To make a likeiamme equall to a triangle appointed, and that
in a right lined angle limited.
First from one of the angles of the triangle, you shall drawe a
gemowe line, whiche shall be a parallele to that syde of the
triangle, on whiche you will make that likeiamme. Then on one
end of the side of the triangle, whiche lieth against the gemowe
lyne, you shall draw forth a line vnto the gemow line, so that
one angle that commeth of those .ij. lines be like to the angle
which is limited vnto you. Then shall you deuide into ij. equall
partes that side of the triangle whiche beareth that line, and
from the pricke of that deuision, you shall raise an other line
parallele to that former line, and continewe it vnto the first
gemowe line, and then of those .ij. last gemowe lynes, and the
first gemowe line, with the halfe side of the triangle, is made
a lykeiamme equall to the triangle appointed, and hath an angle
lyke to an angle limited, accordyng to the conclusion.
[Illustration]
_Example._
B.C.G, is the triangle appoincted vnto, whiche I muste make an
equall likeiamme. And D, is the angle that the likeiamme must
haue. Therfore first entendyng to erecte the likeiamme on the one
side, that the ground line of the triangle (whiche is B.G.) I do
draw a gemow line by C, and make it parallele to the ground line
B.G, and that new gemow line is A.H. Then do I raise a line from
B. vnto the gemowe line, (whiche line is A.B) and make an angle
equall to D, that is the appointed angle (accordyng as the
.viij. conclusion teacheth) and that angle is B.A.E. Then to
procede, I doo parte in y^e middle the said ground line B.G, in
the prick F, from which prick I draw to the first gemowe line
(A.H.) an other line that is parallele to A.B, and that line is
E.F. Now saie I that the likeiamme B.A.E.F, is equall to the
triangle B.C.G. And also that it hath one angle (that is B.A.E.)
like to D. the angle that was limitted. And so haue I mine
intent. The profe of the equalnes of those two figures doeth
depend of the .xli. proposition of Euclides first boke, and is
the .xxxi. proposition of this second boke of Theoremis, whiche
saieth, that whan a tryangle and a likeiamme be made betwene
.ij. selfe same gemow lines, and haue their ground line of one
length, then is the likeiamme double to the triangle, wherof it
foloweth, that if .ij. suche figures so drawen differ in their
ground line onely, so that the ground line of the likeiamme be
but halfe the ground line of the triangle, then be those .ij.
figures equall, as you shall more at large perceiue by the boke
of Theoremis, in y^e .xxxi. theoreme.