rt of it, whiche is
A.D, to lie without the circle, betweene the vtter circumference
of it, and the pointe assigned, whiche was A. Nowe concernyng
the meanyng of the Theoreme, if you make a longsquare of the
whole line A.C, and of that parte of it that lyeth betwene the
circumference and the point, (whiche is A.D,) that longesquare
shall be equall to the full square of the touche line A.B,
accordyng not onely as this figure sheweth, but also the saied
nyneteenth conclusion dooeth proue, if you lyste to examyne the
one by the other.

[Illustration]

_The lxxvii. Theoreme._

If a pointe be assigned without a circle, and from that
pointe .ij. right lynes be drawen to the circle, so that the
one doe crosse the circle, and the other dooe ende at the
circumference, and that the longsquare of the line which
crosseth the circle made with the portion of the same line
beyng without the circle betweene the vtter circumference
and the pointe assigned, doe equally agree with the iuste
square of that line that endeth at the circumference, then
is that lyne so endyng on the circumference a touche line
vnto that circle.

_Example._

In as muche as this Theoreme is nothyng els but the sentence of
the last Theoreme before conuerted, therfore it shall not be
nedefull to vse any other example then the same, for as in that
other Theoreme because the one line is a touche lyne, therfore
it maketh a square iust equal with the longsquare made of that
whole line, whiche crosseth the circle, and his portion liyng
without the same circle. So saith this Theoreme: that if the
iust square of the line that endeth on the circumference, be
equall to that longsquare whiche is made as for his longer sides
of the whole line, which commeth from the pointt assigned, and
crosseth the circle, and for his other shorter sides is made of
the portion of the same line, liyng betwene the circumference of
the circle and the pointe assigned, then is that line whiche
endeth on the circumference a right touche line, that is to
saie, yf the full square of the right line A.B, be equall to the
longsquare made of the whole line A.C, as one of his lines, and
of his portion A.D, as his other line, then must it nedes be,
that the lyne A.B, is a right touche lyne vnto the circle D.B.C.
And thus for this tyme I make an ende of the Theoremes.

+FINIS,+

_IMPRINTED at London in Poules
churcheyarde, at the signe of the Bra-