To make a triangle about a circle assigned which shall haue
corners, equall to the corners of any triangle appointed.
First draw forth in length the one side of the triangle assigned
so that therby you may haue ij. vtter angles, vnto which two
vtter angles you shall make ij. other equall on the centre of
the circle proposed, drawing thre halfe diameters frome the
circumference, whiche shal enclose those ij. angles, then draw
iij. touche lines which shall make ij. right angles, eche 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.