However, a remarkable correlation existed between the two systems. The angle sum of a mathematical triangle was stated to be , if one measured the angles of a physical triangle the angle sum did indeed seem to be , and so it went for a multitude of other relations. Because of this agreement between theory and practice, it is not surprising that many writers came to think of Euclid's axioms as self evident truths . Centuries later, the philosopher Immanuel Kant even took the position that the human mind is essentially Euclidean and can only conceive of space in Euclidean terms. Thus, almost from its inception, Euclidean geometry had something of the character of dogma.
All right angles are congruent to each other.
Before we study the Fifth Postulate, let me say a few words about his definitions. Euclid's methods are imperfect by modern standards. He attempted to define everything in terms of a more familiar notion, sometimes creating more confusion than he removed. A straight line is a line which lies evenly with the points on itself. Euclid did not define length, distance, inclination, or set upon .