To avoid any assertion about the infinitude of the straight line, Euclid says a line segment (he uses the word "line" in this sense) can be extended as far as necessary. Unwillingness to involve the infinitely large is seen also in **Euclid's** statement of the parallel axiom. Instead of considering two lines that extend to infinity and giving a direct condition or assumption under which parallel lines might exist, his parallel axiom gives a condition under which two lines will meet at some finite point.

— Morris Kline,

On an attentive examination of the methods adopted by modern elementary writers, in laying down the first principles of ratios and proportion, and especially in commenting upon Euclid, I long since experienced a conviction of the extremely unsatisfactory nature of most of their views; and this chiefly, as appearing to me to involve inadequate ideas of **Euclid's** real principle in treating of proportionals in his 5th book, and of the nature of the quantities which form the subject of investigation.

— Rev. Baden Powell,

**Euclid's** Elements is certainly one of the greatest books ever written, and one of the most perfect monuments of the Greek intellect.

— Bertrand Russell, A History of Western Philosophy, p. 211

Comparatively few of the propositions and proofs in the Elements are his [**Euclid's**] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.

— Florian Cajori,

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