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 .XVI. CONCLVSION. To make a likeiamme equall to a triangle appoincted, accordyng to an angle limitted, and on a line also assigned.

In the last conclusion the sides of your likeiamme wer left to your libertie, though you had an angle appoincted. Nowe in this conclusion you are somwhat more restrained of libertie sith the line is limitted, which must be the side of the likeiāme. Therfore thus shall you procede. Firste accordyng to the laste conclusion, make a likeiamme in the angle appoincted, equall to the triangle that is assigned. Then with your compasse take the length of your line appointed, and set out two lines of the same length in the second gemowe lines, beginnyng at the one side of the likeiamme, and by those two prickes shall you draw an other gemowe line, whiche shall be parallele to two sides of the likeiamme. Afterward shall you draw .ij. lines more for the accomplishement of your worke, whiche better shall be

perceaued by a shorte exaumple, then by a greate numbre of wordes, only without example, therefore I wyl by example sette forth the whole worke.

Example.

Fyrst, according to the last

[illustration] diagram

conclusion, I make the like∣iamme E. F. C. G, equal to the triangle D, in the appoynted angle whiche is E. Then take I the lengthe of the assigned line (which is A. B,) and with my compas I sette forthe the same lēgth in the ij. gemow li¦nes N. F. and H. G, setting one foot in E, and the other in N, and againe settyng one foote in C, and the other in H. Af∣terward I draw a line from N. to H, whiche is a gemow lyne, to ij. sydes of the likeiamme. thenne drawe I a line also from N. vnto C, and extend it vntyll it crosse the lines, E. L. and F. G, which both must be drawen forth longer then the si∣des of the likeiamme. and where that lyne doeth crosse F. G, there I sette M. Nowe to make an ende, I make an other ge∣mowe line, whiche is parallel to N. F. and H. G, and that ge∣mowe line doth passe by the pricke M, and then haue I done. Now say I that H. C. K. L, is a likeiamme equall to the trian∣gle appointed, whiche was D, and is made of a line assigned that is A. B, for H. C, is equall vnto A. B, and so is K. L, The prose of y^e equalnes of this likeiam vnto the triāgle, depēdeth of the thirty and two Theoreme: as in the hoke of Theoremes doth appear, where it is declared, that in al likeiammes, whē there are more then one made about one bias line, the filsqua∣res of euery of them muste needes be equall.