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Topic: Apollonius of Perga

	Apollonius of Perga \| Macmillan Mathematics
		Apollonius quickly gained a reputation for his thorough and creative approach to mathematics and was made a professor at the university.
		Proegomena Mathematica: From Apollonius of Perga to Late Neoplatonism.
		"Apollonius of Perga." School of Mathematics and Statistics, University of St Andrews, Scotland.
	www.bookrags.com /research/apollonius-of-perga-mmat-01 (541 words)

	Apollonius (250 - 200 B.C.)
		APOLLONIUS of Perga, in Pamphylia, so called from the place of his birth, was a younger contemporary of Archimedes, and probably survived him about ten years.
		Apollonius rises far above his time by a series of propositions on the longest and shortest lines that can be drawn from a given point to the circumference of a conic section.
		Apollonius gneralized the problem of maxima and minima: regarding it, as he expressly says, as one of those things worthy to be considered on the ground of their intrinsic importance.
	www.usefultrivia.com /biographies/apollonius_001.html (869 words)

	Apollonius (Site not responding. Last check: 2007-10-22)
		Apollonius of Perga or "the Geometer" is renowned for his many great works.
		Apollonius was born around 262 B.C. in Perga, Pamphylia known today as Murtina.
		Apollonius was also a founder of Greek mathematical astronomy, which used geometrical models to explain planetary theory.
	www.csca.us /math/precalc/apollonius.htm (579 words)

	Apollonius of Perga Biography \| World of Mathematics
		Apollonius was one of the founding fathers of mathematical astronomy in ancient Greece.
		Apollonius is also said to have visited Pergamum, where there was a new library and museum like the ones in Alexandria, and traveled to Ephesus.
		Apollonius boasted that a Euclidean problem such as finding the locusrelative to three or four lines was completely solvable for the first time, thanks to his new propositions.
	www.bookrags.com /biography/apollonius-of-perga-wom (835 words)

	Sympathetic Vibratory Physics - John W. Keely's Sacred Science.
		Apollonius of Perga should not be confused with other Greek scholars called Apollonius, for it was a common name.
		The mathematician Apollonius was born in Perga, Pamphylia which today is known as Murtina, or Murtana and is now in Antalya, Turkey.
		Perga was a centre of culture at this time and it was the place of worship of Queen Artemis, a nature goddess.
	www.svpvril.com /svpnotes/APOLLONIUS_177274.html (1151 words)

	Apollonius of Perga - Wikipedia, the free encyclopedia
		Apollonius' theorem demonstrates that the two models are equivalent given the right parameters.
		Apollonius also researched the lunar theory, for which he is said to have been called Epsilon (ε).
		The Apollonius crater on the Moon was named in his honour.
	en.wikipedia.org /wiki/Apollonius_of_Perga (1340 words)

	Apollonius of Perge (c. 262-c. 190 B.C.)
		Highly influential Greek mathematician, born in a region of what is now Turkey, who became known as the "Great Geometer." In his famous eight-part work On Conics, he introduced such terms as "ellipse," "parabola," and "hyperbola" –; the conic sections that, as we now know, describe the shapes of various types of orbit.
		Ptolemy says in his Syntaxis that Apollonius introduced the theory of epicycles to explain the apparent motion of the planets across the sky.
		One of the most famous questions he raised is known as the Apollonius problem.
	www.daviddarling.info /encyclopedia/A/Apollonius.html (310 words)

	Apollonius of Perga (Site not responding. Last check: 2007-10-22)
		In book one the relations satisfied by the diameters and tangents of conics are studied while in book two Apollonius investigates how hyperbolas are related to their asymptotes, and he also studies how to draw tangents to given conics.
		Apollonius also wrote a work on the cylindrical helix and another on irrational numbers which is mentioned by Proclus.
		In On the Burning Mirror Apollonius showed that parallel rays of light are not brought to a focus by a spherical mirror (as had been previously thought) and discussed the focal properties of a parabolic mirror.
	html.rincondelvago.com /apollonius-of-perga.html (1327 words)

	Apollonius: Commentary
		This is the reason for the curious "bump" in the diagram; he is assuming that the line AC which we assert in the statement of the proposition to be tangent to the curve is not actually tangent.
		Apollonius also interprets this by stating that the square on the ordinate (y) of a point on the parabola is equal to the rectangle formed by its abscissa (x) and a special fixed length (p) called the parameter of the curve.
		This is what Apollonius is using here: AB is cut into unequal pieces at E, so that the rectangle on AE and BE is less that the square on half of AB; equivalently, 4 times the rectangle is less than the square on all of AB.
	cerebro.xu.edu /math/math147/02f/apollonius/apollonotes.html (1320 words)

	Gray Booksellers > Featured Items
		Apollonius of Perga, a Greek geometer from the southern coast of Turkey, postulated that the planets revolved around the sun and that the sun revolves around the earth.
		Apollonius is believed to be the inventor of the system of epicycles and eccentric circles, used extensively by Hipparchus of Nicaea.
		In its entry for Apollonius of Perga, the Encyclopedia Britannica calls the Conica, “one of the greatest scientific works from the ancient world,” noting that “most of [Apollonius’] other treatises were lost, although their titles and a general indication of their contents were passed on by later writers.”
	www.graybooksellers.com /2005/CAT_31/PAGES/APPOLONII.html (255 words)

	Apollonius of Perga (Site not responding. Last check: 2007-10-22)
		Apollonius was born about 262 BC in Perga.
		Apollonius is a great mystery, because his books have been so hard to revive.
		Apollonius seemed to like his privacy, because there is very little information on his life.
	sps.k12.mo.us /phs/jpetersen/projects/mathematicians/apollonius.htm (292 words)

	TMTh:: APOLLONIUS OF PERGA (Site not responding. Last check: 2007-10-22)
		Ranked with the great mathematicians Archimedes and Euclid for his contribution to mathematics, Apollonius of Perga (in the Ionian kingdom of Pamphylia) studied at Alexandria with Euclid's successors, and later taught in Ephesus and Pergamum.
		Apollonius was the first to consider the two arms of the hyperbola as a curve, gave a method for solving quadratic equations by conic section, constructed a conic section by tangents and determined geometric loci with respect to 3 and 4 lines.
		Apollonius also developed the hydraulis, a musical instrument (an early form of pipe organ, in fact) operated by water power.
	www.tmth.edu.gr /en/aet/1/10.html (803 words)

	Highbeam Encyclopedia - Search Results for Apollonius
		He recorded and enlarged on the results of his predecessors, including Euclid and Apollonius of Perga, in his Mathematical Collection (8 books; date conjectural).
		The sculpture is generally considered to have been executed by Apollonius of Tralles and his brother Tauriscus in the 1st or 2d cent.
		Although its origin is ancient and obscure, its invention is frequently ascribed either to Hipparchus or to Apollonius of Perga.
	www.encyclopedia.com /SearchResults.aspx?Q=Apollonius (505 words)

	Bryn Mawr Classical Review 2002.09.34
		Apollonius' books do not spill over to each other the books are the result not of mere division into papyrus rolls, but of their being genuine separate entities.
		Apollonius, then, appears as a supreme map-maker producing a remarkable survey of the qualitative properties of conic sections.
		In other words, Apollonius has each conic section characterized twice, both by the protasis of the conditional (a cone is cut in a certain way by a plane), as well as by the apodosis of the conditional (the resulting curve has a certain fundamental proportion property).
	ccat.sas.upenn.edu /bmcr/2002/2002-09-34.html (2836 words)

	Apollonius' Tangency Problem
		Apollonius of Perga (born circa 261 BC) subsequently generalized this by showing how to find a circle tangent to three objects in the plane, where the objects can be any combination of points, lines, and/or circles.
		We can invert the entire plane relative to a circle of radius R centered at the origin by allowing each point to remain along the same direction from the origin, but changing the magnitude m of the vector to R^2/m, where R is the radius of the inversion circle.
		With these facts in mind, we can approach Apollonius' problem by first increasing the radius of each of the three given circles by a fixed amount such that two of the circles are just touching each other.
	www.mathpages.com /home/kmath113.htm (1002 words)

	Math Forum: Apollonius and the Conics (Chameleon Graphing: Plane History)
		Apollonius was born around 262 BC in the town of Perga, in what is now Turkey.
		Apollonius was not the first person to write about conic sections, but he discovered many new things about them.
		Apollonius did not use algebra, so he had to study geometry without graphing.
	mathforum.org /cgraph/history/apollonius.html (299 words)

	Apollonius
		In [11] Hogendijk reports that two works of Apollonius, not ly thought to have been translated into Arabic, were in fact known to Muslim geometers of the 10th century.
		Euclid's Data, refers to a general work by Apollonius in which the foundations of mathematics such as the meaning of axioms and definitions are discussed.
		In On the Burning Mirror Apollonius showed that parallel rays of light are not brought to a focus by a spherical mirror (as had been ly thought) and discussed the focal properties of a parabolic mirror.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Apollonius.htm (1369 words)

	Apollonius
		Apollonius of Perga studied in Alexandria and he then visited Pergamum where a university and library similar to Alexandria had been built.
		While Apollonius, 'The Great Geometer', was at Pergamum he wrote the first edition of his famous book Conics.
		In Conics Apollonius introduced for the first time the terms parabola, ellipse and hyperbola which we use so frequently today.
	members.tripod.com /sfabel/mathematik/database/Apollonius.html (249 words)

	Circles of Apollonius - Wikipedia, the free encyclopedia
		Apollonius of Perga was a renowned Greek geometer whose work often involved circles.
		He posed and solved Apollonius' problem, which is to identify a circle that is simultaneously tangent to three specified circles (Figure 1).
		These "circles of Apollonius" should not be confused with the Apollonian circles, which have a different technical definition.
	en.wikipedia.org /wiki/Circles_of_Apollonius (447 words)

	Conic Sections: Apollonius and Menaechmus
		Apollonius used the so-called Symptoms that describes a constant relation between varying magnitudes that depend on the position of an arbitrary point on a curve, example a point C on a parabola.
		Apollonius showed that only a single normal line can be assigned to each point of a conic section (Coolidge).
		Apollonius therefore was of the first who considered the curvature and elements of differential geometry.
	www.mlahanas.de /Greeks/Conics.htm (1771 words)

	Apollonius of Perga - Search Results - ninemsn Encarta
		Apollonius of Perga - Search Results - ninemsn Encarta
		Apollonius of Perga, called the Great Geometer, Greek mathematician, who lived during the late 3rd and early 2nd centuries bc.
		More ninemsn Search results on "Apollonius of Perga"
	au.encarta.msn.com /Apollonius_of_Perga.html (54 words)

	Apollonius Problem
		The problem was posed and solved by one of the greatest Greek geometers, Apollonius of Perga (ca.
		In particular, if the three sides lines of a triangle are looked at as such circles of infinite radius, the incircle and the three excircles of the triangle are solutions to the Apollonius' problem.
		As we know, this means that solutions to the Apollonius problem are constructible with straightedge and compass.
	www.cut-the-knot.org /Curriculum/Geometry/ApolloniusSolution.shtml (539 words)

	Apollonius of Perga \| 262-190 BC \| Greek mathematician
		Apollonius redefined them all as sections, at different angles, of the same cone.
		He is also said by Eutocius (c480-c540 AD) to have extended Euclid's theory of irrationals and improved Archimedes' approximation of 'pi' - though it is not clear whether he did this simply by inscribing and circumscribing the circle with polygons with more sides than Archimedes' 96-gons or whether he did actually find a new method.
		The extent of Apollonius' astronomical work is unknown; the only novelty he is credited with is a study of epicycles that suggested a way of predicting the "stationary" point in a planet's orbit.
	www.nahste.ac.uk /isaar/GB_0237_NAHSTE_P1095.html (360 words)

	Amazon.com: Apollonius: Books: Apollonius of Perga,Apollonius (Site not responding. Last check: 2007-10-22)
		The purpose of the work is to make available, to those interested in the history of science and to mathematicians, a version of the work as close to the original as possible.
		This part of Apollonius' Conics is lost in the original Greek, and only an Arabic translation made in the 9th century survives.
		This text has never been published previously, and all "editions" of this part of Apollonius' work are based on the Latin translation from the Arabic published by Edmund Halley in 1710, which suffers from Halley's insufficient knowledge of Arabic and his use of a single manuscript.
	www.amazon.com /Apollonius-Perga/dp/3540972161 (820 words)

	Apollonius (Site not responding. Last check: 2007-10-22)
		Little is known of the life of Apollonius of Perga.
		When he was a young man, he went to Alexandria where he studied under the followers of Euclid and later he taught there.
		In book 1 the relations satisfied by the diameters and tangents of conics are studied, while in book 2 Apollonius investigates how hyperbolas are related to their asymptotes, and he also studies how to draw tangents to given conics.
	www.stetson.edu /~efriedma/periodictable/html/As.html (506 words)

	Conics, Books I-III, by Apollonius of Perga
		The Conics of Apollonius (3rd Century BCE) is the culmination of the brilliant geometrical tradition of ancient Greece.
		With astonishing virtuosity, and with a storyteller's flair for thematic development, Apollonius leads the reader through the mysteries of these intriguing curved lines, treated as objects of pure mathematics.
		Apollonius of Perga was probably born about 262 B.C.E. in Perga, on the southern coast of what is now Turkey.
	www.greenlion.com /cgi-bin/SoftCart.100.exe/apollon.html?E+scstore (854 words)

	Malaspina Great Books
		Apollonius of Perga was known as 'The Great Geometer';.
		The result is an integrated multi-cultural and multi-disciplinary database built upon the framework of a Great Books Core List developed by Mortimer Adler (1902-2001) nearly 50 years ago.
		For rare and hard to find titles we recommend our Alibris list of titles about Apollonius of Perga.
	www.malaspina.org /Apollonius.htm (193 words)

	Apollonius biography
		In [Dictionary of Scientific Biography (New York 1970-1990).',1)" onmouseover="window.status='Click to see reference';return true">1] details of others with the name of Apollonius are given: Apollonius of Rhodes, born about 295 BC, a Greek poet and grammarian, a pupil of Callimachus who was a teacher of Eratosthenes; Apollonius of Tralles, 2
		Apollonius writes of book three (see [\'Apollonius Saxonicus\' : Die Restitution eines verlorenen Werkes des Apollonius von Perga durch Joachim Jungius, Woldeck Weland und Johannes Müller (Göttingen, 1988).',4)" onmouseover="window.status='Click to see reference';return true">4] or [Apollonius of Perga: Treatise on Conic Sections (1961).',5)" onmouseover="window.status='Click to see reference';return true">5]):-
		Apollonius also wrote a work on the cylindrical helix and another on
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Apollonius.html (1641 words)

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