The third degree of depth is the middle shadow [Footnote 15: We gather from what follows that _q g r_ here means _ombra media_ (the middle shadow).]. But this is not uniform in natural tone; because the nearer it gets to the simple derived shadow the deeper it is [Footnote 18: Compare lines 10-13], and it is the uniformly gradual diminution by increase of distance which is what modifies it [Footnote 20: See Footnote 18]: that is to say the depth of a shadow increases in proportion to the distance from the two lights.
The fourth is the shadow _k r s_ and this is all the darker in natural tone in proportion as it is nearer to _k s_, because it gets less of the light _a o_, but by the accident [of distance] it is rendered less deep, because it is nearer to the light _c d_, and thus is always exposed to both lights.
The fifth is less deep in shadow than either of the others because it is always entirely exposed to one of the lights and to the whole or part of the other; and it is less deep in proportion as it is nearer to the two lights, and in proportion as it is turned towards the outer side _x t_; because it is more exposed to the second light _a b_.
[Footnote: The diagram to this section is given on Pl. V. To the left is the facsimile of the beginning of the text belonging to it.]
Why, at the intersections _a_, _b_ of the two compound shadows _e f_ and _m e_, is a simple shadow pfoduced as at _e h_ and _m g_, while no such simple shadow is produced at the other two intersections _c d_ made by the very same compound shadows?
Compound shadow are a mixture of light and shade and simple shadows are simply darkness. Hence, of the two lights _n_ and _o_, one falls on the compound shadow from one side, and the other on the compound shadow from the other side, but where they intersect no light falls, as at _a b_; therefore it is a simple shadow. Where there is a compound shadow one light or the other falls; and here a difficulty arises for my adversary since he says that, where the compound shadows intersect, both the lights which produce the shadows must of necessity fall and therefore these shadows ought to be neutralised; inasmuch as the two lights do not fall there, we say that the shadow is a simple one and where only one of the two lights falls, we say the shadow is compound, and where both the lights fall the shadow is neutralised; for where both lights fall, no shadow of any kind is produced, but only a light background limiting the shadow. Here I shall say that what my adversary said was true: but he only mentions such truths as are in his favour; and if we go on to the rest he must conclude that my proposition is true. And that is: That if both lights fell on the point of intersection, the shadows would be neutralised. This I confess to be true if [neither of] the two shadows fell in the same spot; because, where a shadow and a light fall, a compound shadow is produced, and wherever two shadows or two equal lights fall, the shadow cannot vary in any part of it, the shadows and the lights both being equal. And this is proved in the eighth [proposition] on proportion where it is said that if a given quantity has a single unit of force and resistance, a double quantity will have double force and double resistance.