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.
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.