- A biography of Cleomedes on a mathematical site
- An article on Cleomedes' description of atmospheric enlargement from
*Perception*(2000)

# .

Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies.

**Placing his work chronologically
**

His birth and death dates are not known--historians have suggested that he wrote his work sometime between the mid-1st Century B.C. and 400 AD. The earlier estimates rely on the fact that Cleomedes refers extensively in his writing to the work of mathematician and astronomer Posidonius of Rhodes (135 BC-51 BC), and yet seemingly not at all to the work of Ptolemy (85-165 AD). These conclusions have been challenged on the grounds that Cleomedes' work was in relatively elementary astronomy, and that reference to Ptolemy would not necessarily be expected. The 20th Century mathematician Otto Neugebauer, however, looked closely at the astronomical observations made by Cleomedes, and concluded that a date of 371 AD. (±50 years) better explains what is found there. Neugebauer's estimate has been challenged on the grounds that Cleomedes makes observational errors with enough frequency that there is difficulty in deciding which observations to trust for the purpose of dating his work.

**On the Circular Motions of the Celestial Bodies
**

The book for which Cleomedes is known is a fairly basic astronomy textbook in two volumes. His purpose in writing seems to have been as philosophical as it was scientific--he spends an extensive amount of time criticizing the (admittedly fallacious) scientific ideas of the Epicureans (Cleomedes appears to have been a dedicated Stoic).

Cleomedes' book is criticized by most modern astronomers as being poorly written--it is valued primarily for preserving, apparently verbatim, much of Posidonius' writings on astronomy (none of Posidonius' books have survived to the modern day). Cleomedes is accurate in some of his remarks on lunar eclipses, especially his conjecture that the shadow on the Moon suggests a spherical Earth. He also remarks presciently that the absolute size of many stars may exceed that of the Sun (and that the Earth might appear as a very small star, if viewed from the surface of the Sun).

This book is the original source for the well-known story of how Eratosthenes measured the Earth's circumference. Although the story is now believed by some to be purely legendary, many modern mathematicians and astronomers believe the description to be reasonable (and believe Eratosthenes' achievement to be one of the more impressive accomplishments of ancient astronomy).

**His legacy
**

Cleomedes is now memorialized in the name of the Cleomedes crater, a prominent feature in the northeast portion of the visible moon.

Cleomedes' lectures on astronomy : a translation of The heavens (Hellenistic Culture and Society) by Cleomedes, Robert B. Todd (Translator), Alan C. Bowen (Translator) University of California Press ISBN: 0520233255

**Links**

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Aglaonice Agrippa Anaximander Andronicus Apollonius Aratus Aristarchus Aristyllus Attalus Autolycus Bion Callippus Cleomedes Cleostratus Conon Eratosthenes Euctemon Eudoxus Geminus Heraclides Hicetas Hipparchus Hippocrates of Chios Hypsicles Menelaus Meton Oenopides Philip of Opus Philolaus Posidonius Ptolemy Pytheas Seleucus Sosigenes of Alexandria Sosigenes the Peripatetic Strabo Thales Theodosius Theon of Alexandria Theon of Smyrna Timocharis

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Ancient Greek and Hellenistic mathematics (Euclidean geometry)

Mathematicians

(timeline)

Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus

Treatises

Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner

Problems

Angle trisection Doubling the cube Squaring the circle Problem of Apollonius

Concepts/definitions

Circles of Apollonius

Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center

Results

In Elements

Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon

Apollonius

Apollonius's theorem

Other

Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Cyrene Library of Alexandria Platonic Academy

Other

Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

Ancient Greece
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