M. Kline, Mathematical thought from ancient to modern times , Oxford University Press, Oxford. Of course, volumes have been written on non Euclidean geometry which the reader must consult for more exhaustive information. Each pair of points can be joined by one and only one straight line segment. Any straight line segment can be indefinitely extended in either direction. There is exactly one circle of any given radius with any given center.
All right angles are congruent to one another.
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 the angles are less than two right angles. Kline, M. Mathematical Thought from Ancient to Modern Times , Oxford University Press, New York, 1972. Consequently, in view of this, I consider that we need yet another kind of analysis, geometric or linear, which deals directly with position, as algebra deals with magnitude . I do not know whether Leibniz had any convincing example of a problem belonging to the geometry of position. We have described a variety of approaches used to solve dierential equations.