Certayn common sentences manifest to
sence, and acknowledged of all men.

_The firste common sentence._

What so euer things be equal to one other thinge, those same
bee equall betwene them selues.

[Illustration]

Examples therof you may take both in greatnes and also in
numbre. First (though it pertaine not proprely to geometry, but
to helpe the vnderstandinge of the rules, whiche may bee wrought
by bothe artes) thus may you perceaue. If the summe of monnye in
my purse, and the mony in your purse be equall eche of them to
the mony that any other man hathe, then must needes your mony
and mine be equall togyther. Likewise, if anye ij. quantities,
as A. and B, be equal to an other, as vnto C, then muste nedes A.
and B. be equall eche to other, as A. equall to B, and B. equall
to A, whiche thinge the better to perceaue, tourne these
quantities into numbre, so shall A. and B. make sixteene, and C.
as many. As you may perceaue by multipliyng the numbre of their
sides togither.

_The seconde common sentence._

And if you adde equall portions to thinges that be equall,
what so amounteth of them shall be equall.

Example, Yf you and I haue like summes of mony, and then receaue
eche of vs like summes more, then our summes wil be like styll.
Also if A. and B. (as in the former example) bee equall, then by
adding an equal portion to them both, as to ech of them, the
quarter of A. (that is foure) they will be equall still.

_The thirde common sentence._

And if you abate euen portions from things that are equal,
those partes that remain shall be equall also.

This you may perceaue by the last example. For that that was
added there, is subtracted heere. and so the one doothe approue
the other.

_The fourth common sentence._

If you abate equalle partes from vnequal thinges, the
remainers shall be vnequall.

As bicause that a hundreth and eight and forty be vnequal if I
take tenne from them both, there will remaine nynetye and eight
and thirty, which are also vnequall. and likewise in quantities
it is to be iudged.

_The fifte common sentence._

When euen portions are added to vnequalle thinges, those
that amounte shalbe vnequall.

So if you adde twenty to fifty, and lyke ways to nynty, you
shall make seuenty and a hundred and ten whiche are no lesse
vnequall, than were fifty and nynty.

_The syxt common sentence._

If two thinges be double to any other, those