To make a likeiamme equal to any right lined figure, and
that on an angle appointed.
The readiest waye to worke this conclusion, is to tourn that
rightlined figure into triangles, and then for euery triangle
together an equal likeiamme, according vnto the eleuen
conclusion, and then to ioine al those likeiammes into one, if
their sides happen to be equal, which thing is euer certain,
when al the triangles happen iustly betwene one pair of gemow
lines. but and if they will not frame so, then after that you
haue for the firste triangle made his likeiamme, you shall take
the length of one of his sides, and set that as a line assigned,
on whiche you shal make the other likeiams, according to the
twelft conclusion, and so shall you haue al your likeiammes with
ij. sides equal, and ij. like angles, so y^t you mai easily
ioyne them into one figure.
[Illustration]
_Example._
If the right lined figure be like vnto A, then may it be turned
into triangles that wil stand betwene ij. parallels anye ways, as
you mai se by C. and D, for ij. sides of both the trianngles ar
parallels. Also if the right lined figure be like vnto E, then
wil it be turned into triangles, liyng betwene two parallels
also, as y^e other did before, as in the example of F.G. But and
if y^e right lined figure be like vnto H, and so turned into
triangles as you se in K.L.M, wher it is parted into iij
triangles, then wil not all those triangles lye betwen one pair of
parallels or gemow lines, but must haue many, for euery triangle
must haue one paire of parallels seuerall, yet it maye happen
that when there bee three or fower triangles, ij. of theym maye
happen to agre to one pair of parallels, whiche thinge I remit
to euery honest witte to serche, for the manner of their draught
wil declare, how many paires of parallels they shall neede, of
which varietee bicause the examples ar infinite, I haue set
forth these few, that by them you may coniecture duly of all
other like.
[Illustration]
Further explicacion you shal not greatly neede, if you remembre
what hath ben taught before, and then diligently behold how these
sundry figures be turned into triangles. In the fyrst you se I
haue made v. triangles, and four paralleles. in the seconde vij.
triangles and foure paralleles. in the thirde thre triangles, and
fiue parallels, in the iiij. you se fiue triangles & four
parallels. in the fift, iiij. triangles and .iiij. parallels, &
in y^e sixt ther ar fiue triangles & iiij. paralels. Howbeit a man
maye at liberty alter them into diuers formes of triangles &
therefore I leue it to the discretion of the woorkmaister, to do
in al suche cases as he shal thinke best, for by these examples
(if they bee well marked) may all other like conclusions be
wrought.