Page:VaricakRel1912.djvu/11

 perpendiculars MP and MQ upon the coordinate axes, then the an coordinates of M are

Those of are

or

From the quadrilateral OPMQ of three right angles we obtain

in addition we have

and thus the coordinates are expressed by the an ones.

In the general case we have Fig. 5. N, R, S are the foot points of the three perpendiculars &xi; &eta;, &zeta; of M upon the coordinate plane, then

are the Lan, and

are the coordinates of point M.

From the quadrilateral MNRT we have

while we obtain from OPNT the equation

From these two relations we obtain the expression for x. From the quadrilateral MNPS we easily find the value for y. The limiting arcs MA, MB and MC are our x, y, and z. We find in addition