Complete quadrilateral

Japanese: 完全四辺形 - かんぜんしへんけい（英語表記）complete quadrilateral

A plane figure made up of four lines AH, BH, AE, and BF, where no three lines intersect at the same point, and six intersection points A, B, E, F, G, and H. For perfect quadrilaterals, important properties in projective geometry can be derived using the invariance of inharmonic ratios. For example, if the intersection point of the line connecting A and B with the line connecting G and H is C, and the intersection point of the line connecting AB with E and F is D, then points A, B, C, and D form a sequence of harmonic points. From this, it is possible to construct the harmonic conjugate point D of any point C for two points A and B.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

どの3直線をとっても，同一点で交わらないような4直線 AH，BH，AE，BFと，6交点A，B，E，F，G，Hとでできている平面図形。完全四辺形については，非調和比の不変性を用いて射影幾何学上重要な性質が導かれる。たとえばA，Bを結んだ直線とG，Hを結んだ直線の交点をC，直線 ABとE，Fを結んだ直線の交点をDとすれば，点A，B，C，Dは調和点列をつくる。このことから，2点A，Bに対して，任意の点Cの調和共役点Dを作図することができる。

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