West of Parha were the "Lukka Lands". Perge returns to history as a Pamphylian Greek city, and with Pamphylia came under successive rule by Persians, Athenians, and Persians again.
For example, Euclid in Book III shows how to draw a circle so as to pass through three given points or to be tangent to… As a youth, Apollonius studied in Alexandria under the pupils of Euclid, according to Pappus and subsequently taught at the university there.
He visited both Ephesus and Pergamumthe latter being the capital of a Hellenistic kingdom in western Anatoliawhere a university and library similar to the Library of Alexandria had recently been built. In Alexandria he wrote the first edition of Conics, his classic treatise concerning the curves—circle, ellipseparabolaand hyperbola—that can be generated by intersecting a plane with a cone; see figure.
Conic sectionsThe conic sections result from intersecting a plane with a double cone, as shown in the figure. There are three distinct families of conic sections: Whereas his predecessors had used finite right circular cones, Apollonius considered arbitrary oblique double cones that extend indefinitely in both directions, as can be seen in the figure.
The first four books of the Conics survive in the original Greek, the next three only from a 9th-century Arabic translation, and an eighth book is now lost. Books I—IV contain a systematic account of the essential principles of conics and introduce the terms ellipse, parabola, and hyperbola, by which they became known.
His genius is most evident in Book V, in which he considers the shortest and the longest straight lines that can be drawn from a given point to points on the curve. Such considerations, with the introduction of a coordinate systemlead immediately to a complete characterization of the curvature properties of the conics.
Many of the lost works were known to medieval Islamic mathematicians, however, and it is possible to obtain a further idea of their contents through citations found in the medieval Arabic mathematical literature.
Sometimes known as the problem of Apollonius, the most difficult case arises when the three given things are circles. Apollonius demonstrated that parallel light rays striking the interior surface of a spherical mirror would not be reflected to the centre of sphericity, as was previously believed; he also discussed the focal properties of parabolic mirrors.
According to the mathematician Hypsicles of Alexandria c. According to the mathematician Eutocius of Ascalon c. Of particular interest was his determination of the points where, under general epicyclic motion, a planet appears stationary.
Learn More in these related Britannica articles:The work of Apollonius of Perga has had such a great impact on the development of mathematics, that he is known as “The Great Geometer”. In fact, in his book Conics he introduces terms, such as parabola, ellipse, and hyperbola that are still used today.
Apollonius of Perga (Greek: Ἀπολλώνιος ὁ Περγαῖος; Latin: Apollonius Pergaeus; late 3rd – early 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections.
Beginning from the theories of Euclid and Archimedes on the topic, he brought them to the state they were in just before the invention of analytic geometry.
APOLLONIUS Pergaeus (ca. ca. B.C.) Conicorum lib.
V. VI. attheheels.com Arabic paraphrase by Abalphatus Asphahanensus [Abū 'l-Fath Mahmūd Ibn Muhammad al-Isfahānī] translated into Latin by Abraham Ecchellensis (d. ). () Polarity of Apollonius A dual relationship between points and lines, with respect to a circle.
Following Apollonius of Perga ( BC) we introduce polarity with respect to a circle, but the concept can be generalized to any conic. Apollonius of Tyana (Ancient Greek: Ἀπολλώνιος ὁ Τυανεύς; c.
15 – c. AD), sometimes also called Apollonios of Tyana, was a Greek Neopythagorean philosopher from the town of Tyana in the Roman province of Cappadocia in Anatolia. Apollonius synonyms, Apollonius pronunciation, Apollonius translation, English dictionary definition of Apollonius.
n?–? bc, Greek mathematician, remembered for his treatise on conic sections. Apollonius - definition of Apollonius by The Free Dictionary.
Apollonius of Perga.