Talk:Eudoxus of Cnidus
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This article would be a bit better if there were either images of Eudoxus or present images of Eudoxus' planetary model to allow people to understand his views on astronomy.
SO much more can be said about Eudoxus. He was extremely important in both astronomy and math. The math is explained fairly well, but the explanation of his influence in astronomy could be much larger than it is now JerDW
- It's better now. Maestlin 01:53, 12 March 2006 (UTC)
- But I think more can be said about the math too. Maestlin 00:33, 14 March 2006 (UTC)
Please, do not replace the whole article with new text that does not contain any wiki markup! Instead, discuss the changes here, or add them within the MoS guidelines, all new text well referenced, to improve this article. Awolf002 11:25, 7 August 2007 (UTC)
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I dispute the rigor of later mathematicians
Was Newton really more rigorous than Archimedes or Eudoxus? It is well know that Newton and Leibnitz's Calculus was not really that rigorous at all. In fact, Euler and virtually everyone up to Gauss and his students were often caught making what are probably now considered classic amateur mistakes on all variety of topics of calculus. And yet, the Archimedean Property of the real numbers is one of the first things taught in the any rigorous and correctly done version of calculus nowadays (in a first course in real analysis, for instance). And, actually given the rigor, it is not even clear to me that Eudoxus and Archimedes were truly exceeded in sophistication, either. It seems to me, their work was more like just relatively crudely extended until those extensions were actually put on the same rigorous basis as the original material.
To get more rigorous than the Greeks you have to come all the way to the modern era of around the 19th century with the efforts to put math (and particularly calculus) on a rigorous basis.
picture of Eudoxus?
Innermost lunar sphere in Eudoxian model
- * The third also completes its revolution in a month, but its axis is tilted at a slightly different angle, explaining motion in latitude (deviation from the ecliptic), and the motion of the lunar nodes.
Is this correct? My understanding of Eudoxus' lunar model is that the innermost sphere rotates westward (same as the outer sphere but opposite to the middle sphere), taking a Saros period (about 18.6 years) to do so. [Correction: a draconitic period, I should say!]
The inclination of the inner sphere does indeed explain why the Moon does not follow the ecliptic exactly (otherwise there would be solar and lunar eclipses every month).
The rotation of the inner sphere explains why the Draconic month is shorter than the Sidereal or Zodiacal month (i.e. it explains the motion of the lunar modes, as the article says), but it cannot do this if it too takes only a month to rotate.Eroica (talk) 19:15, 6 August 2009 (UTC)
- Or is it the middle sphere which rotates eastward in a Saros [Correction again: a draconitic period, I should have said!], while the inner sphere rotates in a Draconic month? This seems to be the description in Jean-Claude Pecker's Understanding the Heavens. - Eroica (talk) 19:35, 6 August 2009 (UTC)
A little research into this matter shows that there is no general consensus about it (or about the correct interpretation of Simlicius's account of the homocentric model). My own understanding is as follows: The motionless spherical Earth sits at the common centre of the three lunar spheres.
- The outer sphere has an axis that is collinear with the Earth's axis - i.e. its equatorial plane coincides with the Earth's equatorial plane. It rotates westward in 23 hours fifty-six minutes. This accounts for the daily revolution of the Moon about the Earth, which we explain today by saying that the Earth rotates on its axis in the opposite direction in 23 hours fifty-six minutes.
- The middle sphere rotates on an axis that is inclined at an angle of 23.45 degrees to the outer sphere's axis - i.e. the equatorial plane of the middle sphere coincides with the plane of the ecliptic. This sphere also rotates westward, taking a Saros cycle (18.6 years)[Correction again: a draconitic period, I should have said!] to complete one rotation. The axis of this sphere extends beyond its poles and skewers the outer sphere. So, as the outer sphere rotates, the axis of the middle sphere gyrates or precesses about the outer axis. The middle sphere rotates on its own axis and gyrates about the outer axis, like a spinning top that has started to wobble.
- The inner sphere rotates on an axis that is inclined at an angle of 5.145 degrees to the axis of the middle sphere - i.e. the equatorial plane of the inner sphere coincides with the plane of the Moon's orbit. This sphere rotates eastward, taking 27.32 days (a sidereal month or zodiacal month) to complete one rotation. The axis of the inner sphere extends beyond its poles and skewers the middle sphere (but not the outer sphere). So, as the middle sphere rotates, the axis of the inner sphere gyrates or precesses about the middle axis. The inner sphere rotates on its axis eastward once a month; its axis precesses westward once a Saros cycle [Correction again: a draconitic period, I should have said!]. The diurnal rotation of the outer sphere is also transmitted mediately to the inner sphere via the middle sphere.
- The Moon is attached to the equator of the inner sphere, like a diamond on a ring. The two inner rings together account for the inclination of the Moon's orbit to the ecliptic, the sidereal revolution of the Moon about the sky in 27.32 days, and the precession of the lunar nodes, which results in the period between two successive passages of the Moon through the same node being less than 27.32 days (actually about 27.22 days or a draconic month).
A number of sources claim that the rotation period of the inner sphere is equal to the draconic month. I just don't get this. surely it is the combination of the sidereal rotation of this sphere with its gyration about the axis of the draconitic-rotating middle sphere that generates the draconic month?
Well, that's my two cents. Quite a bit of research would be required before I would be confident enough to try and create a new Wikipedia article on the Eudoxian homocentric model. - Eroica (talk) 10:59, 7 August 2009 (UTC)
- The source for the Mathematics section of the article is Morris Kline's Mathematical thought from ancient to modern times. Not only does it fail to mention the (dubious) fact that all of Eudoxus' works are lost, but discusses the events of his life and his mathematical works in very specific detail. Whether Eudoxus' original works are lost or not, it seems like Kline relies on secondary sources like Proclus. Kline does at some point say that the astronomical works of Eudoxus are lost, with only fragments surviving, but also that there are other authors that refer to Eudoxus' original works so that today we know at least the essence of the theory. Sławomir Biały (talk) 21:13, 16 May 2016 (UTC)