The shape of a poristic n-gon depends on the location of the initial point [Q.sub.1] but doesn't depend on the clockwise or counter-clockwise rotation of a Poncelet's traverse.
The necessary and sufficient condition for a poristic n-gon in two ellipses.
(1) A Poncelet's traverse creates a poristic n-gon in the sense of Definition 2.2.
So a series of points (4.6) creates a poristic n-gon under the condition of (2).
The poristic relations between the quantities: semi-major and semi-minor axes of two ellipses .
We have only a case: (n, m) = (3, 1) for a poristic triangle from Theorem 4.1.
We have only a case: (n, m) = (4, 1) for a poristic quadrilateral from Theorem 4.1.
In the same manner of the proof of a poristic triangle, let the left-hand side of (5.8) be
There exist two cases: (n, m) = (5, 1) and (5, 2) when a series of points of Poncelet's traverse creates a poristic pentagon in [E.sub.o] and [E.sub.i] from Theorem 4.1.
(a2) An ordinary, poristic pentagon which is circumscribed by a circle and inscribed by an ellipse
(a3) An ordinary, poristic pentagon which is circumscribed by an ellipse and inscribed by a circle
(a4) An ordinary, poristic pentagon which is circumscribed and inscribed by two circles The well known relation: r/R = [1/-1 + [square root of 5]] (= cos [pi]/5) is obtained.