If a plane cuts the sides 
, 
, 
, and 
of a skew quadrilateral 
in points 
, 
, 
, and 
, then
both in magnitude and sign (Altshiller-Court 1979, p. 111).
More generally, if 
, 
, ..., are the polygon vertices
of a finite polygon with no "minimal sides"
and the side 
meets a curve in the points 
and 
, then
where 
denotes the distance from point 
to 
.
See also
Carnot's Theorem
Explore with Wolfram|Alpha
References
Altshiller-Court, N. "Carnot's Theorem." §329 in Modern
Pure Solid Geometry. New York: Chelsea, p. 111, 1979.Carnot,
L. N. M. Géométrie
de position. Paris: Duprat, p. 287, 1803.Carnot, L. N. M.
Mémoir sur la relation qui existe entre les distances respectives de cinq
points quelconques pris dans l'espace; suivi d'un Essai sur la théorie des
transversales. Paris: Courcier, p. 71, 1806.Casey, J. A
Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction
to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges,
Figgis, & Co., p. 160, 1888.Coolidge, J. L. A
Treatise on Algebraic Plane Curves. New York: Dover, p. 190, 1959.Referenced
on Wolfram|Alpha
Carnot's Polygon Theorem
Cite this as:
Weisstein, Eric W. "Carnot's Polygon Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CarnotsPolygonTheorem.html
Subject classifications
