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 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.