Eudoxus

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In existographies, Eudoxus (c.390-337BC) (IQ:175|#212) (GME:#) (GAE:#) [Allen 100:52] (CR:8) was a Greek mathematician, astrophysicist, and philosopher, noted for []

Education

In c.370BC, Eudoxus, as a youth, supposedly, travelled miles to listen to Plato lecture; then, having become un-enamored with Plato’s lack of mathematical ability, travelled to Heliopolis to learn astronomy.

Eudoxus, they say (Plutarch, 100AD), received instruction from Chonuphis of Memphis.[1]

Plato, alternatively, was said to have went, with Eudoxus (or Eudoxus when by himself), as a student to Heliopolis to study for over a decade, to learn what they could about Egyptian knowledge, likely e.g. Nun cosmology, Heliopolis creation myth, etc., therein translating some Egyptian books (or scrolls) to Greek, after which they came back to Greece to open academies for teaching. [2]

Eudoxus was, supposedly, also a pupil of Archytas the Pythagorean. (Ѻ)

Ethics

In 322BC, Aristotle, in his Nicomachean Ethics, states that Eudoxus had the following five points to say about ethics:

1. All things, rational and irrational, aim at pleasure; things aim at what they believe to be good; a good indication of what the chief good is would be the thing that most things aim at.
2. Similarly, pleasure's opposite − pain − is universally avoided, which provides additional support for the idea that pleasure is universally considered good.
3. People don't seek pleasure as a means to something else, but as an end in its own right.
4. Any other good that you can think of would be better if pleasure were added to it, and it is only by good that good can be increased.
5. Of all of the things that are good, happiness is peculiar for not being praised, which may show that it is the crowning good.

Some say he taught Aristotle, and rank him second only to Archimedes in all antiquity (Calinger, 1982).

Astronomy

The geocentric model of Exodus, supposedly. [3]

Eudoxus, building on Plato, developed a mathematical model of the solar system, consisting of a central spherical earth, surrounded by 27 nested or concentric rotating spheres, with the outer sphere carrying the fixed stars; each sphere had its own axis of rotation, and each axis pointed in a different direction.[4] The following is an animation of his mathematical “hippopede” or figure-eight shape motion of planets, which he used to explain retrograde motion:

Eudoxus hippopede model 2.gif

Exodus, via citations of him in Aristotle, supposedly, calculated that it takes 30 years for Saturn to complete its journey; Jupiter 12 years; Mars: 24 months (minus six days); Mercury: one year; Venus: one year. [5] He also made a sundial and, supposedly, discovered the leap year.[6]

Mathematics

He also, supposedly, developed the idea of real numbers, contributed to the theory of ratios, and invented an early form of calculus, called “method of exhaustion”.[6]

Quotes

Quotes | On

The following are quotes on Eudoxus:

Eudoxus first discovered the proof that the cone is one-third of the cylinder of equal height on the same base, and the pyramid one-third of the prism. No small share [of the discovery] should be assigned to Democritus, who first made the assertion about the above-mentioned figure without proof.”
— Archimedes (c.220BC), Mathematical Theorems Addressed to Eratosthenes (see: Eratosthenes) [7]
Eudoxus says that the Egyptians have a mythical tradition in regard to Zeus that, because his legs were grown together, he was not able to walk, and so, for shame, tarried in the wilderness; but Isis, by severing and separating those parts of his body, provided him with means of rapid progress. This fable teaches by its legend that the mind and reason of the god, fixed amid the unseen and invisible, advanced to generation by means of motion.”
— Cicero (c.55BC), Publication (Ѻ)
“Thales [and others] and Democritus of Abdera handed on their discoveries of the laws according to which natural events are ordered and have their effects. Relying on their discoveries Eudoxus, Aratus and others devised the method of calendars to show the rising and setting of the stars and the significance of the seasons and handed it on to their successors.”
— Marcus Vitruvius (c.25BC), Publication (IX.6.3) [7]
“Witness to this also that the wisest of the Greeks: Solon, Thales, Plato, Eudoxus, Pythagoras, who came to Egypt and consorted with the priests; and in this number some would include Lycurgus also. Eudoxus, they say, received instruction from Chonuphis of Memphis, Solon from Sonchis of Sais, and Pythagoras from Oenuphis of Heliopolis. Pythagoras, as it seems, was greatly admired, and he also greatly admired the Egyptian priests, and, copying their symbolism and occult teachings, incorporated his doctrines and enigmas.”
— Plutarch (100AD), On Isis and Osiris [1]
“Eudoxus says that, while many tombs of Osiris are spoken of in Egypt, his body lies in Busiris ; for this was the place of his birth ; moreover, Taphosiris requires no comment, for the name itself means ‘the tomb of Osiris’. I pass over the cutting of wood, a the rending of linen, and the libations that are offered, for the reason that many of their secret rites are involved therein. In regard not only to these gods, but in regard to the other gods, save only those whose existence had no beginning and shall have no end, the priests say that their bodies, after they have done with their labours, have been placed in the keeping of the priests and are cherished there, but that their souls shine as the stars in the firmament, and the soul of Isis is called by the Greeks the Dog-star, but by the Egyptians Sothis, and the soul of Horus is called Orion, and the soul of Typhon the Bear. Also they say that all the other Egyptians pay the agreed assessment for the entombment of the animals held in honour? but that the inhabitants of the Theban territory only do not contribute because they believe in no mortal god, but only in the god whom they call Kneph, whose existence had no beginning and shall have no end. .”
— Plutarch (100AD), On Isis and Osiris [1]
“Greeks, thirsting for knowledge, sought the Egyptian priests for instruction. Thales, Pythagoras, Oenopides, Plato, Democritus, Eudoxus, all visited the land of the pyramids. Egyptian ideas were thus transplanted across the sea and there stimulated Greek thought, directed it into new lines, and gave to it a basis to work upon.”
— Florian Cajori (1991), A History of Mathematics (pg. 15)
“Much of the Book of the Dead is frankly incomprehensible, even for experts. No amount of exegesis can explain many passages. Images and allusions follow one another with bewildering force and frequency, lacking thematic and logical connection. The same can be said for much of the rest of Egyptian mortuary literature. Yet the endurance of the well-administered Egyptian state and its monumental undertakings are proof that the Egyptians were a fundamentally rational people. Their Greek contemporaries [Lycurgus, Orpheus, Solon, Thales, Pythagoras, Empedocles, Herodotus, Democritus, Plato, Eudoxus, Manetho] assure us that the Egyptian’s religion was deeply imbued with profound theological doctrines.”
— Ogden Goelet (1994), “Commentary on the Corpus of Literature and Tradition Which Constitutes the Egyptian Book of the Dead, the Book of Going Forth by Day” (pg. 163) [8]

Quotes | By

The following are quotes by Eudoxus:

“Willingly would I burn to death like Phaeton, were this the price for reaching the sun and learning its shape, its size and its substance.”
— Eudoxus (c.350BC), Publication [6]

References

  1. 1.0 1.1 1.2 Plutarch. (c.100AD). Isis and Osiris; in: Plutarch's Moralia, Volume Five (pdf) (pg. 25-27; Osiris tomb, pg. 53-54) (Introduction: Victor Hanson). Harvard University Press.
  2. Malieth, Monydit (aka Tonnerre). (2013). The Future Affects the Past: What Destination is Time Rushing To? (pgs. 45-47). Red Lead Books.
  3. (a) Zeilik, Michael. (1985). Astronomy: the Evolving Universe. Publisher.
    (b) Kennedy, Robert E. (2012). A Student’s Guide to Einstein’s Major Papers (pg. 3). Oxford.
  4. Eudoxus of Cnidus – FamousScientists.org.
  5. Cicero. (45BC). The Nature of the Gods (Introduction, translation, and notes: Patrick Walsh) (pg. 65-66, pg. 179). Oxford University Press, 1998.
  6. 6.0 6.1 6.2 Locklin, Scott. (2011). “Great Thinkers: Eudoxus of Cnidos”, WordPress, Oct 13.
  7. 7.0 7.1 Taylor, C.C.W. (1999). The Atomists: Leucippus and Democritus: Fragments: a Text and Translation with a Commentary (pg. 100; Archimedes, pg. 136). University of Toronto Press.
  8. Faulkner, Raymond. (1972). The Egyptian Book of the Dead: the Book of Coming Forth by Day: Complete Papyrus of Ani, Featuring Integrated Text and Full-Color Images (translator: Ogden Goelet; Preface: Carol Andrews; Introduction: Daniel Gunther; Foreword: James Wasserman) (Amz) (chapters, pg. 18; recensions, pg. 144). Chronicle Books, 2015.

External links

  • Eudoxus (subdomain) – Hmolpedia 2020.
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