Ruskin, John; Cook, Edward T. [Hrsg.]: The works of John Ruskin: The elements of drawing. The elements of perspective. And the laws of Fésole (London, 1904)

PROBLEM XII

TO DIVIDE A CIRCLE DRAWN IN PERSPECTIVE INTO
ANY GIVEN NUMBER OF EQUAL PARTS
LET A B, Fig. 82, be the circle drawn in perspective. It
is required to divide it into a given number of equal parts ;
in this case, 20.
Let K A L be the semicircle used in the construction.
Divide the semicircle K A L into half the number of parts
required ; in this case, 10.
Produce the line E & laterally in both directions, as far
as may be necessary.
From o, the centre of the semicircle K A L, draw radii
through the points of division of the semicircle, y, 7*, etc.,
and produce them to cut the line E & in p, Q, R, etc.
From the points p Q R draw the lines p p', Q Q', R R', etc.,
through the centre of the circle A B, each cutting the circle
in two points of its circumference.
Then these points divide the perspective circle as re-
quired.
If from each of the points p, a vertical were raised
to the line E G, as in Fig. 81, and from the point where
it cut E G a line were drawn to the vanishing-point, as
Q Q' in Fig. 81, this line would also determine two of the
points of division.
If it is required to divide a circle into any number of
given %7aequal parts (as in the points A, B, and c, Fig. 88),
the shortest way is thus to raise vertical lines from A and
B to the side of the perspective square x Y, and then draw
to the vanishing-point, cutting the perspective circle in a
and the points required. Only notice that if any point,
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