If an extremity of the curve, as _B_, is not in a side of the rectangle, let fall the perpendiculars _Ba_, _Bb_ on the rectangle sides. Determine the correspondent points _a_ and _b_ in Fig. 29., as you have already determined _A_, _B_, _e_, and _f_. From _b_, Fig. 29., draw _bB_ parallel to _CD_,[21] and from _a_ draw _aB_ to the vanishing-point of _DF_, cutting each other in _B_. Then _B_ is the extremity of the curve. Determine any other important point in the curve, as _P_, in the same way, by letting fall _Pq_ and _Pr_ on the rectangle’s sides. Any number of points in the curve may be thus determined, and the curve drawn through the series; in most cases, three or four will be enough. Practically, complicated curves may be better drawn in perspective by an experienced eye than by rule, as the fixing of the various points in haste involves too many chances of error; but it is well to draw a good many by rule first, in order to give the eye its experience.[22] COROLLARY. If the curve required be a circle, Fig. 30., the rectangle which incloses it will become a square, and the curve will have four points of contact, _ABCD_, in the middle of the sides of the square. [Illustration: Fig. 30.] Draw the square, and as a square may be drawn about a circle in any position, draw it with its nearest side, _EG_, parallel to the sight-line. Let _EF_, Fig. 31., be the square so drawn. Draw its diagonals _EF_, _GH_; and through the center of the square (determined by their intersection) draw _AB_ to the vanishing-point of _GF_, and _CD_ parallel to _EG_. Then the points _ABCD_ are the four points of the circle’s contact. [Illustration: Fig. 31.] On _EG_ describe a half square, _EL_; draw the semicircle _KAL_; and from its center, _R_, the diagonals _RE_, _RG_, cutting the circle in _x_, _y_. From the points _x_ _y_, where the circle cuts the diagonals, raise perpendiculars, _Px_, _Qy_, to _EG_. From _P_ and _Q_ draw _PP′_, _QQ′_, to the vanishing-point of _GF_, cutting the diagonals in _m_, _n_, and _o_, _p_. Then _m_, _n_, _o_, _p_ are four other points in the circle. Through these eight points the circle may be drawn by the hand accurately enough for general purposes; but any number of points required may, of course, be determined, as in Problem XI. The distance _EP_ is approximately one-seventh of _EG_, and may be assumed to be so in quick practice, as the error involved is not greater than would be incurred in the hasty operation of drawing the circle and diagonals. It may frequently happen that, in consequence of associated constructions, it may be inconvenient to draw _EG_ parallel to the sight-line, the square being perhaps first constructed in some oblique direction. In such cases, _QG_ and _EP_ must be determined in perspective ratio by the dividing-point, the line _EG_ being used as a measuring-line.