same two
thinges are equal togither.

[Illustration]

Bicause A. and B. are eche of them double to C, therefore must
A. and B. nedes be equall togither. For as v. times viij. maketh
xl. which is double to iiij. times v, that is xx so iiij. times
x, likewise is double to xx. (for it maketh fortie) and
therefore muste neades be equall to forty.

_The seuenth common sentence._

If any two thinges be the halfes of one other thing, then
are thei .ij. equall togither.

So are D. and C. in the laste example equal togyther, bicause
they are eche of them the halfe of A. other of B, as their
numbre declareth.

_The eyght common sentence._

If any one quantitee be laide on an other, and thei agree,
so that the one excedeth not the other, then are they equall
togither.

[Illustration]

As if this figure A.B.C, be layed on that other D.E.F, so that
A. be layed to D, B. to E, and C. to F, you shall see them agre
in sides exactlye and the one not to excede the other, for the
line A.B. is equall to D.E, and the third lyne C.A, is equall to
F.D so that eueryside in the one is equall to some one side of
the other. Wherfore it is playne, that the two triangles are
equall togither.

_The nynth common sentence._

Euery whole thing is greater than any of his partes.

This sentence nedeth none example. For the thyng is more playner
then any declaration, yet considering that other common sentence
that foloweth nexte that.

_The tenthe common sentence._

Euery whole thinge is equall to all his partes taken
togither.

[Illustration]

[Illustration]

It shall be mete to expresse both w^t one example, for of thys
last sentence many men at the first hearing do make a doubt.
Therfore as in this example of the circle deuided into sundry
partes it doeth appere that no parte can be so great as the
whole circle, (accordyng to the meanyng of the eight sentence)
so yet it is certain, that all those eight partes together be
equall vnto the whole circle. And this is the meanyng of that
common sentence (whiche many vse, and fewe do rightly
vnderstand) that is, that _All the partes of any thing are
nothing els, but the whole_. And contrary waies: _The whole is
nothing els, but all his partes taken togither_. whiche saiynges
some haue vnderstand to meane thus: that all the partes are of
the same kind that the whole thyng is: but that that meanyng is
false, it doth plainly appere by this figure A.B