[ The .xxxij. Theoreme.]
In all likeiammes where there are more than
one made aboute one bias line, the fill squares of euery of them must nedes be equall.
Example.
Fyrst before I declare the examples, it shal be mete to shew the true vnderstãdyng of this theorem. Bias lyne. Therfore by the Bias line, I meane that lyne, whiche in any square figure dooth runne from corner to corner. And euery square which is diuided by that bias line into equall halues from corner to corner (that is to say, into .ij. equall triangles) those be counted to stande aboute one bias line, and the other squares, whiche touche that bias line, with one of their corners onely, those doo I call Fyll squares, Fyll squares. accordyng to the greke name, which is anapleromata, ἀναπληρώματα and called in latin supplementa, bycause that they make one generall square, includyng and enclosyng the other diuers squares, as in this exãple H.C.E.N. is one square likeiamme, and L.M.G.C. is an other, whiche bothe are made aboute one bias line, that is N.M, than K.L.H.C. and C.E.F.G. are .ij. fyll squares, for they doo fyll vp the sydes of the .ij. fyrste square lykeiammes, in suche sorte, that all them foure is made one greate generall square K.M.F.N.
Nowe to the sentence of the theoreme, I say, that the .ij. fill squares, H.K.L.C. and C.E.F.G. are both equall togither, (as it shall bee declared in the booke of proofes) bicause they are the fill squares of two likeiammes made aboute one bias line, as the exaumple sheweth. Conferre the twelfthe conclusion with this theoreme.