of
them with one of those semidiameters. Those iij. lines will make
a triangle equally cornered to the triangle assigned, and that
triangle is drawen about a circle apointed, as the conclusion did
wil.

_Example._

A.B.C, is the triangle assigned, and G.H.K, is the circle
appointed, about which I muste make a triangle hauing equall
angles to the angles of that triangle A.B.C. Fyrst therefore I
draw A.C. (which is one of the sides of the triangle) in length
that there may appeare two vtter angles in that triangle, as you
se B.A.D, and B.C.E.

[Illustration]

Then drawe I in the circle appointed a semidiameter, which is
here H.F, for F. is the centre of the circle G.H.K. Then make I
on that centre an angle equall to the vtter angle B.A.D, and
that angle is H.F.K. Like waies on the same centre by drawyng an
other semidiameter, I make an other angle H.F.G, equall to the
second vtter angle of the triangle, whiche is B.C.E. And thus
haue I made .iij. semidiameters in the circle appointed. Then at
the ende of eche semidiameter, I draw a touche line, whiche
shall make righte angles with the semidiameter. And those .iij.
touch lines mete, as you see, and make the trianagle L.M.N,
whiche is the triangle that I should make, for it is drawen
about a circle assigned, and hath corners equall to the corners
of the triangle appointed, for the corner M. is equall to C.
Likewaies L. to A, and N. to B, whiche thyng you shall better
perceiue by the vi. Theoreme, as I will declare in the booke of
proofes.

THE XXXI. CONCLVSION.

To make a portion of a circle on any right line assigned,
whiche shall conteine an angle equall to a right lined angle
appointed.

The angle appointed, maie be a sharpe angle, a right angle,
other a blunte angle, so that the worke must be diuersely
handeled according to the diuersities of the angles, but
consideringe the hardenes of those seuerall woorkes, I wyll
omitte them for a more meter time, and at this tyme wyll shewe
you one light waye which serueth for all kindes of angles, and
that is this. When the line is proposed, and the angle assigned,
you shall ioyne that line proposed so to the other twoo lines
contayninge the angle assigned, that you shall make a triangle
of theym, for the easy dooinge whereof, you may enlarge or
shorten as you see cause, anye of the two lynes contayninge the
angle appointed. And when you haue made a triangle of those iij.
lines, then accordinge to the doct