The mathematician, following the lead of the great French all-around genius, Descartes, shows us very clearly how to set up, for the measurement of space, the framework known as the Cartesian coordinate system. The person of most ordinary mathematical attainments will realize that to locate a point in a plane we must have two measurements; and we could probably show this person, without too serious difficulty, that we can locate a point in any surface by two measurements. An example of this is the location of points on the earth's surface by means of their latitude and longitude. It is equally clear that if we add a third dimension and attempt to locate points in space, we must add a third measurement. In the case of points on the earth's surface, this might be the elevation above sea level, which would define the point not as part of the spherical surface of the earth but as part of the solid sphere. Or we may fall back on Dr. Slosson's suggestion that in order to define completely the position of his laboratory, we must make a statement about Broadway, and one about 116th Street, and one telling how many flights of stairs there are to climb. In any event, it should be clear enough that the complete definition of a point in space calls for three measurements. The mathematician formulates all this with the utmost precision. He asks us to]* [pick out any point whatever in space and call it $O$. We then draw or conceive to be drawn through this point three mutually perpendicular lines called coordinate axes, which we may designate $OX$, $OY$ and $OZ$, respectively. Finally, we consider the three planes also mutually perpendicular like the two walls and the floor of a room that meet in one common corner, which are formed by the lines $OX$ and $OY$, $OY$ and $OZ$, and $OZ$ and $OX$, respectively. These three planes are called coordinate planes. And then any other point $P$ in space can be represented with respect to $O$ by its perpendicular distances from each of the three coordinate planes--the distances $x$, $y$, $z$ in the figure. These quantities are called the coordinates of the point.]272