of their own spirit. – H. FREUDENTHAL v

of their own spirit. – H. FREUDENTHAL v . Introduction We are familiar with two-dimensional coordinate geometry from earlier classes. Mainly, it is a combination of algebra and geometry . A systematic study of geometry by the use of algebra was first carried out by celebrated French philosopher and mathematician René Descartes, in his book ‘La Géométry, published in . This book introduced the notion of the equation of a curve and related analytical methods into the study of geometry. The resulting combination of analysis and geometry is referred now as analytical geometry. In the earlier classes, we initiated the study of coordinate geometry, where we studied about coordinate axes, coordinate plane, plotting of points in a plane, distance between two points, section formulae, etc. All these concepts are the basics of coordinate geometry. Let us have a brief recall of coordinate geometry done in earlier classes. To recapitulate, the location of the points ( , – ) and ( , ) in the XY-plane is shown in Fig . . We may note that the point ( , – ) is at units distance from the y -axis measured along the positive x -axis and at units distance from the x -axis measured along the negative y -axis. Similarly, the point ( , ) is at units distance from the y -axis measured along the positive x -axis and has zero distance from the x -axis. We also studied there following important formulae: