Talk:History of astronomy

History of Science B‑class Top‑importance

This article is part of the History of Science WikiProject, an attempt to improve and organize the history of science content on Wikipedia. If you would like to participate, you can edit the article attached to this page, or visit the project page, where you can join the project and/or contribute to the discussion. You can also help with the History of Science Collaboration of the Month.History of ScienceWikipedia:WikiProject History of ScienceTemplate:WikiProject History of Sciencehistory of science articles B This article has been rated as B-class on Wikipedia's content assessment scale. Top This article has been rated as Top-importance on the project's importance scale.

Template:FAOL

What about the equipment in use - astrolabes etc?

I can write an overview of Mesopotamian astronomy (note that it is an empty section at the moment), but I think that the current subheadings look arbitrary (i.e., "Sumerian," etc.). They do not reflect any periodization or organizational scheme in any work on the subject I have read (admittedly a short reading list, though).

Given its importance to the history of astronomy, I think this subject deserves its own page. If nobody objects, I will remove the subheadings and write a short overview without the subheadings and start a new page where it can receive the attention it merits. Something like "Mesopotamian Astronomy and Astrology." If there is such a page, I have not found it.Maestlin 00:32, 24 February 2006 (UTC)[reply]

If you don't like the sub-headings, go ahead and change them. One of the principles of Wikipedia is WP:Be bold.--ragesoss 02:00, 24 February 2006 (UTC)[reply]

Done. It is long but not any longer than the section on Indian astronomy. I also added more references and, in a separate edit, moved around the sections so that all the east asia material goes together. Maestlin 22:26, 10 March 2006 (UTC)[reply]

I removed the link to the Astronomical Code of the Rigveda since it is about a fairly narrow topic. I added a link to it in the article on Hindu astronomy where it is more relevant. Maestlin 01:25, 11 April 2006 (UTC)[reply]

The writings of western historians provide a quite different outlook than appears in the current section on Indian astronomy. There are two issues at hand:

• The dating of the Vedic texts and their astronomical interpretation.
• The claim for the discovery of calculus.

An essay by the late historian of Indian science, David Pingree, frames the issue well. He regretted that "many non-Westerners ... are deluded into believing that the greatest glory an Indian, a Chinese, an Arab, or an African scientist can have acquired is that gained by having anticipated a Greek or a modern westerner." Turning to the claim that Madhava discoverd calculus, he noted that "now [that] we have the Sanskrit texts properly edited,... we understand the clever way that Madhava derived the series without calculus.... In this case the elegance and brilliance of Madhava's mathematics are being distorted as they are buried under the current mathematical solution." Isis, 83(1992):554-563.

I am not an expert on Indian science, but I hope someone who is familiar with the literature will be able to add a few balancing citations. --SteveMcCluskey 21:19, 13 May 2006 (UTC)[reply]

Steve, I flagged the section on astrology in the RgVeda (in History of Astrology) for the same reason. (perhaps some material on Indian astronomy should be excised until further notice). With the recent loss of Pingree and the scattering of the dept. at Brown, we can only hope that some qualified researchers take up this challenge soon. I do not have plans to learn Sanskrit and get involved in this research, but I'm always on the lookout for works correcting this problem - have yet to find any in a book form of the History of Indian astronomy/astrology. I recall hearing that the development of the Nakshatras occurs in the latest of the Vedas - Atharva Veda. While there is a good chance that the mythology of earlier Vedas has some (perhaps significant) starlore intertwined, interpreting the presence of astronomical observations is a more difficult claim to make. If the dating of the Atharva can be worked out, then astronomical observations of the moon cycle through the 27 (or 28) mansions would support the Nakshatra ritualistic astrology. Zeusnoos 16:17, 14 May 2006 (UTC)[reply]

Articles about the history of science in India and in Islamic regions tend to bring out strong feelings on Wikipedia. I won't cut or alter existing material on these subjects, in most cases, until I have all my ducks lined up, so to speak--and there are better uses of my time. Two subjects that I would particularly like to see addressed are the alleged heliocentrism of Aryabhata and the rather peculiar article on Ibn al-Shatir, which seems to be trying to make him into a precursor of Copernicus. Maestlin 22:34, 14 May 2006 (UTC)[reply]

Slightly off topic. Since I just spent a day on Ibn al-Shatir last semester, I revised that entry adding references and tempering the claims of influence on Copernicus. --SteveMcCluskey 13:59, 15 May 2006 (UTC)[reply]

The article mentions a vernal equinox in Orion. I don't think that is possible: precession of the earth's axis of rotation (precession of the equinoxes) puts the sun in different constellations in different eras, but the sun is still limited to the constellations of the zodiac. Am I confused?Evelyn Kinzel 23:31, 5 January 2007 (UTC)[reply]

alineations? What is it? --darklilac 19:18, 5 September 2006 (UTC)[reply]

Structures lacking straight lines? I suspect alignments is the word someone wanted. Zeusnoos 20:47, 5 September 2006 (UTC)[reply]

As I have mentioned in other discussions, I think we need to be careful about how much space we devote to Asian science. It seems that in every science article in Wikipedia, there is always an extra long section on India (as well as China and Islam) while many times Greece isn't given as much attention as it should be given. Wikipedia is the first online encyclopedia I have seen that devotes more space to Asian civilizations (when discussing the history of any science) than it does Greece. Can we really say that what these Asian civilizations did was really science? The other (more respectable) encyclopedias I read give me enough solid facts (not speculations) to believe otherwise. Modern science, as we now understand it as a subject, like it or not, was largely a Western creation. Cftiger 22:33 27 November 2006.

Well, color me shocked. I never expected to find such a narrow-minded perspective on the world from a Wikipedian. Most of those "respected encyclopedias" you mention are written in English by people in America or England. Every culture colors its history to make itself seem like the most important. While the Western Scientific Method is a Western invention, that doesn't mean that the work in other countries is irrelevant to the history of, in this case, Astronomy. Just like the work done in the west before the invention of the modern Scientific Method is not suddenly invalid. Korval 05:25, 8 December 2006 (UTC)[reply]

I agree. Much of the history of Western astronomy doesn't really qualify as science either. To exclude the history of other cultures just because they aren't part of the traditional picture of the Western march of progress towards modern science is to ignore their actual accomplishments. — Laura Scudder ☎ 15:49, 8 December 2006 (UTC)[reply]

You two are criticizing my original comment, which is fine, but can you really present any facts that prove that science wasn't mostly developed in the West? It is easy to say that Westerners have been Eurocentric, but most of the sources I read clearly aren't, in that they give plenty of credit to other cultures. The only difference between them and Wikipedia is that they acknowledge that at least 80% of science in the form that we now understand it was developed in the West. When you examine the facts, you really can't say otherwise. Why didn't the Eastern cultures create the modern world first? And how can you say that what the Greeks were working with wasn't science? Just because you would like for something to be true, doesn't mean it is. Cftiger 14:19 17 December 2006 (UTC)

I think the amount of the work represents the amount of the participation of the people to some degree. There is no rule to quata the space for each culture. In fact, Korea and Japan have their own history of astronomy which is a bit different from that of China, but, none of them were described until now. Jtm71 02:22, 3 February 2007 (UTC)[reply]

I requested some citation of sources in the section on Indian Astronomy on the talk page almost a year ago (on 13 May 2006). A request for sources template has been displayed on the Indian Astronomy section since February.

Recently User:202.179.64.9 has twice removed that template without providing any sources. I am restoring the template and, once again, requesting that some knowledgable editors document the claims in this section or it will become liable for removal. --SteveMcCluskey 22:37, 8 May 2007 (UTC)[reply]

• I agree, that section is a complete incoherent mess. --Etacar11 22:46, 8 May 2007 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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.^[1]

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^[2] 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"^[3] 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))[reply]

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.... ^[4]

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.^[5]

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.^[6]

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).^[7]

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)^[8]

[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.^[9]

[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".^[10]

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....^[11]

* 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....

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.^[12]

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.^[13]

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)^[14]

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 thae 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).]^[15]

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^[16]

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.^[17]

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.]^[18]

[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.^[19]

[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)][reply]

[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.^[20]

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.^[21]