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 .XV. CONCLVSION. To make a likeiāme equall to a triangle ap∣pointed, and that in a right lined āgle limited.

First from one of the angles of the triangle, you shall drawe a gemowe line, whiche shall be a parallele to that syde of the triangle, on whiche you will make that likeiamme. Then on one end of the side of the triangle, whiche lieth against the ge∣mowe lyne, you shall draw forth a line vnto the gemow line, so that one angle that commeth of those .ij. lines be like to the angle whiche is limited vnto you. Then shall you deuide into ij. equall partes that side of the triangle whiche beareth that line, and from the pricke of that deuision, you shall raise an o∣ther line parallele to that former line, and continewe it vnto the first gemowe line, and thē of those .ij. last gemowe lynes, and the first gemowe line, with the halfe side of the triangle, is made a lykeiamme equall to the triangle appointed, and hath an angle lyke to an angle limited, accordyng to the conclusion.

Example.

[illustration] diagram

B. C. G, is the tri∣angle appoincted vnto, whiche I muste make an e∣quall likeiamme. And D, is the an∣gle that the like∣iamme must haue. Therfore first en∣tendyng to erecte the likeiāme on the one side, that the ground line of the trian∣gle (whiche is B. G.) I do draw a gemow line by C, and make it parallele to the ground line B. G, and that new gemow line is A. H. Then do I raise a line from B. vnto the gemowe line, (whiche line is A. B) and make an angle equall to D, that is the appointed angle (accordyng as the .viij. cōclusion teacheth, and that angle is B. A. E. Then to procede, I doo parte in y^e middle the said groūd line B. G, in the prick F, frō which prick I draw

to the first gemowe line (A. H.) an other line that is parallale to A. B, and that line is E. F. Now saie I that the likeiāme B. A. E. F, is equall to the triangle B. C. G. And also that it hath one angle (that is B. A. E. like to D. the angle that was limitted. And so haue I mine intent. The prose of the equal∣nes of those two figures doeth depend of the .xli. proposition of Euclides first boke, and is the .xxxi. proposition of this se∣cond boke of Theoremis, whiche saieth, that whan a tryangle and a likeiamme be made betwene .ij. selfe same gemow lines, and haue their ground line of one length, then is the likeiamme double to the triangle, wherof it foloweth, that if .ij. suche fi∣gures so drawen differ in their ground line onely, so that the ground line of the likeiamme be but halfe the ground line of the triangle, then be those .ij. figures equall, as you shall more at large perceiue by the boke of Theoremis, in y^e .xxxi. theoreme.