FACTOID # 10: The total number of state executions in 2005 was 60: 19 in Texas and 41 elsewhere. The racial split was 19 Black and 41 White.
 
 Home   Encyclopedia   Statistics   States A-Z   Flags   Maps   FAQ   About 
   
 
WHAT'S NEW
 

SEARCH ALL

FACTS & STATISTICS    Advanced view

Search encyclopedia, statistics and forums:

 

 

(* = Graphable)

 

 


Encyclopedia > Eudoxus of Cnidus

Eudoxus of Cnidus (Greek Εύδοξος) (410 or 408 BC355 or 347 BC) was a Greek astronomer, mathematician, physician, scholar and student of Plato. Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus's poem on astronomy. Theodosius of Bithynia's Sphaerics may be based on a work of Eudoxus. Another article treats of Eudoxus of Cnidus. ... Knidos or Cnidus (modern-day Tekir in Turkey) is an ancient Greek city in Asia Minor, once part of the country of Caria. ... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 460s BC 450s BC 440s BC 430s BC 420s BC - 410s BC - 400s BC 390s BC 380s BC 370s BC 360s BC 415 BC 414 BC 413 BC 412 BC 411 BC - 410 BC - 409 BC 408 BC 407... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 450s BC 440s BC 430s BC 420s BC 410s BC - 400s BC - 390s BC 380s BC 370s BC 360s BC 350s BC Years: 413 BC 412 BC 411 BC 410 BC 409 BC - 408 BC - 407 BC 406 BC... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 400s BC 390s BC 380s BC 370s BC 360s BC - 350s BC - 340s BC 330s BC 320s BC 310s BC 300s BC 360 BC 359 BC 358 BC 357 BC 356 BC 355 BC 354 BC 353 BC 352... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 390s BC 380s BC 370s BC 360s BC 350s BC - 340s BC - 330s BC 320s BC 310s BC 300s BC 290s BC 352 BC 351 BC 350 BC 349 BC 348 BC 347 BC 346 BC 345 BC 344... Galileo is often referred to as the Father of Modern Astronomy. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... For other uses, see Doctor. ... For other uses, see Plato (disambiguation). ... Aratus (Greek Aratos) (ca. ... For other uses, see Astronomy (disambiguation). ... Theodosius of Bithynia (ca. ...

Contents

Life

Eudoxus was the son of Aeschines of Cnidus, located in Asia Minor. Eudoxus first travelled to Tarentum to study with Archytas, from whom he learned mathematics. While in Italy, Eudoxus visited Sicily, where he studied medicine with Philiston. Taranto is a coastal city in Apulia, southern Italy. ... Archytas Archytas (428 BC - 347 BC) was a Greek philosopher, mathematician, astronomer, statesman, strategist and commander-in-chief. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ...


Around 387 BC, at the age of 23, he traveled with the physician Theomedon to Athens to study with the followers of Socrates. He eventually became the pupil of Plato, with whom he studied for several months, but due to a disagreement they had a falling out. Eudoxus was quite poor and could only afford an apartment at the Piraeus. To attend Plato's lectures, he walked the seven miles each direction, each day. Due to his poverty, his friends raised funds sufficient to send him to Heliopolis, Egypt to pursue his study of astronomy and mathematics. He lived there 16 months. From Egypt, he then traveled north to Cyzicus, located on the south shore of the Sea of Marmara, and the Propontis. He traveled south to the court of Maussolus. During his travels he gathered many students of his own. Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 430s BC 420s BC 410s BC 400s BC 390s BC - 380s BC - 370s BC 360s BC 350s BC 340s BC 330s BC Years: 392 BC 391 BC 390 BC 389 BC 388 BC - 387 BC - 386 BC 385 BC... This page is about the Classical Greek philosopher. ... For other uses, see Plato (disambiguation). ... Heliopolis (Greek Ἡλίου πόλις) was one of the most ancient cities of Egypt, and capital of the 13th Lower Egyptian nome. ... Cyzicus was an ancient town of Mysia in Asia Minor, situated on the shoreward side of the present peninsula of Kapu-Dagh (Arctonnesus), which is said to have been originally an island in the Sea of Marmara, and to have been artificially connected with the mainland in historic times. ... The Sea of Marmara (Turkish: Marmara denizi, Modern Greek: Μαρμαρα̃ Θάλασσα or Προποντίδα) (also known as the Sea of Marmora or the Marmara Sea) is an inland sea that separates the Black Sea from the Aegean Sea (thus the Asian part of Turkey from its European part) by Bosporus and...


Around 368 BC, he returned to Athens with his students. Eudoxus eventually returned to his native Cnidus, where he served in the city assembly. While in Cnidus, he built an observatory and continued writing and lecturing on theology, astronomy and meteorology. He had one son, Aristagoras, and three daughters, Actis, Philtis and Delphis. Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 410s BC 400s BC 390s BC 380s BC 370s BC - 360s BC - 350s BC 340s BC 330s BC 320s BC 310s BC 373 BC 372 BC 371 BC 370 BC 369 BC - 368 BC - 367 BC 366 BC 365...


In mathematical astronomy his fame is due to the introduction of the astronomical globe, and his early contributions to understanding the movement of the planets. This article is about a spherical model of the Earth, or similar. ... This article is about the astronomical term. ...


His work onproportions shows tremendous insight into numbers; it allows rigorous treatment of continuous quantities and not just whole numbers or even rational numbers. When it was revived by Tartaglia and others in the 1500s, it became the basis for quantitative work in science for a century, until it was replaced by the algebraic methods of Descartes. This article is about proportionality, the mathematical relation. ... For other uses, see Number (disambiguation). ... The integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3, ...) and the number zero. ... In mathematics, a rational number is a number which can be expressed as a ratio of two integers. ... Niccolo Fontana Tartaglia. ... The decade of years from 1500 to 1509, inclusive. ... René Descartes René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. ...


Eudoxus rigorously developed Antiphon's method of exhaustion, which was used in a masterly way by Archimedes. The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Indian Mathematician Bhaskara II (1200s) and by Newton (1600s). To meet Wikipedias quality standards, this article or section may require cleanup. ... The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. ... For other uses, see Archimedes (disambiguation). ... For other uses, see Calculus (disambiguation). ... Bhāskara (1114-1185), also called Bhāskara II and Bhāskarācārya (Bhaskara the teacher) was an Indian mathematician. ... Centuries: 12th century - 13th century - 14th century Decades: 1150s 1160s 1170s 1180s 1190s - 1200s - 1210s 1220s 1230s 1240s 1250s Years: 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 Events and Trends 1200 University of Paris receives charter from Philip II of France 1202-1204 Fourth Crusade - diverted to... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Many inventions and institutions are created, including Hans Lippershey with the telescope (1608, used by Galileo the next year), the newspaper Avisa Relation oder Zeitung in Augsburg, and Cornelius Drebbel with the thermostat (1609). ...


An algebraic curve (the Kampyle of Eudoxus) is named after him In algebraic geometry, an algebraic curve is an algebraic variety of dimension equal to 1. ... Graph of Kampyle of Eudoxus The Kampyle of Eudoxus (Greek: καμπύλη [γραμμή], meaning simply curved [line], curve) is a curve, with a Cartesian equation of or, in polar coordinates, This quartic curve was studied by the Greek astronomer and mathematician Eudoxus of Cnidus (c. ...

a2x4 = b4(x2 + y2).

Also, craters on Mars and the Moon are named in his honor. Tycho crater on Earths moon. ... Mars is the fourth planet from the Sun in the solar system, named after the Roman god of war (the counterpart of the Greek Ares), on account of its blood red color as viewed in the night sky. ... This article is about Earths moon. ...


Mathematics

The Pythagoreans had discovered that the diagonal of a square does not have a common unit of measurement with the sides of the square; this is the famous discovery that the square root of 2 cannot be expressed as the ratio of two integers. This discovery had heralded the existence of incommensurable quantities beyond the integers and rational fractions, but at the same time it threw into question the idea of measurement and calculations in geometry as a whole. For example, Euclid provides an elaborate proof of the Pythagorean theorem, by using addition of areas instead of the much simpler proof from similar triangles, which relies on ratios of line segments.


Ancient Greek mathematicians calculated not with quantities and equations as we do today, but instead they used proportionalities to express the relationship between quantities. Thus the ratio of two similar quantities was not just a numerical value, as we think of it today; the ratio of two similar quantities was a primitive relationship between them.


Eudoxus was able to restore confidence in the use of proportionalities by providing an astounding definition for the meaning of the equality between two ratios. This definition of proportion forms the subject of Euclid's Book V.


In Definition 5 of Euclid's Book V we read: Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.


Let us clarify it by using modern-day notation. If we take four quantities: a, b, c, and d, then the first and second have a ratio a/b; similarly the third and fourth have a ratio c/d.


Now to say that a/b = c/d we do the following: For any two arbitrary integers, m and n, form the equimultiples m*a and m*c of the first and third; like-wise form the equimultiples n*b and n*d of the second and fourth.


Now, if it happens that m*a > n*b, then we must also have m*c > n*d. If it happens that m*a = n*b, then we must also have m*c = n*d. Finally, if it happens that m*a < n*b, then we must also have m*c < n*d.


Notice that the definition depends on comparing the similar quantities m*a and n*b, and the similar quantities m*c and n*d, and does not depend on the existence of a common unit of measuring these quantities.


The complexity of the definition reflects the deep conceptual and methodological innovation involved. It brings to mind the famous Fifth postulate of Euclid concerning parallels, which is more extensive and complicated in its wording than the other postulates.


The Eudoxian definition of proportionality uses the quantifier, "for every ..." to harness the infinite and the infinitesimal, just as the modern epsilon-delta definitions of limit and continuity.


Astronomy

In ancient Greece, astronomy was a branch of mathematics; astronomers sought to create geometrical models that could imitate the appearances of celestial motions. Identifying the astronomical work of Eudoxus as a separate category is therefore a modern convenience. Some of Eudoxus' astronomical texts whose names have survived include: The term ancient Greece refers to the periods of Greek history in Classical Antiquity, lasting ca. ...

  • Disappearances of the Sun, possibly on eclipses
  • Oktaeteris, on an eight-year lunisolar cycle of the calendar
  • Phaenomena and Entropon, on spherical astronomy, probably based on observations made by Eudoxus in Egypt and Cnidus
  • On Speeds, on planetary motions

We are fairly well informed about the contents of Phaenomena, for Eudoxus' prose text was the basis for a poem of the same name by Aratus. Hipparchus quoted from the text of Eudoxus in his commentary on Aratus. Spherical astronomy is the branch of astronomy that is used to determine the location of objects on the celestial sphere, as seen at a particular date, time, and location on the Earth. ... Aratus (Greek Aratos) (ca. ... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ...


Eudoxan planetary models

A general idea of the content of On Speeds can be gleaned from Aristotle's Metaphysics XII, 8, and a commentary by Simplicius of Cilicia (6th century CE) on De caelo, another work by Aristotle. According to a story reported by Simplicius, Plato posed a question for Greek astronomers: "By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?" (quoted in Lloyd 1970, p. 84). Plato proposed that the seemingly chaotic wandering motions of the planets could be explained by combinations of uniform circular motions centered on a spherical Earth, apparently a novel idea in the 4th century. For other uses, see Aristotle (disambiguation). ... Simplicius, a native of Cilicia, a disciple of Ammonius and of Damascius, was one of the last of the Neoplatonists. ...


Eudoxus rose to the challenge by assigning to each planet a set of nested concentric spheres. By tilting the axes of the spheres, and by assigning each a different period of revolution, he was able to approximate the celestial "appearances."


In most modern reconstructions of the Eudoxan model, the Moon is assigned three spheres:

  • The outermost rotates westward once in 24 hours, explaining rising and setting.
  • The second rotates eastward once in a month, explaining the monthly motion of the Moon through the zodiac.
  • 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.

The Sun is also assigned three spheres. The second completes its motion in a year instead of a month. The inclusion of a third sphere implies that Eudoxus mistakenly believed that the Sun had motion in latitude. For other uses, see Zodiac (disambiguation). ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... The lunar nodes are the orbital nodes of the Moon, that is, the points where the orbit of the Moon crosses the ecliptic (which is the apparent path of the Sun across the heavens against the background stars). ...


The five visible planets (Venus, Mercury, Mars, Jupiter, and Saturn) are assigned four spheres each:

  • The outermost explains the daily motion.
  • The second explains the planet's motion through the zodiac.
  • The third and fourth together explain retrogradation, when a planet appears to slow down, then briefly reverse its motion through the zodiac. By inclining the axes of the two spheres with respect to each other, and rotating them in opposite directions but with equal periods, Eudoxus could make a point on the inner sphere trace out a figure-eight shape, or hippopede.

Prograde motion is the rotational or orbital motion of a body in a direction similar to that of other bodies within a given system, and is sometimes called direct motion. ... Or horse fetter. ...

Importance of Eudoxan system

Callippus, a Greek astronomer of the 4th century, added seven spheres to Eudoxus' original 27 (in addition to the planetary spheres, Eudoxus included a sphere for the fixed stars). Aristotle described both systems, but insisted on adding "unrolling" spheres between each set of spheres to cancel the motions of the outer set. Aristotle was concerned about the physical nature of the system; without unrollers, the outer motions would be transferred to the inner planets. Calippus of Syracuse Callippus (or Calippus) (ca. ...


A major flaw in the Eudoxan system is its inability to explain changes in the brightness of planets as seen from Earth. Because the spheres are concentric, planets will always remain at the same distance from Earth. This problem was pointed out in Antiquity by Autolycus of Pitane. Astronomers responded by introducing the deferent and epicycle, which caused a planet to vary its distance. However, Eudoxus' importance to Greek astronomy is considerable, as he was the first to attempt a mathematical explanation of the planets. Autolycus of Pitane (c. ... In the Ptolemaic system of astronomy, the epicycle (literally: on the cycle in Greek) was a geometric model to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. ... A recreation of the famous Library of Alexandria Greek astronomy is the astronomy of those who spoke Greek in classical antiquity. ...


References

  • Evans, James (1998). The History and Practice of Ancient Astronomy. Oxford University Press. ISBN 0-19-509539-1. 
  • Huxley, GL (1980). Eudoxus of Cnidus p. 465-7 in: the Dictionary of Scientific Biography, volume 4. 
  • Lloyd, GER (1970). Early Greek Science: Thales to Aristotle. W.W. Norton. 

External links

A Java Virtual Machine (JVM) is a set of computer software programs and data structures which implements a specific virtual machine model. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... For other uses, see Plato (disambiguation). ... Speusippus was an ancient Greek philosopher, nephew and successor of Plato. ... Heraclides Ponticus (387 - 312 BCE), also known as Heraklides, was a Greek philosopher who lived and died at Heraclea, now Eregli, Turkey. ... Philip of Opus was a philosopher and a member of the Academy during Platos lifetime. ... Xenocrates of Chalcedon (396 - 314 BC) was a Greek philosopher and scholarch or rector of the Academy from 339 to 314 BC. Removing to Athens in early youth, he became the pupil of the Socratic Aeschines, but presently joined himself to Plato, whom he attended to Sicily in 361. ... Crantor was a Greek philosopher of the Old Academy, born probably about the middle of the 4th century BC, at Soli in Cilicia. ... Polemon (Greek: Πολέμων) of Athens was an eminent Platonic philosopher and Platos third successor as scholarch or head of the Academy from 314/313 to 270/269 BC. // Polemon was the son of Philostratus, a man of wealth and political distinction. ... Crates of Athens (Greek: Κράτης; died 268-265 BC) was the son of Antigenes of the Thriasian deme, the pupil and friend of Polemo, and his successor as scholarch of the Academy, perhaps about 270 BC. The intimate friendship of Crates and Polemo was celebrated in antiquity, and Diogenes Laertius has... Arcesilaus (Ἀρκεσίλαος) (c. ... Lacydes of Cyrene, Greek philosopher, was head of the Academy at Athens in succession to Arcesilaus about 241 B.C. Though some regard him as the founder of the New Academy, the testimony of antiquity is that he adhered in general to the theory of Arcesilaus, and, therefore, that he... Carneades (c. ... For other persons named Kleitomachos, see Kleitomachos (disambiguation). ... PHILO OF LARISSA, Greek philosopher of the first half of the ist century B.C. During the Mithradatk wars he left Athens and took up his residence in Rome. ... Antiochus of Ascalon (c. ... Philo (20 BC - 50 AD), known also as Philo of Alexandria and as Philo Judaeus And as Yedidia, was a Hellenized Jewish philosopher born in Alexandria, Egypt. ... Mestrius Plutarchus (Greek: Πλούταρχος; 46 - 127), better known in English as Plutarch, was a Greek historian, biographer, essayist, and Middle Platonist. ... Alcinous was a Middle Platonist philosopher of the second century A.D. Resources Alcinous, The Handbook of Platonism, John Dillon, Oxford 1993. ... Atticus, all of what is known of this philosopher are fragments of his book preserved in Eusebius Preparatio Evangelica, Atticus was vehemently anti-Peripatetic. ... Cassius Maximus Tyrius (Maximus of Tyre), a Greek rhetorician and philosopher who flourished in the time of the Antonines and Commodus (2nd century A.D). ... Numenius of Apamea was a Greek philosopher, who lived in Apamea in Syria and flourished during the latter half of the 2nd century A.D. He was a Neo-Pythagorean and forerunner of the Neo-Platonists. ... Cassius Dionysius Longinus (c. ... Ammonius Saccas (3rd century AD) was a Greek philosopher of Alexandria, often called the founder of the Neoplatonic school. ... Plotinus (Greek: ) (ca. ... Porphyry of Tyre (Greek: , c. ... Iamblichus, also known as Iamblichus Chalcidensis, (ca. ... Aedesius (died 355), Neoplatonist philosopher, was born of a noble Cappadocian family. ... Chrysanthius was a Greek philosopher of the 4th century AD who studied at the school of Iamblichus. ... Flavius Claudius Iulianus (331–June 26, 363), was a Roman Emperor (361–363) of the Constantinian dynasty. ... Sallust (Gaius Sallustius Crispus) (86-34 BC), Roman historian, belonging to a well-known plebeian family, was born at Amiternum in the country of the Sabines. ... Maximus of Ephesus was a 4th century pagan Greek neo-Platonist. ... Hypatia, as depicted in Raphaels The School of Athens. ... Ambrosius Theodosius Macrobius, Roman grammarian and Neoplatonist philosopher, flourished during the reigns of Honorius and Arcadius (395–423). ... Hierocles of Alexandria, Neoplatonist writer, flourished c. ... Syrianus was a Greek Neoplatonist philosopher, and head of Platos Academy in Athens; he succeeded and taught Plutarch. ... This article is about Proclus Diadochus, the Neoplatonist philosopher. ... Ammonius Hermiae (5th century AD) was a Greek philosopher, and the son of Hermias or Hermeias, a fellow-pupil of Proclus. ... Marinus (Μαρίνος ο Νεαπολίτης) was neo-Platonist philosopher born in Neapolis (modern Nablus), Palestine in the mid 5th century CE. He was probably a Samaritan, or possibly a Jew. ... Isidore of Alexandria was a Greek philosopher and one of the last of the Neoplatonists. ... Damascius, the last of the Neoplatonists, was born in Damascus about AD 480. ... Simplicius, a native of Cilicia, a disciple of Ammonius and of Damascius, was one of the last of the Neoplatonists. ... Olympiodorus the Younger (c. ... A recreation of the famous Library of Alexandria Greek astronomy is the astronomy of those who spoke Greek in classical antiquity. ... Acoreus was the name of a wise man consulted by Julius Caesar, according to the Roman writer Lucan, asking him many questions about ancient Egypt’s history and its calendar. ... Aglaonike (dates unknown), also known as Aganice of Thessaly is cited as the first female Astronomer in Ancient Greece. ... For other people named Agrippa, see Agrippa. ... This article is about the Pre-Socratic philosopher. ... Andronicus of Cyrrhus was a Greek astronomer who flourished about 100 BC. He built a horologium at Athens, the so-called Tower of the Winds, a considerable portion of which still exists. ... Apollonius of Perga [Pergaeus] (ca. ... Aratus (Greek Aratos) (ca. ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... For the crater, see Aristillus (crater). ... Autolycus of Pitane (c. ... Calippus of Syracuse Callippus (or Calippus) (ca. ... Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies. ... Cleostratus (ca. ... Conon of Samos (circa 280 BC - circa: 220 BC) was a Greek mathematician and astronomer. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ... Euctemon (unknown-fl. ... Geminus of Rhodes was a Greek astronomer and mathematician. ... Heraclides Ponticus (387 - 312 BCE), also known as Heraklides, was a Greek philosopher who lived and died at Heraclea, now Eregli, Turkey. ... Hicetas (around 400 BC – around 335 BC) was a Greek philosopher of the Pythagorean School. ... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ... Hippocrates of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived c. ... Hypsicles (ca. ... Menelaus of Alexandria (c. ... Meton of Athens was a Greek mathematician, astronomer, geometer, and engineer who lived in Athens in the 5th century BCE. He is best known for the 19-year Metonic cycle which he introduced in 432 BCE into the lunisolar Attic calendar as a method of calculating dates. ... Oenopides of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived around 450 BCE. He was born shortly after 500 BC on the island of Chios, but mostly worked in Athens. ... Philip of Opus was a philosopher and a member of the Academy during Platos lifetime. ... Philolaus (circa 480 BC – circa 405 BC) was a Greek mathematician and philosopher. ... The bust of Posidonius as an older man depicts his character as a Stoic philosopher. ... This article is about the geographer, mathematician and astronomer Ptolemy. ... Seleucus (or Seleukos) of Seleucia (born circa 190 BC - ?) was a Greek philosopher. ... Sosigenes of Alexandria was named by Pliny the Elder as the astronomer consulted by Julius Caesar for the design of the Julian calendar. ... Sosigenes the Peripatetic was a peripatetic philosopher living at the end of the 2nd century A.D. He was the tutor of Alexander of Aphrodisias and wrote a work on Revolving Spheres, from which some important extracts have been preserved in Simpliciuss commentary on Aristotles De caelo. ... Sporus of Nicaea was a Greek mathematician and astronomer, born: circa 240, probably Nicaea (Greek Nikaia), ancient district Bithynia, (modern-day Iznik) in province Bursa, in modern day Turkey, died: circa 300. ... For the Defense and Security Company, see Thales Group. ... Theodosius of Bithynia (ca. ... Theon (c. ... Theon of Smyrna (ca. ... Timocharis of Alexandria (ca. ... Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i. ... On Sizes and Distances [of the Sun and Moon] (Peri megethoon kai apostèmátoon) is a text by the ancient Greek astronomer Hipparchus. ... Aristarchuss 3rd century BC calculations on the relative sizes of the Earth, Sun and Moon, from a 10th century CE Greek copy On the Sizes and Distances [of the Sun and Moon] is the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa... On the Heavens (or De Caelo) is Aristotles chief cosmological treatise: it contains his astronomical theory. ... The Antikythera mechanism (main fragment). ... Armillary sphere An armillary sphere (variations known as a spherical astrolabe, armilla, or armil) is a model of the celestial sphere, invented by the ancient Greek Eratosthenes in 255 BC. Its name comes from the Latin armilla (circle, bracelet), since it has a skeleton made of graduated metal circles linking... A 16th century astrolabe. ... A dioptra is a instrument dating back to ancient Greece, at least 300 B.C.E. It is said to have been long used by Greek astronomers, such as Hipparchus(sometimes credited with inventing it). ... Tycho Brahes mural quadrant A mural instrument is an angle measuring device mounted on or built into a wall. ... Drawing of a triquetrum by Wilhelm Schickard, Basel University Library A triquetrum, or three-staff, is an ancient astronomical instrument developed by Ptolemy in the 2nd century A.D. Comprised of two intersecting arms hinged to a vertical post, the triquetrum enabled calculation of the angular elevation of a heavenly... Eclipses may occur repeatedly, separated by some specific interval of time: this interval is called an eclipse cycle. ... The celestial spheres relate to Johannes Keplers work Harmonia Mundi in which he drew together theories from the world of music, architecture, planetary motion and astronomy and linked them together to form an idea of a harmony and cohesion underlying all world phenomena and ruled by a divine force. ... Counter-Earth is an Earth-like hypothetical planet, usually sharing an orbit with Earth but on the opposite side of the Sun. ... In the Ptolemaic system of astronomy, the epicycle (literally: on the cycle in Greek) was a geometric model to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. ... Equant is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of heavenly bodies. ... This article is about the historical term. ... Heliocentric Solar System Heliocentrism (lower panel) in comparison to the geocentric model (upper panel) In astronomy, heliocentrism is the theory that the sun is at the center of the Universe and/or the Solar System. ... Eclipses may occur repeatedly, separated by some specific interval of time: this interval is called an eclipse cycle. ... The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal tropical year) and the synodic month. ... In astronomy, an octaeteris is the period of eight solar years after which the moon phase occurs on the same day of the year plus one or two days. ... Medieval artistic representation of a spherical Earth - with compartments representing earth, air, and water (c. ... The Sublunary Sphere is a concept derived from Greek astronomy. ... Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. ... Anaxagoras Anaxagoras (Greek: Αναξαγόρας, c. ... Anthemius of Tralles (c. ... Archytas Archytas (428 BC - 347 BC) was a Greek philosopher, mathematician, astronomer, statesman, strategist and commander-in-chief. ... Aristaeus the Elder (370 BCE-300 BCE) Aristaeus the Elder was a Greek mathematician who worked on conic sections. ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... Apollonius of Perga [Pergaeus] (ca. ... For other uses, see Archimedes (disambiguation). ... Autolycus of Pitane (c. ... For other people of the same name, see Boethius (disambiguation). ... Bryson of Heraclea (ca. ... Calippus of Syracuse Callippus (or Calippus) (ca. ... Chrysippus of Soli (279-207 BC) was Cleanthess pupil and eventual successor to the head of the stoic philosophy (232-204 BC). ... Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies. ... Conon of Samos (circa 280 BC - circa: 220 BC) was a Greek mathematician and astronomer. ... Ctesibius or Ktesibios or Tesibius (Greek Κτησίβιος) (flourished 285–222 BC) was a Greek[1] inventor and mathematician in Alexandria. ... ‎ Democritus (Greek: ) was a pre-Socratic Greek materialist philosopher (born at Abdera in Thrace ca. ... Dicaearchus (also Dicearchos, Dicearchus or Dikæarchus, Greek Δικαιαρχος; circa 350 BC – circa 285 BC) was a Greek philosopher, cartographer, geographer, mathematician and author. ... Diocles was a Greek mathematician and geometer, who probably flourished sometime around the end of the second century and the beginning of the first century BC. He was probably the first to prove the focal property of a parabola. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ... Dinostratus (b. ... Dionysodorus of Caunus (ca. ... Domninus of Larissa (ca. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ... Eudemus (350-290 BC) was the second major companion of Aristotle besides Theophrastus. ... For other uses, see Euclid (disambiguation). ... Geminus of Rhodes was a Greek astronomer and mathematician. ... Hero (or Heron) of Alexandria (Greek: Ήρων ο Αλεξανδρεύς) (c. ... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ... Hippasus of Metapontum, born circa 500 B.C. in Magna Graecia, was a Greek philosopher. ... Hippias can also refer to a son of Pisistratus and a tyrant of Athens. ... Hippocrates of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived c. ... Hypatia, as depicted in Raphaels The School of Athens. ... Hypsicles (ca. ... Marinus (Μαρίνος ο Νεαπολίτης) was neo-Platonist philosopher born in Neapolis (modern Nablus), Palestine in the mid 5th century CE. He was probably a Samaritan, or possibly a Jew. ... Greek mathematician and geometer said to have been the tutor of Alexander the Great. ... Menelaus of Alexandria (c. ... Nicomachus (Gr. ... Oenopides of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived around 450 BCE. He was born shortly after 500 BC on the island of Chios, but mostly worked in Athens. ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... Perseus (c. ... Philolaus (circa 480 BC – circa 405 BC) was a Greek mathematician and philosopher. ... Philon, Athenian architect of the 4th century BC, is known as the planner of two important works: the portico of the great Hall of the Mysteries at Eleusis and an arsenal at Athens. ... Porphyry of Tyre (Greek: , c. ... The bust of Posidonius as an older man depicts his character as a Stoic philosopher. ... This article is about Proclus Diadochus, the Neoplatonist philosopher. ... This article is about the geographer, mathematician and astronomer Ptolemy. ... Pythagoras of Samos (Greek: ; born between 580 and 572 BC, died between 500 and 490 BC) was an Ionian Greek mathematician[1] and founder of the religious movement called Pythagoreanism. ... Serenus of Antinouplis (ca. ... Simplicius, a native of Cilicia, a disciple of Ammonius and of Damascius, was one of the last of the Neoplatonists. ... Sosigenes of Alexandria was named by Pliny the Elder as the astronomer consulted by Julius Caesar for the design of the Julian calendar. ... Sporus of Nicaea was a Greek mathematician and astronomer, born: circa 240, probably Nicaea (Greek Nikaia), ancient district Bithynia, (modern-day Iznik) in province Bursa, in modern day Turkey, died: circa 300. ... For the Defense and Security Company, see Thales Group. ... Theaetetus (ca. ... Theano was one of the few women in ancient mathematics. ... This article is about Theodorus the mathematician from Cyrene. ... Theodosius of Bithynia (ca. ... Theon (c. ... Theon of Smyrna (ca. ... Thymaridas of Paros (ca. ... Xenocrates of Chalcedon (396 - 314 BC) was a Greek philosopher and scholarch or rector of the Academy from 339 to 314 BC. Removing to Athens in early youth, he became the pupil of the Socratic Aeschines, but presently joined himself to Plato, whom he attended to Sicily in 361. ... Zeno of Elea (IPA:zÉ›noÊŠ, É›lɛɑː)(circa 490 BC? – circa 430 BC?) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. ... Zeno of Sidon, Epicurean philosopher of the 1st century BC and contemporary of Cicero. ... Zenodorus (ca. ... Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i. ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... Arithmetica, an ancient text on mathematics written by classical period Greek mathematician Diophantus in the second century AD is a collection of 130 algebra problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. ... Apollonius of Perga [Pergaeus] (ca. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Aristarchuss 3rd century BC calculations on the relative sizes of the Earth, Sun and Moon, from a 10th century CE Greek copy On the Sizes and Distances [of the Sun and Moon] is the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa... On Sizes and Distances [of the Sun and Moon] (Peri megethoon kai apostèmátoon) is a text by the ancient Greek astronomer Hipparchus. ... Autolycus of Pitane (c. ... For other uses, see Academy (disambiguation). ... Inscription regarding Tiberius Claudius Balbilus of Rome (d. ... Cyrene (Greek Κυρήνη, Kurene) was an ancient Greek colony in present-day Libya, the oldest and most important of the five Greek cities in the region. ... Babylonian clay tablet YBC 7289 with annotations. ... This article or section is in need of attention from an expert on the subject. ... For a timeline of events in mathematics, see timeline of mathematics. ... In the history of mathematics, Islamic mathematics or Arabic mathematics refers to the mathematics developed by the Islamic civilization between 622 and 1600. ... This article is under construction. ...

  Results from FactBites:
 
Eudoxus of Cnidus (198 words)
Eudoxus of Cnidus (Greek Eυδοξοσ) (circa 408 BC - circa 347 BC) was a Greek astronomer, mathematician, physician, scholar and friend of Plato.
Eudoxus invented the method of exhaustion, which was used in a masterly way by Archimedes.
The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Newton himself.
Eudoxus of Cnidus (759 words)
Eudoxus was born in Cnidos, on the Black Sea.
Eudoxus was the most reknown astronomer and mathematician of his day.
Eudoxus also demonstrated that the ratios of the volumes of two spheres is as the cube
  More results at FactBites »

 
 

COMMENTARY     


Share your thoughts, questions and commentary here
Your name
Your comments

Want to know more?
Search encyclopedia, statistics and forums:

 


Press Releases |  Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms, 1022, m