Proclus (412–485) Greek philosopher
Book III. Concerning Petitions and Axioms.
The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 2 (1789)
The Notebooks of Leonardo da Vinci (1883), II Linear Perspective
Proclus (412–485) Greek philosopher
Book III. Concerning Petitions and Axioms.
The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 2 (1789)
“The relationship of point to line”
Morris Kline (1908–1992) American mathematician
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 176
Context: The relationship of point to line bothered the Greeks and led Aristotle to separate the two. Though he admits points are on lines, he says that a line is not made up of points and that the continuous cannot be made up of the discrete. This distinction contributed also to the presumed need for separating number from geometry, since to the Greeks numbers were discrete and geometry dealt with continuous magnitudes.
“When no point of a line is at a finite distance, the line itself is at an infinite distance.”
Girard Desargues (1591–1661) French mathematician and engineer
Brouillion project (1639) as quoted by Harold Scott MacDonald Coxeter, Projective Geometry (1987)
“A straight line is not the shortest distance between two points.”
Madeleine L'Engle (1918–2007) American writer
Source: A Wrinkle in Time: With Related Readings
Ronald Fisher (1890–1962) English statistician, evolutionary biologist, geneticist, and eugenicist
25 February 1933, in a letter to L. Hogben. Printed in Natural Selection, Heredity, and Eugenics, J.H.Bennett, Oxford: Clarendon Press, 1983, p. 218.
1930s
“Parallel lines have a common end point at an infinite distance.”
Girard Desargues (1591–1661) French mathematician and engineer
Brouillion project (1639) as quoted by Harold Scott MacDonald Coxeter, Projective Geometry (1987)
“Two points defined a line, but three defined the playing field.”
Daniel Abraham (1969) speculative fiction writer from the United States
The Churn (2014)
John Dee (1527–1608) English mathematican, astrologer and antiquary
Theorem II
Monas Hieroglyphica (1564)
“In philosophy, as in politics, the longest distance between two points is a straight line.”
Will Durant (1885–1981) American historian, philosopher and writer
Source: The Story of Philosophy: The Lives and Opinions of the World's Greatest Philosophers
George S. Patton (1885–1945) United States Army general
Quoted in How We Are Changed by War: A Study of Letters and Diaries from Colonial Conflicts to Operation Iraqi Freedom (2010) http://books.google.com/books?id=h-Fens34378C&pg=PA70 by D.C. Gill, p. 70