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Volume  Volume1\Light and Shade\Book4

Entry#  199.

 Contents: Vol. 1  |  Vol. 2

 

OF THE OPINION OF SOME THAT A TRIANGLE CASTS NO SHADOW ON A PLANE

SURFACE.

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.

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