t that plumb line touch the vtter circle, as it doth here in
the point F, so shall B.F. bee that plumbe lyne. Then from F.
vnto E. drawe an other line whiche shal be F.E, and it will
cutte the inner circle, as it doth here in the point C, from
which pointe C. if you erect a plumb line vnto A, then is that
line A.C, the touche line, whiche you shoulde finde. Not
withstandinge that this is a certaine waye to fynde any touche
line, and a demonstrable forme, yet more easyly by many folde
may you fynde and make any suche line with a true ruler, layinge
the edge of the ruler to the edge of the circle and to the
pricke, and so drawing a right line, as this example sheweth,
where the circle is E, the pricke assigned is A. and the ruler
C.D. by which the touch line is drawen, and that is A.B, and as
this way is light to doo, so is it certaine inoughe for any
kinde of workinge.

[Illustration]

THE XXV. CONCLVSION.

When you haue any peece of the circumference of a circle
assigned, howe you may make oute the whole circle agreynge
therevnto.

First seeke out of the centre of that arche, according to the
doctrine of the seuententh conclusion, and then setting one
foote of your compas in the centre, and extending the other foot
vnto the edge of the arche or peece of the circumference, it is
easy to drawe the whole circle.

_Example._

A peece of an olde pillar was found, like in forme to thys
figure A.D.B. Now to knowe howe muche the compasse of the hole
piller was, seing by this parte it appereth that it was round,
thus shal you do. Make in a table the like draught of y^t
circumference by the self patron, vsing it as it wer a croked
ruler. Then make .iij. prickes in that arche line, as I haue
made, C. D. and E. And then finde out the common centre to them
all, as the .xvij. conclusion teacheth. And that centre is here
F, nowe settyng one foote of your compas in F, and the other
in C. D, other in E, and so makyng a compasse, you haue youre
whole intent.

[Illustration]

THE XXVI. CONCLVSION.

To finde the centre to any arche of a circle.

If so be it that you desire to find the centre by any other way
then by those .iij. prickes, consideryng that sometimes you can
not haue so much space in the thyng where the arche is drawen,
as should serue to make those .iiij. bowe lines, then shall you
do thus: Parte that arche line into two partes, equall other
vnequall, it maketh no force, and vnto ech portion