To find the commen centre belongyng to anye three prickes
appointed, if they be not in an exacte right line.
It is to be noted, that though euery small arche of a greate
circle do seeme to be a right lyne, yet in very dede it is not
so, for euery part of the circumference of al circles is
compassed, though in litle arches of great circles the eye
cannot discerne the crokednes, yet reason doeth alwais declare
it, therfore iij. prickes in an exact right line can not bee
brought into the circumference of a circle. But and if they be
not in a right line how so euer they stande, thus shall you find
their common centre. Open your compas so wide, that it be somewhat
more then the halfe distance of two of those prickes. Then sette
the one foote of the compas in the one pricke, and with the
other foot draw an arche lyne toward the other pricke, Then
againe putte the foot of your compas in the second pricke, and
with the other foot make an arche line, that may crosse the
firste arch line in ij. places. Now as you haue done with those
two pricks, so do with the middle pricke, and the thirde that
remayneth. Then draw ij. lines by the poyntes where those arche
lines do crosse, and where those two lines do meete, there is
the centre that you seeke for.
_Example_
[Illustration]
The iij. prickes I haue set to be A.B, and C, whiche I wold
bring into the edg of one common circle, by finding a centre
commen to them all, fyrst therefore I open my compas, so that thei
occupye more then y^e halfe distance betwene ij. pricks (as are
A.B.) and so settinge one foote in A. and extendinge the other
toward B, I make the arche line D.E. Likewise setting one foot in
B, and turninge the other toward A, I draw an other arche line
that crosseth the first in D. and E. Then from D. to E, I draw a
right lyne D.H. After this I open my compasse to a new distance,
and make ij. arche lines betwene B. and C, whiche crosse one the
other in F. and G, by whiche two pointes I draw an other line,
that is F.H. And bycause that the lyne D.H. and the lyne F.H.
doo meete in H, I saye that H. is the centre that serueth to
those iij. prickes. Now therfore if you set one foot of your
compas in H, and extend the other to any of the iij. pricks, you
may draw a circle w^{ch} shal enclose those iij. pricks in the
edg of his circumference & thus haue you attained y^e vse of this
conclusion.