To make a likeiamme equall to a triangle appoincted,
accordyng to an angle limitted, and on a line also assigned.
In the last conclusion the sides of your likeiamme wer left to
your libertie, though you had an angle appoincted. Nowe in this
conclusion you are somwhat more restrained of libertie sith the
line is limitted, which must be the side of the likeiamme.
Therfore thus shall you procede. Firste accordyng to the laste
conclusion, make a likeiamme in the angle appoincted, equall to
the triangle that is assigned. Then with your compasse take the
length of your line appointed, and set out two lines of the same
length in the second gemowe lines, beginnyng at the one side of
the likeiamme, and by those two prickes shall you draw an other
gemowe line, whiche shall be parallele to two sides of the
likeiamme. Afterward shall you draw .ij. lines more for the
accomplishement of your worke, which better shall be perceaued
by a shorte exaumple, then by a greate numbre of wordes, only
without example, therefore I wyl by example sette forth the
whole worke.
_Example._
[Illustration]
Fyrst, according to the last conclusion, I make the likeiamme
E.F.C.G, equal to the triangle D, in the appoynted angle whiche
is E. Then take I the lengthe of the assigned line (which is
A.B,) and with my compas I sette forthe the same length in the
ij. gemow lines N.F. and H.G, setting one foot in E, and the
other in N, and againe settyng one foote in C, and the other
in H. Afterward I draw a line from N. to H, whiche is a gemow
lyne, to ij. sydes of the likeiamme. thenne drawe I a line also
from N. vnto C. and extend it vntyll it crosse the lines, E.L.
and F.G, which both must be drawen forth longer then the sides
of the likeiamme. and where that lyne doeth crosse F.G, there I
sette M. Nowe to make an ende, I make an other gemowe line,
whiche is parallel to N.F. and H.G, and that gemowe line doth
passe by the pricke M, and then haue I done. Now say I that
H.C.K.L, is a likeiamme equall to the triangle appointed, whiche
was D, and is made of a line assigned that is A.B, for H.C, is
equall vnto A.B, and so is K.L. The profe of y^e equalnes of
this likeiam vnto the triangle, dependeth of the thirty and two
Theoreme: as in the boke of Theoremes doth appear, where it is
declared, that in al likeiammes, when there are more then one
made about one bias line, the filsquares of euery of them muste
needes be equall.