Sacred Texts
Age of Reason
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III. Six Books on Light and Shade Index

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*The Da Vinci Notebooks at sacred-texts.com*

### 199.

p. 111

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

A disputed proposition.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.

98

### Footnotes

111:98 : 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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