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In projective geometry, Desargues' theorem, named after Girard Desargues, states: :Two triangles are in perspective ''axially'' if and only if they are in perspective ''centrally''. Denote the three vertices of one triangle by and , and those of the other by and . Axial perspectivity means that lines and meet in a point, lines and meet in a second point, and lines and meet in a third point, and that these three points all lie on a common line called the ''axis of perspectivity''. Central perspectivity means that the three lines and are concurrent, at a point called the ''center of perspectivity''. This intersection theorem is true in the usual Euclidean plane but special care needs to be taken in exceptional cases, as when a pair of sides are parallel, so that their "point of intersection" recedes to infinity. Mathematically the most satisfying way of resolving the issue of exceptional cases is to "complete" the Euclidean plane to a projective plane by "adding" points at infinity following Poncelet. Desargues's theorem is true for the real projective plane, for any projective space defined arithmetically from a field or division ring, for any projective space of dimension unequal to two, and for any projective space in which Pappus's theorem holds. However, there are some non-Desarguesian planes in which Desargues' theorem is false. ==History== Desargues never published this theorem, but it appeared in an appendix entitled ''Universal Method of M. Desargues for Using Perspective (Maniére universelle de M. Desargues pour practiquer la perspective)'' of a practical book on the use of perspective published in 1648 by his friend and pupil Abraham Bosse (1602 – 1676). 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「Desargues' theorem」の詳細全文を読む スポンサード リンク
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