To drawe a touche line onto a circle, from any poincte
assigned.
Here must you vnderstand that the pricke must be without the
circle, els the conclusion is not possible. But the pricke or
poinct beyng without the circle, thus shall you procede: Open
your compas, so that the one foote of it maie be set in the
centre of the circle, and the other foote on the pricke
appoincted, and so draw an other circle of that largenesse about
the same centre: and it shall gouerne you certainly in makyng
the said touche line. For if you draw a line from the pricke
appointed vnto the centre of the circle, and marke the place
where it doeth crosse the lesser circle, and from that poincte
erect a plumbe line that shall touche the edge of the vtter
circle, and marke also the place where that plumbe line crosseth
that vtter circle, and from that place drawe an other line to
the centre, takyng heede where it crosseth the lesser circle, if
you drawe a plumbe line from that pricke vnto the edge of the
greatter circle, that line I say is a touche line, drawen from
the point assigned, according to the meaning of this conclusion.
[Illustration]
_Example._
Let the circle be called B.C.D, and his centre E, and y^e prick
assigned A, open your compas now of such widenes, y^t the one
foote may be set in E, w^{ch} is y^e centre of y^e circle, & y^e
other in A, w^{ch} is y^e pointe assigned, & so make an other
greter circle (as here is A.F.G) then draw a line from A. vnto E,
and wher that line doth cross y^e inner circle (w^{ch} heere is
in the prick B.) there erect a plumb line vnto the line. A.E. and
let 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]