ABSTRACT
Euclid began with a set of 10 principles he called common notions and postulates. The Šve common notions were algebraic in nature (“if equals are added to equals, the wholes are equal”), and the Šve postulates were those dealing with geometric objects (e.g., points, lines, circles, angles). For example, one of the postulates reads “a Šnite straight line [a segment in our development] can be produced continuously in a line.” The famous Postulate Five basically states: If two lines do not make either equal or supplementary angles with a transversal, they intersect. This Šfth postulate of parallels started a controversy in mathematics about which much will be said later. Despite the many shortcomings found in the Elements, this work serves as the beginners’ handbook. The presentation is concise, and the objects of study can be easily drawn and visualized through diagrams. This method of development has come to be known as synthetic geometry (geometry without numbers).
