ause they haue one
ground line, that is, F.E, And are made betwene one payre of
gemow lines, I meane A.D. and E.H. By this Theoreme may you know
the arte of the righte measuringe of likeiammes, as in my booke
of measuring I wil more plainly declare.

_The xxvi. Theoreme._

All likeiammes that haue equal grounde lines and are drawen
betwene one paire of paralleles, are equal togither.

_Example._

Fyrste you muste marke the difference betwene this Theoreme and
the laste, for the laste Theoreme presupposed to the diuers
likeiammes one ground line common to them, but this theoreme
doth presuppose a diuers ground line for euery likeiamme, only
meaning them to be equal in length, though they be diuers in
numbre. As for example. In the last figure ther are two
parallels, A.D. and E.H, and betwene them are drawen thre
likeiammes, the firste is, A.B.E.F, the second is E.C.D.F, and
the thirde is C.G.H.D. The firste and the seconde haue one
ground line, (that is E.F.) and therfore in so muche as they are
betwene one paire of paralleles, they are equall accordinge to
the fiue and twentye Theoreme, but the thirde likeiamme that is
C.G.H.D. hathe his grounde line G.H, seuerall frome the other,
but yet equall vnto it. wherefore the third likeiam is equall to
the other two firste likeiammes. And for a proofe that G.H.
being the ground or ground line of the third likeiamme, is equal
to E.F, whiche is the ground line to both the other likeiams,
that may be thus declared, G.H. is equall to C.D, seynge they
are the contrary sides of one likeiamme (by the foure and twenty
theoreme) and so are C.D. and E.F. by the same theoreme.
Therfore seynge both those ground lines E.F. and G.H, are equall
to one thirde line (that is C.D.) they must nedes bee equall
togyther by the firste common sentence.

_The xxvii. Theoreme._

All triangles hauinge one grounde lyne, and standing betwene
one paire of parallels, ar equall togither.

_Example._

[Illustration]

A.B. and C.F. are twoo gemowe lines, betweene which there be
made two triangles, A.D.E. and D.E.B, so that D.E, is the common
ground line to them bothe. wherfore it doth folow, that those
two triangles A.D.E. and D.E.B. are equall eche to other.

_The xxviij. Theoreme._

All triangles that haue like long ground lines, and bee made
betweene one paire of gemow lines, are equall togither.

_Example._

Example of this Theoreme you may see in the last figure, wh