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Certain mathematicians have maintained that a triangle, of which the
base is turned to the light, casts no shadow on a plane; and this
they prove by saying [5] that no spherical body smaller than the
light can reach the middle with the shadow. The lines of radiant
light are straight lines [6]; therefore, suppose the light to be g
h and the triangle l m n, and let the plane be i k; they say
the light g falls on the side of the triangle l n, and the
portion of the plane i q. Thus again h like g falls on the
side l m, and then on m n and the plane p k; and if the whole
plane thus faces the lights g h, it is evident that the triangle
has no shadow; and that which has no shadow can cast none. This, in
this case appears credible. But if the triangle n p g were not
illuminated by the two lights g and h, but by i p and g and
k neither side is lighted by more than one single light: that is
i p is invisible to h g and k will never be lighted by g;
hence p q will be twice as light as the two visible portions that
are in shadow.
[Footnote: 5--6. This passage is so obscure that it would be rash to
offer an explanation. Several words seem to have been omitted.]
On the relative depth of cast shadows (200-202).
2
00.
A spot is most in the shade when a large number of darkened rays
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