Geminus of Rhodes (Greek: Γεμῖνος ὁ Ῥόδιος), was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the Introduction to the Phenomena, still survives; it was intended as an introductory astronomy book for students. He also wrote a work on mathematics, of which only fragments quoted by later authors survive.

Life

Nothing is known about the life of Geminus. It is not even certain that he was born in Rhodes, but references to mountains on Rhodes in his astronomical works suggests that he worked there. His dates are not known with any certainty either. A passage in his works referring to the Annus Vagus (Wandering Year) of the Egyptian calendar of 120 years before his own time, has been used to imply a date of c. 70 BC for the time of writing,[1] which would be consistent with the idea that he may have been a pupil of Posidonius, but a date as late as 50 AD has also been suggested.[2]

The crater Geminus on the Moon is named after him.

Astronomy

The only work of Geminus to survive is his Introduction to the Phenomena (Greek: Εἰσαγωγὴ εἰς τὰ Φαινόμενα), often just called the Isagoge. This introductory astronomy book, based on the works of earlier astronomers such as Hipparchus, was intended to teach astronomy for beginning students in the subject. In it, Geminus describes the zodiac and the motion of the Sun; the constellations; the celestial sphere; days and nights; the risings and settings of the zodiacal signs; luni-solar periods and their application to calendars; phases of the Moon; eclipses; star phases; terrestrial zones and geographical places; and the foolishness of making weather predictions by the stars.[3]

He also wrote a commentary on Posidonius' work On Meteorology. Fragments of this commentary are preserved by Simplicius in his commentary on Aristotle's Physics.

Mathematics

Geminus also wrote extensively on mathematics, including a comprehensive Doctrine, (or Theory) of Mathematics.[4] Although this work has not survived, many extracts are preserved by Proclus, Eutocius, and others. He divided mathematics into two parts: Mental (Greek: νοητά) and Observable (Greek: αἰσθητά), or in other words, Pure and Applied. In the first category he placed geometry and arithmetic (including number theory), and in the second category he placed mechanics, astronomy, optics, geodesy, canonics (musical harmony), and logistics. Long extracts of his work are also preserved by Al-Nayrizi in his commentary on Euclid's Elements.

Notes

Dicks, D., Dictionary of Scientific Biography. New York. (1970).

Neugebauer, O., A History of Ancient Mathematical Astronomy. New York. (1975).

Evans, J., The History and Practice of Ancient Astronomy, page 91. Oxford University Press. (1998).

Heath, T., A Manual of Greek Mathematics, Dover Publications. (2003).

Bibliography

Evans, J., Berggren, J.L., Geminos's Introduction to the Phenomena: A Translation and Study of a Hellenistic Survey of Astronomy. (Princeton University Press, 2006.) (This is the first complete English translation of this book.)

External links

Εἰσαγωγή εἰς τὰ Φαινόμενα (Introduction to Phaenomena), original text online

Technology Museum of Thessaloniki Entry

O'Connor, John J.; Robertson, Edmund F., "Geminus", MacTutor History of Mathematics archive, University of St Andrews.

PDF scans of Manitius' edition of the Geminus' Elementa Astronomiae ("Elements of Astronomy") - public domain (Classical Greek with German translation)]

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Ancient Greek astronomy

Astronomers

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

Works

Almagest (Ptolemy) On Sizes and Distances (Hipparchus) On the Sizes and Distances (Aristarchus) On the Heavens (Aristotle)

Instruments

Antikythera mechanism Armillary sphere Astrolabe Dioptra Equatorial ring Gnomon Mural instrument Triquetrum

Concepts

Callippic cycle Celestial spheres Circle of latitude Counter-Earth Deferent and epicycle Equant Geocentrism Heliocentrism Hipparchic cycle Metonic cycle Octaeteris Solstice Spherical Earth Sublunary sphere Zodiac

Influences

Babylonian astronomy Egyptian astronomy

Influenced

Medieval European science Indian astronomy Medieval Islamic astronomy

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Stoicism

Philosophers

Early

Zeno of Citium Persaeus Aristo Sphaerus Herillus Cleanthes Chrysippus Zeno of Tarsus Crates of Mallus Diogenes of Babylon Dioscorides Zenodotus Dionysius of Cyrene Apollodorus Antipater of Tarsus

Middle

Panaetius Dardanus Mnesarchus Hecato Posidonius Diodotus Diotimus Geminus Antipater of Tyre Athenodorus Cananites

Late

Seneca Cornutus Musonius Rufus Euphrates Cleomedes Epictetus Hierocles Junius Rusticus Marcus Aurelius Chaeremon Mara bar Serapion

Philosophy

Stoicism

categories logic passions physics Neostoicism Modern Stoicism

Concepts

Adiaphora Apatheia Ataraxia Ekpyrosis Eudaimonia Katalepsis Kathekon Logos Oikeiôsis Pneuma Prohairesis Sophos

Works

Epictetus

Discourses Enchiridion

Marcus

Aurelius

Meditations

Seneca

Letters to Lucilius Essays:

Anger Benefits Clemency Constancy Happiness Leisure Providence Shortness of Life Tranquillity Consolations

Other

Lectures (Musonius Rufus) On Passions (Chrysippus) Republic (Zeno)

Related articles

Paradoxa Stoicorum Stoicorum Veterum Fragmenta Stoic Opposition Moral intellectualism

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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

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