Part 9 (2/2)

Then sette I the one foote of the compa.s.se in B, and drawe twoo arche lines F. and G. Like wise setting the compa.s.se foote in C, I drawe twoo other arche lines, G. and H, and on D. I make twoo other, H. and E. Then frome the crossinges of those eighte arche lines I drawe iiij. straighte lynes, that is to saye, E.F, and F.G, also G.H, and H.E, whiche iiij. straighte lynes do make the square quadrate that I should draw about the circle a.s.signed.

THE x.x.xV. CONCLVSION.

To draw a circle in any square quadrate appointed.

Fyrste deuide euery side of the quadrate into twoo equall partes, and so drawe two lynes betwene eche two contrary poinctes, and where those twoo lines doo crosse, there is the centre of the circle. Then sette the foote of the compa.s.se in that point, and stretch forth the other foot, according to the length of halfe one of those lines, and so make a compas in the square quadrate a.s.signed.

_Example._

[Ill.u.s.tration]

A.B.C.D. is the quadrate appointed, in whiche I muste make a circle. Therefore first I do deuide euery side in ij. equal partes, and draw ij. lines acrosse, betwene eche ij. ctrary p.r.i.c.kes, as you se E.G, and F.H, whiche mete in K, and therfore shal K, be the centre of the circle. Then do I set one foote of the compas in K. and op? the other as wide as K.E, and so draw a circle, which is made accordinge to the conclusion.

THE x.x.xVI. CONCLVSION.

To draw a circle about a square quadrate.

Draw ij. lines betwene the iiij. corners of the quadrate, and where they mete in crosse, ther is the centre of the circle that you seeke for. Th? set one foot of the compas in that centre, and extend the other foote vnto one corner of the quadrate, and so may you draw a circle which shall iustely inclose the quadrate proposed.

_Example._

[Ill.u.s.tration]

A.B.C.D. is the square quadrate proposed, about which I must make a circle. Therfore do I draw ij. lines crosse the square quadrate from angle to angle, as you se A.C. & B.D. And where they ij. do crosse (that is to say in E.) there set I the one foote of the compas as in the centre, and the other foote I do extend vnto one angle of the quadrate, as for exple to A, and so make a compas, whiche doth iustly inclose the quadrate, according to the minde of the conclusion.

THE x.x.xVII. CONCLVSION.

To make a twileke triangle, whiche shall haue euery of the ij. angles that lye about the ground line, double to the other corner.

Fyrste make a circle, and deuide the circ.u.mference of it into fyue equall partes. And thenne drawe frome one p.r.i.c.ke (which you will) two lines to ij. other p.r.i.c.kes, that is to say to the iij.

and iiij. p.r.i.c.ke, counting that for the first, wherhence you drewe both those lines, Then drawe the thyrde lyne to make a triangle with those other twoo, and you haue doone according to the conclusion, and haue made a twelike trigle, whose ij.

corners about the grounde line, are eche of theym double to the other corner.

_Example._

[Ill.u.s.tration]

A.B.C. is the circle, whiche I haue deuided into fiue equal portions. And from one of the p.r.i.c.kes (which is A,) I haue draw?

ij. lines, A.B. and B.C, whiche are drawen to the third and iiij. p.r.i.c.kes. Then draw I the third line C.B, which is the grounde line, and maketh the triangle, that I would haue, for the gle C. is double to the angle A, and so is the angle B.

also.

THE x.x.xVIII. CONCLVSION.

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

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