euclidselements - Math 230 E Fall 2011 Euclid’s Elements...

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Unformatted text preview: Math 230 E Fall 2011 Euclid’s Elements Drew Armstrong Euclid wrote The Elements around 300BC. This was the definitive state- ment of the deductive method , which uses logic to rigorously derive (prove) theorems from self-evident first principles (axioms). What was self-evident to Euclid? His work is based on 10 axioms broken into two categories: 5 “postulates” and 5 “common notions”. The postulates describe the contruc- tion of geometric figures. Euclid’s “Postulates” Let the following be postulated: (P1) To draw a straight line from any point to any point. (P2) To produce a finite straight line continuously in a straight line. (P3) To describe a circle with any center and radius. (P4) That all right angles are equal to one another. (P5) That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than the two right angles.are less than the two right angles....
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This note was uploaded on 01/08/2012 for the course MATH 461 taught by Professor Armstrong during the Fall '11 term at University of Miami.

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