Example.
For the declaration of this theoreme and the next also, whose vse are wonderfull in the practise of Geometrie, and in measuryng especially, it shall be nedefull to declare that euery triangle that hath no ryght angle as those whyche are called (as in the boke of practise is declared) sharp cornered triangles, and blunt cornered triangles, yet may they be brought to haue a ryght angle, eyther by partyng them into two lesser triangles,
or els by addyng an other triangle vnto them, whiche may be a great helpe for the ayde of measuryng, as more largely shall be sette foorthe in the boke of measuryng. But for this present place, this forme wyll I vse, (whiche Theon also vseth) to adde one triangle vnto an other, to bryng the blunt cornered triangle into a ryght angled triangle, whereby the proportion of the squares of the sides in suche a blunt cornered triangle may the better bee knowen.
Fyrst therfore I sette foorth the triangle A.B.C, whose corner by C. is a blunt corner as you maye well iudge, than to make an other triangle of yt with a ryght angle, I must drawe forth the side B.C. vnto D, and frõ the sharp corner by A. I brynge a plumbe lyne or perpẽdicular on D. And so is there nowe a newe triangle A.B.D. whose angle by D. is a right angle. Nowe accordyng to the meanyng of the Theoreme, I saie, that in the first triangle A.B.C, because it hath a blunt corner at C, the square of the line A.B. whiche lieth against the said blunte corner, is more
then the square of the line A.C, and also of the lyne B.C, (whiche inclose the blunte corner) by as muche as will amount twise of the line B.C, and that portion D.C. whiche lieth betwene the blunt angle by C, and the perpendicular line A.D.
The square of the line A.B, is the great square marked with E. The square of A.C, is the meane square marked with F. The square of B.C, is the least square marked with G. And the long square marked with K, is sette in steede of two squares made of B.C, and C.D. For as the shorter side is the iuste lengthe of C.D, so the other longer side is iust twise so longe as B.C, Wherfore I saie now accordyng to the Theoreme, that the greatte square E, is more then the other two squares F. and G, by the quantitee of the longe square K, wherof I reserue the profe to a more conuenient place, where I will also teache the reason howe to fynde the lengthe of all suche perpendicular lynes, and also of the line that is drawen betweene the blunte angle and the perpendicular line, with sundrie other very pleasant conclusions.
Labeling of rectangle K is conjectural. Other configurations of B, C and D will also fit, but the printed illustration (B and D on the right, nothing on the left) will not. The text requires a rectangle with BC as one side and CD as the other, doubled as in the next illustration (H.K).