When any two quadrates be set forth, howe to make a squire
about the one quadrate, whiche shall be equall to the other
quadrate.
Determine with your selfe about whiche quadrate you wil make the
squire, and drawe one side of that quadrate forth in lengte,
accordyng to the measure of the side of the other quadrate,
whiche line you maie call the grounde line, and then haue you a
right angle made on this line by an other side of the same
quadrate: Therfore turne that into a right cornered triangle,
accordyng to the worke in the laste conclusion, by makyng of a
byas line, and that byas lyne will performe the worke of your
desire. For if you take the length of that byas line with your
compasse, and then set one foote of the compas in the farthest
angle of the first quadrate (whiche is the one ende of the
groundline) and extend the other foote on the same line,
accordyng to the measure of the byas line, and of that line make
a quadrate, enclosyng y^e first quadrate, then will there appere
the forme of a squire about the first quadrate, which squire is
equall to the second quadrate.
[Illustration]
_Example._
The first square quadrate is A.B.C.D, and the seconde is E. Now
would I make a squire about the quadrate A.B.C.D, whiche shall
bee equall vnto the quadrate E.
Therfore first I draw the line A.D, more in length, accordyng to
the measure of the side of E, as you see, from D. vnto F, and so
the hole line of bothe these seuerall sides is A.F, then make I a
byas line from C, to F, whiche byas line is the measure of this
woorke. wherefore I open my compas accordyng to the length of
that byas line C.F, and set the one compas foote in A, and
extend thother foote of the compas toward F, makyng this pricke
G, from whiche I erect a plumbeline G.H, and so make out the
square quadrate A.G.H.K, whose sides are equall eche of them to
A.G. And this square doth contain the first quadrate A.B.C.D,
and also a squire G.H.K, whiche is equall to the second quadrate
E, for as the last conclusion declareth, the quadrate A.G.H.K,
is equall to bothe the other quadrates proposed, that is
A.B.C.D, and E. Then muste the squire G.H.K, needes be equall to
E, consideryng that all the rest of that great quadrate is
nothyng els but the quadrate self, A.B.C.D, and so haue I
thintent of this conclusion.