“Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.”
As quoted by Sir Thomas Little Heath, The Thirteen Books of Euclid's Elements (1908) Vol.1 https://books.google.com/books?id=UhgPAAAAIAAJ Introduction and Books I, II p.1, citing Proclus ed. Friedlein, p. 68, 6-20.
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Proclus18
Greek philosopher 412–485Related quotes
Proclus (412–485) Greek philosopher
Source: The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 1 (1788), Ch. IV. On the Origin of Geometry, and its Inventors.
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Abdelhamid I. Sabra, in “Ibn al-Haytham Brief life of an Arab mathematician: died circa 1040 (September-October 2003)”
Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)
A Budget of Paradoxes (1872)
Florian Cajori book A History of Mathematics
Source: A History of Mathematics (1893), p. 30, Reported in Moritz (1914)
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Ante-Nicene Christian library: v. 3 p. 42
Address to the Greeks
Thomas Little Heath (1861–1940) British civil servant and academic
The Thirteen Books of Euclid's Elements (1908)
“Euclid's postulates came from the Pythagorean theorem, not the other way around.”
Richard Hamming (1915–1998) American mathematician and information theorist
The Unreasonable Effectiveness of Mathematics (1980)
Context: The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.