The pathvvay to knowledg containing the first principles of geometrie, as they may moste aptly be applied vnto practise, bothe for vse of instrumentes geometricall, and astronomicall and also for proiection of plattes in euerye kinde, and therefore much necessary for all sortes of men.

The tenthe common sentence. Euery whole thinge is equall to all his partes taken togither.

It shall be mete to expresse both w^t one example, for of thys last sētence many mē at the first hearing do make a doubt. Ther¦fore as in this example of the circle deuided into sūdry partes

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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 par∣tes 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

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A. B, whose partes A. and B, are trian∣gles, 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 thin¦ges (as some do) then is it moste false, for e∣uery compound thyng is made of partes of diuerse matter and substance. Take for example a man, a house, a boke, and all o∣ther compound thinges. Some vnderstand it thus, that the par∣tes 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 seasō take for an exāple this square figure folowing A. B. C. D, w^ch is deuided but into two parts, and yet (as youse) 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

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hath for his gro¦ūdes soche pla∣yne truthes, & as I may say, suche vndow∣btfull and sensi¦ble principles, And this is the cause why all learned menne dooth approue the certenty of geometry, and cōsequently of the other artes mathematical, which haue the grounds (as A∣rithmetike, mu¦sike and astro∣nomy) aboue all other artes and sciences, that be vsed amōgest men. Thus muche haue I sayd of the first principles, and now will I go on with the theoremes, whiche I do only by exam∣ples declae, minding to reserue the proofes to a peculiar boke which I will then set forth, when I perceaue this to be thank∣fully taken of the readers of it.