® The coordinates of the mid-point of the line segment joining two points

® The coordinates of the mid-point of the line segment joining two points P( x , y , z ) and Q( x , y , z ) are z z , ,  . MATHEMATICS ® The coordinates of the centroid of the triangle, whose vertices are ( x , y , z ) ( x , y , z ) and ( x , y , z ), are z z , ,  . Historical Note Rene’ Descartes ( – ), the father of analytical geometry, essentially dealt with plane geometry only in . The same is true of his co-inventor Pierre Fermat ( - ) and La Hire ( - ). Although suggestions for the three dimensional coordinate geometry can be found in their works but no details. Descartes had the idea of coordinates in three dimensions but did not develop it. J.Bernoulli ( - ) in a letter of to Leibnitz introduced the three coor- dinate planes which we use today. It was Antoinne Parent ( - ), who gave a systematic development of analytical solid geometry for the first time in a paper presented to the French Academy in . L.Euler ( - ) took up systematically the three dimensional coordinate ge- ometry, in Chapter of the appendix to the second volume of his “Introduction to Geometry” in . It was not until the middle of the nineteenth century that geometry was extended to more than three dimensions, the well-known application of which is in the Space-Time Continuum of Einstein’s Theory of Relativity. — v v v v v —