Euclid’s Postulates

Euclid, a Greek mathematician of Alexandria was the founder of the Euclidean geometry about 300 B.C. He acknowledged -as most philosophers and mathematicians- that not everything can be proved and hence the need to make assumptions is not an option. Euclid set 10 assumptions, 5 of which were classified as common notions and the others as postulates. These postulates were usually driven by instinct and intuition; their validity would only appear in that of their results. Even though the postulates may seem empirically flawless, the mere change of one of them directly alters the Euclidean geometry. The 5th postulate of Euclid held that chance; in fact, it held so many chances that mathematicians never stopped investing in it bringing to life various geometrical settings.

Reference: Wolf, H.E. (1945). Introduction to non-Euclidean geometry.
Euclid's postulates, n.d., n.t., google image, retrieved on 4/11/2009

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