Proof of Desargues' Theorem
Desargues's theorem holds for projective space of any dimension over any field or division ring, and also holds for abstract projective spaces of dimension at least 3. In dimension 2 the planes for which it holds are called Desarguesian planes and are the same as the planes that can be given coordinates over a division ring. There are also many non-Desarguesian planes where Desargues's theorem does not hold.
Read more about this topic: Desargues' Theorem
Famous quotes containing the words proof of, proof and/or theorem:
“Ah! I have penetrated to those meadows on the morning of many a first spring day, jumping from hummock to hummock, from willow root to willow root, when the wild river valley and the woods were bathed in so pure and bright a light as would have waked the dead, if they had been slumbering in their graves, as some suppose. There needs no stronger proof of immortality. All things must live in such a light. O Death, where was thy sting? O Grave, where was thy victory, then?”
—Henry David Thoreau (1817–1862)
“Ah! I have penetrated to those meadows on the morning of many a first spring day, jumping from hummock to hummock, from willow root to willow root, when the wild river valley and the woods were bathed in so pure and bright a light as would have waked the dead, if they had been slumbering in their graves, as some suppose. There needs no stronger proof of immortality. All things must live in such a light. O Death, where was thy sting? O Grave, where was thy victory, then?”
—Henry David Thoreau (1817–1862)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)