1 4 – c – b a

Give me the position of the object that produces shadows of equal darkness.

On opposite derivative shadows created by one and the same object interposed at various distances between lights of various sizes.

On opposite derivative shadows created by one and the same object, which is interposed at various distances between lights of different sizes. Let two opposite shadows be given around a single object interposed between 2 lights of double power, and let these shadows be of equal darkness between themselves. It is asked what proportion the spaces interposed between these lights and the said object have between themselves.

You will give 2 shadows of one and the same body interposed between 2 lights of double power, and let such shadows be of triple darkness one to the other. You will give 2 shadows born around one and the same body, which are of double darkness between themselves, and let the greater darkness be toward the greater light.

sun sun sun — object object — d – c b a — e f

To know the semidiameter of the earth, observe how many times the shadow of an object contains within itself the width of its base, when the sun is risen exactly off the horizon, and then do the same again when the sun is at midday, and the pyramid [of shadow] will be shorter by as much as half the diameter. But because the sun is larger when it rises, on account of the interposed moistures, one would need to take fine weather, and to take it about mid-June, because then the sun is nearer than at any other time.

sun

To make a base of shadow that ...