Divide the half-diameter of a circle into 20 equal parts; then measure
the half-diameter of the circle by inches, and if said result does not
give a required size multiply the same as in a square; use the same
units, and the same result will be obtained. All this must be done as in
a square of 20, but afterwards the square of 17½ may be produced as shown
in the diagram.
Fractional multiplication will result in the same thing, but may result
in the fractional sizes, as 34½, 35¼ and 36¾, and so on. The six points
of the compass will give all the base lines correctly on the square of
20 as well as on the square of 17½. It requires no scale, for one main
point will give the other complete. The full diameter of the circle is 40
parts, and the triangle, as shown in Dia. XII, contains 35, half of which
is 20 and 17½, for which reason the square of 20 and the square of 17½ is
adopted as a base.
With the aid of the above calculations a person can go to any cutter,
obtain from him any graduated scale, and with it cut a garment before he
knows the size thereof. Or he can select for himself a scale from any
set for a certain size by simply finding a scale whose 20 units will
correspond with the size. Should the scales contain too large or too
small units, they may be multiplied or divided, and a new unit found by
doubling or halving the units, or by dividing or multiplying them with
any number, to gain the desired result.
The conundrum is this: To use an unknown square or an unknown circle to
cut a garment, and produce the smaller sizes large enough and the larger
ones small enough for all practical purposes.
[Illustration]
[Illustration]