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Thales, who had travelled to [[Egypt]] where he observed the practical usage of geometrical measuring techniques, took the first steps in placing geometry on a theoretical basis. He is credited with having demonstrated several basic propositions of geometry. Thales' method of "proof" was based on repeated, empirical measurements and induction.  

Thales, who had travelled to [[Egypt]] where he observed the practical usage of geometrical measuring techniques, took the first steps in placing geometry on a theoretical basis. He is credited with having demonstrated several basic propositions of geometry. Thales' method of "proof" was based on repeated, empirical measurements and induction.  

Among the propositions which he demonstrated in this manner are: 1) that a circle is bisected by a diameter; 2) the angles at the base of an isoceles triangle are equal; 3) the angle of a semi-circle is a right angle; 4) if two straight lines intersect each other, the opposite angles are equal, and; 5) he demonstrated certain properties of similar triangles, including the principle of ratio, or proportionality. It is this latter property (of simiilar triangles) which Thales used to measure the previously unknown height of the pyramids as well as the distance of ships at sea.

Among the propositions which he demonstrated in this manner are:  

#that a circle is bisected by a diameter

#the angles at the base of an isoceles triangle are equal

#the angle of a semi-circle is a right angle

#if two straight lines intersect each other, the opposite angles are equal, and

#he demonstrated certain properties of similar triangles, including the principle of ratio, or proportionality. It is this latter property (of simiilar triangles) which Thales used to measure the previously unknown height of the pyramids as well as the distance of ships at sea.

==See also==

==See also==