“For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.”
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 177
Context: Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length—for example in Book I, Propositions 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.
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Morris Kline 42
American mathematician 1908–1992Related quotes
“The strength of faith is… no proof of the objective truth of faith.”
p, 125
New Fragments (1892)
“History is written for the purpose of narration and not in order to give proof.”
Historia et scribitur ad narrandum non ad probandum.
Book X, Chapter I, 31
De Institutione Oratoria (c. 95 AD)
In a letter to Heinrich Wilhelm Matthias Olbers (14 May 1826), defending Chevalier d'Angos against presumption of guilt (by Johann Franz Encke and others), of having falsely claimed to have discovered a comet in 1784; as quoted in Calculus Gems (1992) by George F. Simmons
“The best proof that there’s intelligent life in outer space is the fact that it hasn’t come here.”
Disputed
As quoted in Who's Who in Contemporary Gay & Lesbian History: From World War II to the Present Day (2001) by Robert Aldrich and Gary Wotherspoon ISBN 041522974X
L24
Aphorisms (1765-1799), Notebook L (1793-1796)
Source: Guide for the Perplexed (c. 1190), Part III, Ch.12
Context: You will see the mercy of God toward His creatures, how He has provided that which is required, in proper proportions, and treated all individual beings of the same species with perfect equality.... for it is an act of great and perfect goodness that He gave us existence; and the creation of the controlling faculty in animals is a proof of His mercy towards them, as has been shown by us.