If the three straight lines joining the corresponding vertices of two triangles and all meet in a point (the perspector ),
then the three intersections of pairs of corresponding sides lie on a straight line (the perspectrix ). Equivalently,
if two triangles are perspective
from a point , they are perspective
from a line .
The 10 lines and 10 3-line intersections form a configuration sometimes
called Desargues' configuration .
Desargues' theorem is self-dual .
See also Desargues' Configuration ,
Duality Principle ,
Pappus's
Hexagon Theorem ,
Pascal Lines ,
Pascal's
Theorem ,
Perspector ,
Perspective
Triangles ,
Perspectrix ,
Self-Dual
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References Coxeter, H. S. M. The Beauty of Geometry: Twelve Essays. New York: Dover, p. 244, 1999. Coxeter,
H. S. M. and Greitzer, S. L. "Perspective Triangles; Desargues's
Theorem." §3.6 in Geometry
Revisited. Washington, DC: Math. Assoc. Amer., pp. 70-72, 1967. Durell,
C. V. Modern
Geometry: The Straight Line and Circle. London: Macmillan, p. 44, 1928. Eves,
H. "Desargues' Two-Triangle Theorem." §6.2.5 in A
Survey of Geometry, rev. ed. Boston, MA: Allyn & Bacon, pp. 249-251,
1965. Graustein, W. C. Introduction
to Higher Geometry. New York: Macmillan, pp. 23-25, 1930. Ogilvy,
C. S. Excursions
in Geometry. New York: Dover, pp. 89-92, 1990. Johnson,
R. A. Modern
Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.
Boston, MA: Houghton Mifflin, p. 231, 1929. Wells, D. The
Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England:
Penguin Books, p. 77, 1986. Wells, D. The
Penguin Dictionary of Curious and Interesting Geometry. London: Penguin,
pp. 54-55, 1991. Referenced on Wolfram|Alpha Desargues' Theorem
Cite this as:
Weisstein, Eric W. "Desargues' Theorem."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/DesarguesTheorem.html
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