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 doctrine of the seuen and twenty
coclusion, make a circle about that triangle. And so haue you
wroughte the request of this conclusion. Whyche yet you maye
woorke by the twenty and eight conclusion also, so that of your
line appointed, you make one side of the triangle be equal to y^e
angle assigned as youre selfe mai easily gesse.
[Illustration]
_Example._
First for example of a sharpe angle let A. stand & B.C shal be y^e
lyne assigned. Then do I make a triangle, by adding B.C, as a
thirde side to those other ij. which doo include the angle
assigned, and that triangle is D.E.F, so y^t E.F. is the line
appointed, and D. is the angle assigned. Then doo I drawe a
portion of a circle about that triangle, from the one ende of
that line assigned vnto the other, that is to saie, from E.
a long by D. vnto F, whiche portion is euermore greatter then
the halfe of the circle, by reason that the angle is a sharpe
angle. But if the angle be right (as in the second exaumple you
see it) then shall the portion of the circle that containeth
that angle, euer more be the iuste halfe of a circle. And when
the angle is a blunte angle, as the thirde exaumple dooeth
propounde, then shall the portion of the circle euermore be
lesse then the halfe circle. So in the seconde example, G. is
the right angle assigned, and H.K. is the lyne appointed, and
L.M.N. the portion of the circle aunsweryng thereto. In the
third exaumple, O. is the blunte corner assigned, P.Q. is the
line, and R.S.T. is the portion of the circle, that containeth
that blunt corner, and is drawen on R.T. the line appointed.