, whose partes
A. and B, are triangles, and the whole figure is a square, and
so are they not of one kind. But and if they applie it to the
matter or substance of thinges (as some do) then it is most
false, for euery compound thyng is made of partes of diuerse
matter and substance. Take for example a man, a house, a boke,
and all other compound thinges. Some vnderstand it thus, that
the partes all together can make none other forme, but that that
the whole doth shewe, whiche is also false, for I maie make fiue
hundred diuerse figures of the partes of some one figure, as you
shall better perceiue in the third boke. And in the meane season
take for an example this square figure following A.B.C.D, w^{ch}
is deuided but in two parts, and yet (as you se) I haue made
fiue figures more beside the firste, with onely diuerse ioynyng
of those two partes. But of this shall I speake more largely in
an other place. In the mean season content your self with these
principles, whiche are certain of the chiefe groundes wheron all
demonstrations mathematical are fourmed, of which though the
moste parte seeme so plaine, that no childe doth doubte of them,
thinke not therfore that the art vnto whiche they serue, is
simple, other childishe, but rather consider, howe certayne the
profes of that arte is, y^t hath for his groundes soche playne
truthes, & as I may say, suche vndowbtfull and sensible
principles, And this is the cause why all learned menne dooth
approue the certenty of geometry, and consequently of the other
artes mathematical, which haue the grounds (as Arithmeticke,
musike and astronomy) aboue all other artes and sciences, that
be vsed amongest men. Thus muche haue I sayd of the first
principles, and now will I go on with the theoremes, whiche I do
only by examples declare, minding to reserue the proofes to a
peculiar boke which I will then set forth, when I perceaue this
to be thankfully taken of the readers of it.

[Illustration]

The theoremes of Geometry brieflye
declared by shorte examples.

_The firste Theoreme._

When .ij. triangles be so drawen, that the one of them hath
ij. sides equal to ij sides of the other triangle, and that
the angles enclosed with those sides, bee equal also in
bothe triangles, then is the thirde side likewise equall in
them. And the whole triangles be of one greatnes, and euery
angle in the one equall to his matche angle in the other,
I meane those angles tha