetry.... Now comparing the Ptolemaic with the Nasīrian curve and, on the other hand, with an ellipse having the same axes, we find (Fig. 10) that the Ptolemaic curve is comprised between the Nasīrian (exterior) and the ellipse (interior, dotted).

George Saliba (1996)

After this general review of the planetary theories which were developed by Arabic writing astronomers after the twelfth century, it has become clear that the two major achievements of this long tradition were,... two mathematical theorems: ... `Urdī's lemma and ... the so-called Tūsī Couple. With the help of these two theorems ... it was possible to transfer segments of these [Ptolemaic] models from the central parts to the peripheries and back. This freedom of movement not only allowed the retention of the effect of the equant in the Ptolemaic models, but also allowed the development of sets of uniform [circular] motions that would not violate any physical principles. The Tūsī Couple allowed, in addition, the production of linear motion as a combination of circular motions,... [Note that Saliba makes no mention of ellipses in his lengthy study, a point which also applies to the discussion of al-Biruni's "elliptical orbits", below] --SteveMcCluskey 20:49, 20 June 2007 (UTC)