XXI.—On the Determination of the Curve, on one of the coordinate planes, which forms the Outer Limit of the Positions of the point of contact of an Ellipsoid which always touches the three planes of reference

Extract

The question is the following:—We consider the solid angle formed by three planes at right angles to each other, and into the space of this single octant we introduce a given ellipsoid, and cause its surface to be tangent to each of the three sides of the solid angle. The position of the points of tangence will of course be variable in each plane according to the orientation given to the axes of the ellipsoid, but it is evident that on each of the planes the positions of the point of contact will be unable to outpass certain limits so long as the ellipsoid fulfils the condition of remaining tangent simultaneously to the three planes: these limiting positions of the point of contact in one, as for example, of the planes, will form a certain curve, and the proposed question will be: the determination of that curve, the limiting curve as we shall call it in the Sequel.