ue, as I haue often saide, to a
conuenient boke, wherein they shall be all set at large.

_The .lxxv. Theoreme._

In any circle when .ij. right lines do crosse one an other,
the likeiamme that is made of the portions of the one line,
shall be equall to the lykeiamme made of the partes of the
other lyne.

[Illustration]

Because this Theoreme doth serue to many vses, and wold be wel
vnderstande, I haue set forth .ij. examples of it. In the
firste, the lines by their crossyng do make their portions
somewhat toward an equalitie. In the second the portions of the
lynes be very far from an equalitie, and yet in bothe these and
in all other y^e Theoreme is true. In the first example the
circle is A.B.C.D, in which thone line A.C, doth crosse thother
line B.D, in y^e point E. Now if you do make one likeiamme or
longsquare of D.E, & E.B, being y^e .ij. portions of the line
D.B, that longsquare shall be equall to the other longsquare
made of A.E, and E.C, beyng the portions of the other line A.C.
Lykewaies in the second example, the circle is F.G.H.K, in
whiche the line F.H, doth crosse the other line G.K, in the
pointe L. Wherfore if you make a lykeiamme or longsquare of the
two partes of the line F.H, that is to saye, of F.L, and L.H,
that longsquare will be equall to an other longsquare made of
the two partes of the line G.K. which partes are G.L, and L.K.
Those longsquares haue I set foorth vnder the circles containyng
their sides, that you maie somewhat whet your own wit in
practisyng this Theoreme, accordyng to the doctrine of the
nineteenth conclusion.

_The .lxxvi. Theoreme._

If a pointe be marked without a circle, and from that pointe
two right lines drawen to the circle, so that the one of
them doe runne crosse the circle, and the other doe touche
the circle onely, the long square that is made of that whole
lyne which crosseth the circle, and the portion of it, that
lyeth betwene the vtter circumference of the circle and the
pointe, shall be equall to the full square of the other
lyne, that onely toucheth the circle.

_Example._

The circle is D.B.C, and the pointe without the circle is A,
from whiche pointe there is drawen one line crosse the circle,
and that is A.D.C, and an other lyne is drawn from the said
pricke to the marge or edge of the circumference of the circle,
and doeth only touche it, that is the line A.B. And of that
first line A.D.C, you maie perceiue one pa