appears smaller; the one in the middle faces the whole hemisphere that is e f and those on the side have only a strip; that is q r faces a b ; and m n faces c d ; the body in the middle having a larger quantity of light than those at the sides is lighted from a point much below its centre, and thus the shadow is shorter. And the pyramid g 4 goes into l y exactly as often as a b goes into e f . The axis of every derivative shadow passes through 6 1/2 [Footnote 31: passa per 6 1/2 (passes through 6 1/2). The meaning of these words is probably this: Each of the three axes of the derived shadow intersects the centre ( mezzo ) of the primary shadow ( ombra originale ) and, by prolongation upwards crosses six lines.
This is self evident only in the middle diagram; but it is equally true of the side figures if we conceive of the lines 4 f , x n v m , y l k v , and 4 e , as prolonged beyond the semicircle of the horizon.] and is in a straight line with the centre of the primary shadow, with the centre of the body casting it and of the derivative light and with the centre of the window and, finally, with the centre of that portion of the source of light which is the celestial hemisphere, y h is the centre of the derived shade, l h of the primary shadow, l of the body throwing it, l k of the derived light, v is the centre of the window, e is the final centre of