If they intersect one another, as in the figure, and they are below the eye, part of the bottom of the dish is seen within it. [Illustration: Fig. 66.] To avoid confusion, let us take then two intersecting circles without the inclosing squares, as in Fig. 66. Draw right lines, _ab_, _cd_, touching both circles externally. Then the parts of these lines which connect the circles are the sides of the dish. They are drawn in Fig. 65. without any prolongations, but the best way to construct them is as in Fig. 66. If the circles do not intersect each other, the smaller must either be within the larger or not within it. If within the larger, the whole of the bottom of the dish is seen from above, Fig. 67. _a_. [Illustration: Fig. 67.] If the smaller circle is not within the larger, none of the bottom is seen inside the dish, _b_. If the circles are above instead of beneath the eye, the bottom of the dish is seen beneath it, _c_. If one circle is above and another beneath the eye, neither the bottom nor top of the dish is seen, _d_. Unless the object be very large, the circles in this case will have little apparent curvature. II. The preceding problem is simple, because the lines of the profile of the object (_ab_ and _cd_, Fig. 66.) are straight. But if these lines of profile are curved, the problem becomes much more complex: once mastered, however, it leaves no farther difficulty in perspective. Let it be required to draw a flattish circular cup or vase, with a given curve of profile. The basis of construction is given in Fig. 68., half of it only being drawn, in order that the eye may seize its lines easily. [Illustration: Fig. 68.] Two squares (of the required size) are first drawn, one above the other, with a given vertical interval, _AC_, between them, and each is divided into eight parts by its diameters and diagonals. In these squares two circles are drawn; which are, therefore, of equal size, and one above the other. Two smaller circles, also of equal size, are drawn within these larger circles in the construction of the present problem; more may be necessary in some, none at all in others. It will be seen that the portions of the diagonals and diameters of squares which are cut off between the circles represent radiating planes, occupying the position of the spokes of a wheel. Now let the line _AEB_, Fig. 69., be the profile of the vase or cup to be drawn. Inclose it in the rectangle _CD_, and if any portion of it is not curved, as _AE_, cut off the curved portion by the vertical line _EF_, so as to include it in the smaller rectangle _FD_. Draw the rectangle _ACBD_ in position, and upon it construct two squares, as they are constructed on the rectangle _ACD_ in Fig. 68.; and complete the construction of Fig. 68., making the radius of its large outer circles equal to _AD_, and of its small inner circles equal to _AE_.