SCIENTIFIC CONUNDRUM IN THE CIRCLE.
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.
