The term 'axiom' was used by Proclus, but not by Euclid. He speaks, instead, of 'common notions'—common either to all men or to all sciences.
--
Florian Cajori, A History of Mathematics (1893)Euclid
Professor Klein then speaks of "that artistic finish that we admire in Euclid's Elements," and mentions Allman's important historical work. I heartily concur in this estimate of Euclid, and desire to contrast it with the error of Charles S. Peirce, in the Nation, where he speaks of "Euclid's proof (Elements Bk. I., props. 16 and 17)" as "really quite fallacious, because it uses no premises not as true in the case of spherics." Our bright American seems to have forgotten Euclid's Postulate 6 (Axiom 12 in Gregory, Axiom 9 in Heiberg), "Two straight lines cannot enclose a space;" that is, two straights having crossed never recur.
Euclid
Professor Klein then speaks of "that artistic finish that we admire in Euclid's Elements," and mentions Allman's important historical work. I heartily concur in this estimate of Euclid, and desire to contrast it with the error of Charles S. Peirce, in the Nation, where he speaks of "Euclid's proof (Elements Bk. I., props. 16 and 17)" as "really quite fallacious, because it uses no premises not as true in the case of spherics." Our bright American seems to have forgotten Euclid's Postulate 6 (Axiom 12 in Gregory, Axiom 9 in Heiberg), "Two straight lines cannot enclose a space;" that is, two straights having crossed never recur.
Charles Sanders Peirce
I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.
Isaac Newton
If mind is common to us, then also the reason, whereby we are reasoning beings, is common.' If this be so, then also the reason which enjoins what is to be done or left undone is common. If this be so, law also is common; if this be so, we are citizens; if this be so, we are partakers in one constitution; if this be so, the Universe is a kind of Commonwealth.
Marcus Aurelius
Astronomers... have a common ground for discussion with musicians in the harmony of the stars and musical concords in tetrads and triads of the fourth and the fifth, and with geometricians in the subject of vision; and in all other sciences many points, perhaps all, are common so far as the discussion of them is concerned. But the actual undertaking of works which are brought to perfection by the hand and its manipulation is the function of those who have been specially trained to deal with a single art.
Vitruvius
Euclid
Euler, Leonhard
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