When any ij. right lines doth touche and couple .ij. other righte lines, whiche are equall in length and paralleles, and if those .ij. lines bee drawen towarde one hande, then are thei also equall together, and paralleles. _Example._ [Illustration] A.B. and C.D. are ij. ryght lynes and paralleles and equall in length, and they ar touched and ioyned togither by ij. other lynes A.C. and B.D, this beyng so, and A.C. and B.D. beyng drawen towarde one syde (that is to saye, bothe towarde the lefte hande) therefore are A.C. and B.D. bothe equall and also paralleles. _The .xxiiij. theoreme._ In any likeiamme the two contrary sides ar equall togither, and so are eche .ij. contrary angles, and the bias line that is drawen in it, dothe diuide it into two equall portions. _Example._ [Illustration] Here ar two likeiammes ioyned togither, the one is a longe square A.B.E, and the other is a losengelike D.C.E.F. which ij. likeiammes ar proued equall togither, bycause they haue one ground line, that is, F.E, And are made betwene one payre of gemow lines, I meane A.D. and E.H. By this Theoreme may you know the arte of the righte measuringe of likeiammes, as in my booke of measuring I wil more plainly declare. _The xxvi. Theoreme._ All likeiammes that haue equal grounde lines and are drawen betwene one paire of paralleles, are equal togither. _Example._ Fyrste you muste marke the difference betwene this Theoreme and the laste, for the laste Theoreme presupposed to the diuers likeiammes one ground line common to them, but this theoreme doth presuppose a diuers ground line for euery likeiamme, only meaning them to be equal in length, though they be diuers in numbre. As for example. In the last figure ther are two parallels, A.D. and E.H, and betwene them are drawen thre likeiammes, the firste is, A.B.E.F, the second is E.C.D.F, and the thirde is C.G.H.D. The firste and the seconde haue one ground line, (that is E.F.) and therfore in so muche as they are betwene one paire of paralleles, they are equall accordinge to the fiue and twentye Theoreme, but the thirde likeiamme that is C.G.H.D. hathe his grounde line G.H, seuerall frome the other, but yet equall vnto it. wherefore the third likeiam is equall to the other two firste likeiammes. And for a proofe that G.H. being the ground or groũd line of the third likeiamme, is equal to E.F, whiche is the ground line to both the other likeiams, that may be thus declared, G.H. is equall to C.D, seynge they are the contrary sides of one likeiamme (by the foure and twẽty theoreme) and so are C.D. and E.F. by the same theoreme. Therfore seynge both those ground lines E.F. and G.H, are equall to one thirde line (that is C.D.) they must nedes bee equall togyther by the firste common sentence. _The xxvii. Theoreme._ All triangles hauinge one grounde lyne, and standing betwene one paire of parallels, ar equall togither. _Example._ [Illustration]