SHADES AND SHADOWS
32
the side of the square; the shadow of the diagonal which hes in the direction of the light on the first plane, is at right angles with the projection of th'e square upon that plane, and is equal in length to the side of the square.
The diagonal which lies across the square being 1 and it makes with the ,
square root of 5, the side of the projection an angle of 26 degrees and 34 minutes, the angle whose tangent is J. light has a
shadow equal
in length to the
L
G
G
L
/
/ Fig. 17
L G
/ ^
y
/
€.
y y
y
y y
y
y
/ ^'
Fig. 20
Fig. 18
31. __. I
\
L G
/
/
L I
Parallelograms.
—Under similar conditions, the shadow
of a parallelogram is (Pig. 18) a parallelogram
two of whose and parallel to the projection of the given parallelogram, and the other two lie at 45 degrees in the direction of light, and are equal in length to the diagonal of
^
sides are equal
i j
the other side of the parallelogram. of the parallelogram itself.)
_k
(This
is
not the diagonal
—
The Lozenge. The rectangular lozenge, or diamond, is 32. another figure with the shadow of which it is well to become familiar (Fig. 19). The student may formulate the result for himself.
Crosses.—'^h.Q diagonals of the square and of the loz33. enge form two crosses. The diagonals of the square form an incHned cross, or X, like the cross of St. Andrew (Fig. 20 A, Fig. 19 B, and C) those of the lozenge form a vertical cross like the The student may formulate these results for himself. Since the cross of St. George (Fig. 20 D, E, and F). diagonal of a square is longer than the side, both the crosses and the shadows in A, B, and C are larger than in D, E, and F. ;