folium of Descartes

Japanese: folium of Descartes（英語表記）foliumofDescartes

... The above (1), (2), and (3) are curves used to solve cube multiplication problems and angle trisection problems. (4) The cubic curve expressed by the equation x ³ + y ³ = 3axy (where a is a positive constant) is called the folium of Descartes (Figure 10). For a moving point Q on the ellipse x ² - xy + y ² - ax - ay = 0, let R be the intersection point of the line OQ and the line x + y + a = 0. If you take a point P on the longer of the line segments OQ and OR so that the length of OP is equal to the difference between the lengths of OQ and OR, then P will draw this curve. ...

*Some of the terminology that mentions "folium of Descartes" is listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…　以上の(1)(2)(3)は立方倍積問題や角の三等分問題を解くのに利用された曲線である。(4)方程式x³＋y³＝3axy(aは正の定数)で表される三次曲線をデカルトの葉線folium of Descartesという(図10)。楕円x²－xy＋y²－ax－ay＝0上の動点Qに対し，直線OQと直線x＋y＋a＝0との交点をRとして，線分OQ,ORのうちの長いほうの上に点PをOPの長さがOQとORの長さの差に等しくなるようにとれば，Pはこの曲線を描く。…