Next, the letter S you shall make as follows in its square, a. b. c. d.
First draw the horizontal line e. f. and the median & vertical one g. h.
and let them bisect one another in the point m. Then choose the main
thickness of the letter, and set it in the line g. h. so that the point
m. may divide it, having one-third of the thickness below it; next, set
the lesser thickness, at the top beneath g., indicating it by the point
i., and at bottom, above h. in the point k.; and the thickness of the
letter indicate above by n. and below by l.
Next, set a leg of your compasses on the line g. h. in the mid-point
between i. and n., and with the other describe a circle passing through
i. and n.; in like manner, upon the line g. h. set your compasses upon
the mid-point of g. l. and describe a circle passing through g. & l.
Then once more set your compass on the same line g. h. in the mid-point
of n. h. and describe a circle through n. & h.; and lastly, in the
mid-point of l. k. you must set one leg, & with the other is a circle to
be described through these same points l. & k.; afterwards cut off by
vertical section the upper portion of this letter, so that the part thus
cut off may contain in its extremity the maximum thickness of the letter
and a third part besides, & also that its tip may project downwards so
far as to stand midway between the centre of the circle i. n. and the
side b. d.; in other words, let the tip be distant on the right, from
the circle i. n. the first third of the interval between the greater and
lesser circles.
Next cut the lower limb of the letter to the left, by a vertical line
through the mid-point between the two circles, & in such fashion that
the part so cut off may be a fourth part wider & higher than the upper,
and that its tip may rise to the height of the centre of the circle
n. h.
Another method.
Yet another way may you make the letter S. In the square a. b. c. d.
bisect the horizontal line e. f. in the point m.; then set one leg of
your compass upon the mid-point between g. and m. & with the other
describe a segment of a circle in the direction of a. e. passing through
the points m. and g.; next, set your compass upon the mid-point between
m. and h. and describe a segment of a circle through m. and h. in the
direction of f. d. The two arcs will touch above, in front, and below,
in the rear, the exterior curvatures of this same letter S.
Next, draw through m. the diameter c. b. and at its middle indicate the
maximum thickness of the letter by the two points p. and q. from which
let there be drawn two right lines, one up, & one down, to those two
arcs; & next, from the two points p. & q. draw two curved parallels to
the same arcs, regulating the distance between them, their elevation &
depression from the centres of the same circles. Next, indicate below g.
and above h. the minimum thickness of the letter; and from these points
you will with your hand fashion the inner shape of the letter, both
above and below, & produce the limb of S, above towards b. Cut it off so
that its lower tip may touch the segment, & that the part cut off
upwards may contain a tenth part of a. b. and that the segment may still
exceed the part cut off. Then construct a vertical line r. s. to the
right of e. c. and distant from it a fifth part of c. d.; let it cut the
diagonal c. b. in t. and to the angle just formed produce the extremity
of the letter, making the part so cut off a third broader than the upper
portion. Lastly, you will have to produce the tip ever so little beyond
t.; as I have briefly indicated.
[Illustration: S]