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 XVII. CONCLVSION. To make a likeiamme equal to any right lined figure, and that on an angle appointed.

The readiest waye to worke this conclusion, is to tourn that right lined figure into triangles, and then for euery triangle to gether an equal likeiamme, according vnto the eleuen cōclusi¦on, and then to ioine al those likeiammes into one, if their si∣des happen to be equal, which thing is euer certain, when al the triangles happē iustly betwene one pair of gemow lines. but and if they will not frame so, then after that you haue for the firste triangle made his likeiamme, you shall take the lēgth of one of his sides, and set that as a line assigned, on whiche you shal make al the other likeiams, according to the twelft cō¦clusion,

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and so shall you haue al your likeiammes with ij. sides equal, and ij. like angles, so y^t you mai¦easily ioyne thē into one figure.

Example.

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If the right lined fi∣gure be like vnto A, thē may it be turned into tri¦angles that wil stād be∣twene ij. parallels anye ways, as you maise by C and D, for ij. sides of both

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the triāgls ar parallels. Also if the right lined fi¦gure be like vnto E, thē wil it be turned into triā¦gles, liyng betwene two parallels also, as y^e other did before. as in the exā∣ple of F. G. But and if y^e

right lined figure be like vnto H, and so turned into triāgles as you se in K. L. M, wher it is parted into iij triāgles, thē wil not all those triangles lye betwen one pair of parallels or ge∣mow lines, but must haue many, for euery triangle must haue one paire of parallels seuerall, yet it maye happen that when there bee three or sower triangles, ij. of theym maye hap∣pen to agre to one pair of parallels, whiche thinge I remit to euery honest witte to serche, for the manner of their draught wil declare, how many paires of parallels they shall neede, of which varietee bicause the examples ar infinite, I haue set forth these few, that by them you may coniecture duly of all other like.

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Further explicacion you shal not greatly neede, if you re∣membre what hath ben taught before, and then diligētly be∣hold how these sundry figures be turned into triāgles. In the fyrst you se I haue made v. triangles, and four paralleles. in the seconde vij. triangles and foure paralleles. in the thirde thre triāgles, and fiue parallels, in the iiij. you se fiue triāgles & four parallels. in the fift, iiij. triāgles and .iiij. parallels, & in y^e sixt ther ar fiue triāgles & iiij. paralels. Howbeit a mā maye at liberty alter them into diuers formes of triāgles & therefore I

leue it to the discretion of the woorkmaister, to do in al suche cases as he shal thinke best, for by these examples (if they bee well marked) may all other like conclusions be wrought.