Book 1 of the Elements
Euclid's Axioms
Euclid’s axioms: http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html
Postulate 1. “To draw a straight line from any point to any point.”
Postulate 2. “To produce a finite straight line continuously in a straight line.”
Postulate 3. “To describe a circle with any center and radius.”
Postulate 4. “That all right angles equal one another.”
Postulate 5. “That, if a straight line falling on two straight lines makes 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 are the angles less than the two right angles.”
*Notice that the first three postulates (axioms) are essentially Plato's rules for construction.
Proving Euclid's Propositions
Many of Euclid's propositions concern geometric constructions: (a) showing how to complete a construction and then (b) proving that the construction satisfies the specified properties. Use the applet below to (a) complete constructions related to Euclid's propositions, and then use the text box to (b) write up a related proof, explaining how the construction works.
In each case, you should assume only the given postulates and previously proven propositions.
Begin with Euclid's second proposition: "To place a straight line equal to a given straight line with one end at a given point."
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI2.html