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Apollonius of Perga (; (ラテン語:Apollonius Pergaeus); c. 262 BC – c. 190 BC) was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Johannes Kepler, Isaac Newton, and René Descartes. Apollonius gave the ellipse, the parabola, and the hyperbola their modern names. The hypothesis of eccentric orbits, or equivalently, deferent and epicycles, to explain the apparent motion of the planets and the varying speed of the Moon, is also attributed to him. Ptolemy describes Apollonius' theorem in the ''Almagest'' XII.1. Apollonius also researched the lunar history, for which he is said to have been called Epsilon (ε). The crater Apollonius on the Moon is named in his honor. == ''Conics'' == The degree of originality of the ''Conics'' () can best be judged from Apollonius's own prefaces. Books i–iv he describes as an "elementary introduction" containing essential principles, while the other books are specialized investigations in particular directions. He then claims that, in Books i–iv, he only works out the generation of the curves and their fundamental properties presented in Book i more fully and generally than did earlier treatises, and that a number of theorems in Book iii and the greater part of Book iv are new. Allusions to predecessor's works, such as Euclid's four ''Books on Conics'', show a debt not only to Euclid but also to Conon and Nicoteles. He defines the fundamental conic property as the equivalent of the Cartesian equation applied to ''oblique'' axes—i.e., axes consisting of a diameter and the tangent at its extremity—that are obtained by cutting an oblique circular cone. The way the cone is cut does not matter. He shows that the oblique axes are only a ''particular'' case after demonstrating that the basic conic property can be expressed in the same form with reference to ''any'' new diameter and the tangent at its extremity. It is the form of the fundamental property (expressed in terms of the "application of areas") that leads him to give these curves their names: ''parabola'', ''ellipse'', and ''hyperbola''. Thus Books v–vii are clearly original. In Book v, Apollonius treats normals as minimum and maximum straight lines drawn from given points to the curve (independently of tangent properties); discusses how many normals can be drawn from particular points; finds their feet by construction; and gives propositions that both determine the center of curvature at any point and lead at once to the Cartesian equation of the evolute of any conic. Apollonius in the ''Conics'' further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of Descartes by some 1800 years. His application of reference lines, a diameter and a tangent, is essentially no different than our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates. He further developed relations between the abscissas and the corresponding ordinates that are equivalent to rhetorical equations of curves. However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve ''a posteriori'' instead of ''a priori''. That is, equations were determined by curves, but curves were not determined by equations. Coordinates, variables, and equations were subsidiary notions applied to a specific geometric situation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Apollonius of Perga」の詳細全文を読む スポンサード リンク
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