Part 10 (1/2)

Deuide the circle appointed into fiue equall partes, as you didde in the laste conclusion, and drawe ij. lines from euery p.r.i.c.ke to the other ij. that are nexte vnto it. And so shall you make a cinkangle after the meanynge of the conclusion.

_Example._

Yow se here this circle A.B.C.D.E. deuided into fiue equall portions. And from eche p.r.i.c.ke ij. lines drawen to the other ij.

nexte p.r.i.c.kes, so from A. are drawen ij. lines, one to B, and the other to E, and so from C. one to B. and an other to D, and likewise of the reste. So that you haue not only learned hereby how to make a sinkangle in anye circle, but also how you shal make a like figure spedely, whanne and where you will, onlye drawinge the circle for the intente, readylye to make the other figure (I meane the cinkangle) thereby.

[Ill.u.s.tration]

THE x.x.xIX. CONCLVSION.

How to make a cinkangle of equall sides and equall angles about any circle appointed.

Deuide firste the circle as you did in the last conclusion into fiue equall portions, and draw fiue semidiameters in the circle.

Then make fiue touche lines, in suche sorte that euery touche line make two right angles with one of the semidiameters. And those fiue touche lines will make a cinkangle of equall sides and equall angles.

[Ill.u.s.tration]

_Example._

A.B.C.D.E. is the circle appointed, which is deuided into fiue equal partes. And vnto euery prycke is draw? a semidiameter, as you see. Then doo I make a touche line in the p.r.i.c.ke B, whiche is F.G, making ij. right angles with the semidiameter B, and lyke waies on C. is made G.H, on D. standeth H.K, and on E, is set K.L, so that of those .v. touche lynes are made the .v.

sides of a cinkeangle, accordyng to the conclusion.

An other waie.

Another waie also maie you drawe a cinkeangle aboute a circle, drawyng first a cinkeangle in the circle (whiche is an easie thyng to doe, by the doctrine of the .x.x.xvij. conclusion) and then drawing .v. touche lines whiche shall be iuste paralleles to the .v. sides of the cinkeangle in the circle, forseeyng that one of them do not crosse ouerthwarte an other and then haue you done. The exaumple of this (because it is easie) I leaue to your owne exercise.

THE XL. CONCLVSION.

To make a circle in any appointed cinkeangle of equall sides and equall corners.

Drawe a plumbe line from any one corner of the cinkeangle, vnto the middle of the side that lieth iuste against that angle. And do likewaies in drawyng an other line from some other corner, to the middle of the side that lieth against that corner also. And those two lines wyll meete in crosse in the p.r.i.c.ke of their crossyng, shall you iudge the centre of the circle to be.

Therfore set one foote of the compas in that p.r.i.c.ke, and extend the other to the end of the line that toucheth the middle of one side, whiche you liste, and so drawe a circle. And it shall be iustly made in the cinkeangle, according to the conclusion.

_Example._

The cinkeangle a.s.signed is A.B.C.D.E, in whiche I muste make a circle, wherefore I draw a right line from the one angle (as from B,) to the middle of the contrary side (whiche is E. D,) and that middle p.r.i.c.ke is F. Then lykewaies from an other corner (as from E) I drawe a right line to the middle of the side that lieth against it (whiche is B.C.) and that p.r.i.c.ke is G. Nowe because that these two lines do crosse in H, I saie that H. is the centre of the circle, whiche I would make. Therfore I set one foote of the compa.s.se in H, and extend the other foote vnto G, or F. (whiche are the endes of the lynes that lighte in the middle of the side of that cinkeangle) and so make I the circle in the cinkangle, right as the cclusion meaneth.

[Ill.u.s.tration]

THE XLI. CONCLVSION

To make a circle about any a.s.signed cinkeangle of equall sides, and equall corners.

Drawe .ij. lines within the cinkeangle, from .ij. corners to the middle on tbe .ij. contrary sides (as the last conclusion teacheth) and the pointe of their crossyng shall be the centre of the circle that I seke for. Then sette I one foote of the compas in that centre, and the other foote I extend to one of the angles of the cinkangle, and so draw I a circle about the cinkangle a.s.signed.

_Example._