Let _AH_, Fig. 60., be the vertical profile of the capital of a pillar, _AB_ the semi-diameter of its head or abacus, and _FD_ the semi-diameter of its shaft. Let the shaft be circular, and the abacus square, down to the level _E_. Join _BD_, _EF_, and produce them to meet in _G_. Therefore _ECG_ is the semi-profile of a reversed pyramid containing the capital. Construct this pyramid, with the square of the abacus, in the required perspective, as in Fig. 61.; making _AE_ equal to _AE_ in Fig. 60., and _AK_, the side of the square, equal to twice _AB_ in Fig. 60. Make _EG_ equal to _CG_, and _ED_ equal to _CD_. Draw _DF_ to the vanishing-point of the diagonal _DV_ (the figure is too small to include this vanishing-point), and _F_ is the level of the point _F_ in Fig. 60., on the side of the pyramid. Draw _Fm_, _Fn_, to the vanishing-points of _AH_ and _AK_. Then _Fn_ and _Fm_ are horizontal lines across the pyramid at the level _F_, forming at that level two sides of a square. [Illustration: Fig. 62.] Complete the square, and within it inscribe a circle, as in Fig. 62., which is left unlettered that its construction may be clear. At the extremities of this draw vertical lines, which will be the sides of the shaft in its right place. It will be found to be somewhat smaller in diameter than the entire shaft in Fig. 60., because at the center of the square it is more distant than the nearest edge of the square abacus. The curves of the capital may then be drawn approximately by the eye. They are not quite accurate in Fig. 62., there being a subtlety in their junction with the shaft which could not be shown on so small a scale without confusing the student; the curve on the left springing from a point a little way round the circle behind the shaft, and that on the right from a point on this side of the circle a little way within the edge of the shaft. But for their more accurate construction see Notes on Problem XIV. PROBLEM XI. It is seldom that any complicated curve, except occasionally a spiral, needs to be drawn in perspective; but the student will do well to practice for some time any fantastic shapes which he can find drawn on flat surfaces, as on wall-papers, carpets, etc., in order to accustom himself to the strange and great changes which perspective causes in them. [Illustration: Fig. 63.]