Then diagonals and diameters are drawn as in Fig. 68., and, at their extremities, semicircles in perspective, as in Fig. 69. The letters _A_, _B_, _C_, _D_, and _E_, indicate the upper and exterior angles of the rectangles in which these semicircles are to be drawn; but the inner vertical line is not dotted in the rectangle at _C_, as it would have confused itself with other lines. Then the visible contour of the fillet is the line which incloses and touches[33] all the semicircles. It disappears behind the shaft at the point _H_, but I have drawn it through to the opposite extremity of the diameter at _d_. Turned upside down the figure shows the construction of a basic fillet. The capital of a Greek Doric pillar should be drawn frequently for exercise on this fourteenth problem, the curve of its echinus being exquisitely subtle, while the general contour is simple. [32] This point coincides in the figure with the extremity of the horizontal diameter, but only accidentally. [33] The engraving is a little inaccurate; the inclosing line should touch the dotted semicircles at _A_ and _B_. The student should draw it on a large scale. PROBLEM XVI. It is often possible to shorten other perspective operations considerably, by finding the vanishing-points of the inclined lines of the object. Thus, in drawing the gabled roof in Fig. 43., if the gable _AYC_ be drawn in perspective, and the vanishing-point of _AY_ determined, it is not necessary to draw the two sides of the rectangle, _A′D′_ and _D′B′_, in order to determine the point _Y′_; but merely to draw _YY′_ to the vanishing-point of _AA′_ and _A′Y′_ to the vanishing-point of _AY_, meeting in _Y′_, the point required. Again, if there be a series of gables, or other figures produced by parallel inclined lines, and retiring to the point _V_, as in Fig. 72.,[34] it is not necessary to draw each separately, but merely to determine their breadths on the line _AV_, and draw the slopes of each to their vanishing-points, as shown in Fig. 72. Or if the gables are equal in height, and a line be drawn from _Y_ to _V_, the construction resolves itself into a zigzag drawn alternately to _P_ and _Q_, between the lines _YV_ and _AV_. The student must be very cautious, in finding the vanishing-points of inclined lines, to notice their relations to the horizontals beneath them, else he may easily mistake the horizontal to which they belong. Thus, let _ABCD_, Fig. 73., be a rectangular inclined plane, and let it be required to find the vanishing-point of its diagonal _BD_. Find _V_, the vanishing-point of _AD_ and _BC_. Draw _AE_ to the opposite vanishing-point, so that _DAE_ may represent a right angle. Let fall from _B_ the vertical _BE_, cutting _AE_ in _E_. Join _ED_, and produce it to cut the sight-line in _V′_. [Illustration: Fig. 72.]