long will each side be?

Now half of 4 is 2, hence from B to _b_ is the length of each side.

But suppose that from the length of each side, and the number of sides,
it is required to find the diameter to which to turn the piece; that is,
its diameter across corners, and we simply reverse the process thus: A
body has 9 sides, each side measures 27/32: what is its diameter across
corners?

Take a rule, apply it horizontally on the figure, and pass it along till
the distance from the line O B to the diagonal line marked 9 sides
measures 27/32, which is from 1-1/4 on O B to _a_, and the 1-1/4 is the
radius, which, multiplied by 2, gives 2-1/2 inches, which is the
required diameter across corners.

For any other number of sides the process is just the same. Thus: A
body is 3-1/2 inches in diameter, and is to have 5 sides: what will be
the length of each side? Now half of 3-1/2 is 1-3/4; hence from 1-3/4 on
the line O B to the point C, where the diagonal line crosses the 1-3/4
line, is the length of each of the sides.

2. It will be found that the length of a side of a square being given,
the size of the square, measured across corners, will be the length of
the diagonal line marked 45 degrees, from the point O to the figures
indicating, on the line O B or on the line O P, the length of one side.

EXAMPLE.--A square body measures 1 inch on each side: what does it
measure across the corners? Answer: From the point O, along diagonal
line marked 45 degrees, to the point where it crosses the lines 1 (as
denoted in the figure by a dot).

Again: A cylindrical piece of wood requires to be squared, and each side
of the square must measure an inch: what diameter must the piece be
turned to?

Now the diagonal line marked 45 degrees passes through the 1-inch line
on O B, and the inch line on O P, at the point where these lines meet;
hence all we have to do is to run the eye along either of the lines
marked inch, and from its point of meeting the 45 degrees line, to the
point O, is the diameter to turn the piece to.

There is another way, however, of getting this same measurement, which
is to set a pair of compasses from the line 1 on O B, to line 1 on O P,
as shown by the line D, which is the full diameter across corners. This
is apparent, because from point O, along line O B, to 1, thence to the
dot, thence down to line 1 on O P, and along that to O, encloses a
square, of which either from O to the dot, or the length of th