e 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.

THE XXIIII. CONCLVSION.

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
le