The Path-Way to Knowledg, Containing the First Principles of GeometrieRecord, Robert
Science
The Path-Way to Knowledg, Containing the First Principles of Geometrie
Record, Robert
Geometry -- Early works to 1800
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 lẽgth 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 triãgle, depẽdeth of the thirty and two
Theoreme: as in the boke of Theoremes doth appear, where it is
declared, that in al likeiammes, whẽ there are more then one
made about one bias line, the filsquares of euery of them muste
needes be equall.
THE XVII. CONCLVSION.
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
cõclusion, 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 happẽ 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 lẽgth of one of his sides, and set that as a line assigned,
on whiche you shal make the other likeiams, according to the
twelft cõclusion, and so shall you haue al your likeiammes with
ij. sides equal, and ij. like angles, so y^t you mai easily
ioyne thẽ into one figure.
[Illustration]
_Example._
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