1.1.2 Fig 2
graphic
That this circle is worth the 4 lines which are the sides of the minor square, plus another one equal to any one of the 4, is shown as follows in Figure 2.
With a compass, let us draw a straight line whose 5 units are worth e.f.g.h.i.k.l.m.n.o.p.q., and then let us divide it into 4 equal units or lines, then draw a square worth r.s.t.u., which we can sense, and let us put one foot of the compass in the center of this square, and with the other foot, let us draw a circle of the same value as the circle in the master figure, and we have the circle in which the square is circled and the square in which the circle is squared, so that they are equivalent in capacity.
Given that e.f.g.h. and r.s.t.v. are equivalent, we have therefore proved that the circle is squared by a 5th line added to the 4 lines of the minor square, which gives 5 lines that we make into one straight line x.y. That neither more nor less than a fifth unit must be added to the 4 units of the minor square, is shown by square r.s.t.u. in the master figure, where it stands between squares a.b.c.d. and i.k.l.m.n.o.p.q. as does circle e.f.g.h. Indeed, if the long line x.y. were not simply made of 5 constituent lines, and if it were worth more or less, it could not be made into a square standing halfway between 8 and 16, as do e.f.g.h. and r.s.t.v.