togither, that is C.D, and E.F, now this beeynge true,
and considering that they are made towarde one side, it
foloweth, that they are made betwene one paire of parallels when
I saye, drawen towarde one side, I meane that the triangles must
be drawen other both vpward frome one parallel, other els both
downward, for if the one be drawen vpward and the other
downward, then are they drawen betwene two paire of parallels,
presupposinge one to bee drawen by their ground line, and then
do they ryse toward contrary sides.

_The xxxi. theoreme._

If a likeiamme haue one ground line with a triangle, and be
drawen betwene one paire of paralleles, then shall the
likeiamme be double to the triangle.

_Example._

[Illustration]

A.H. and B.G. are .ij. gemow lines, betwene which there is made
a triangle B.C.G, and a lykeiamme, A.B.G.C, whiche haue a
grounde lyne, that is to saye, B.G. Therfore doth it folow that
the lyke iamme A.B.G.C. is double to the triangle B.C.G. For
euery halfe of that lykeiamme is equall to the triangle, I meane
A.B.F.E. other F.E.C.G. as you may coniecture by the .xi.
conclusion geometrical.

And as this Theoreme dothe speake of a triangle and likeiamme
that haue one groundelyne, so is it true also, yf theyr
groundelynes bee equall, though they bee dyuers, so that thei be
made betwene one payre of paralleles. And hereof may you
perceaue the reason, why in measuryng the platte of a triangle,
you must multiply the perpendicular lyne by halfe the grounde
lyne, or els the hole grounde lyne by halfe the perpendicular,
for by any of these bothe waies is there made a lykeiamme equall
to halfe suche a one as shulde be made on the same hole grounde
lyne with the triangle, and betweene one payre of paralleles.
Therfore as that lykeiamme is double to the triangle, so the
halfe of it, must needes be equall to the triangle. Compare the
.xi. conclusion with this theoreme.

_The .xxxij. Theoreme._

In all likeiammes where there are more than one made aboute
one bias line, the fill squares of euery of them must nedes
be equall.

[Illustration]

_Example._

Fyrst before I declare the examples, it shal be mete to shew the
true vnderstandyng of this theorem. [Sidenote: _Bias lyne._]
Therfore by the _Bias line_, I meane that lyne, whiche in any
square figure dooth runne from corner to corner. And euery
square which is diuided by that bias line into equall halues
from corner to corner (th