[Illustration] 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. _The nynth common sentence._ Euery whole thing is greater than any of his partes. This sentence nedeth none example. For the thyng is more playner then any declaration, yet considering that other common sentence that foloweth nexte that. _The tenthe common sentence._ Euery whole thinge is equall to all his partes taken togither. [Illustration] [Illustration] It shall be mete to expresse both w^t one example, for of thys last sentence many mẽ at the first hearing do make a doubt. Therfore as in this example of the circle deuided into sũdry partes it doeth appere that no parte can be so great as the whole circle, (accordyng to the meanyng of the eight sentence) so yet it is certain, that all those eight partes together be equall vnto the whole circle. And this is the meanyng of that common sentence (whiche many vse, and fewe do rightly vnderstand) that is, that _All the partes of any thing are nothing els, but the whole_. And contrary waies: _The whole is nothing els, but all his partes taken togither_. whiche saiynges some haue vnderstand to meane thus: that all the partes are of the same kind that the whole thyng is: but that that meanyng is false, it doth plainly appere by this figure A.B, whose partes A. and B, are triangles, and the whole figure is a square, and so are they not of one kind. But and if they applie it to the matter or substance of thinges (as some do) then it is most false, for euery compound thyng is made of partes of diuerse matter and substance. Take for example a man, a house, a boke, and all other compound thinges. Some vnderstand it thus, that the partes all together can make none other forme, but that that the whole doth shewe, whiche is also false, for I maie make fiue hundred diuerse figures of the partes of some one figure, as you shall better perceiue in the third boke. And in the meane seasõ take for an exãple this square figure following A.B.C.D, w^{ch} is deuided but in two parts, and yet (as you se) I haue made fiue figures more beside the firste, with onely diuerse ioynyng of those two partes. But of this shall I speake more largely in an other place. In the mean season content your self with these principles, whiche are certain of the chiefe groundes wheron all demonstrations mathematical are fourmed, of which though the moste parte seeme so plaine, that no childe doth doubte of them, thinke not therfore that the art vnto whiche they serue, is simple, other childishe, but rather consider, howe certayne the profes of that arte is, y^t hath for his groũdes soche playne