PROPOSITION III.

To circumfcribe a Triangle round a Circle, equiangular to a Triangle given.

Let DEV be the Circle round which a Triangle is to be formed like the Triangle FGH.

Parallel to the Diameter

AB.

INO will be the Triangle required, equiangular to the Triangle FGH, and circumfcribed round the Circle DEV.

PROPOSITION IV.

To circumfcribe a Square round a Circle.

Let ABCD be the Circle round which a Square is to be cir

cumfcribed.

PRACTICE.

Draw the Diameters

AB, CD.

Cutting each other at Right Angles in O.

From the Points

And the Space

A, B, C, D.

AO

Defcribe the Semi-Circles HOG, HOE, EOF, FOG.

Draw the Right Lines EF, FG, GH, HE.

Through the Sections

E, F, G, H.

E, F, G, H, will be the Square required.

PRO

PROPOSITION V.

To circumfcribe a Pentagon round a given Circle. Let ABCDE be the Circle round which a Pentagon is to be circumfcribed.

PRACTICE.

B. 3. P. 3. Infcribe the Pentagon
From the Center

ABCDE.

F

Draw the Lines

And thro' the Middle of each of its Sides

FO, FP, FQ, FR, FS.

Draw the Line

FA

PQ

Α

F

FP

OPQRS.

Then draw the Sides of the Pentagon required through the

Sections

OPQRS.

PROPOSITION VI.

To circumfcribe a Regular Polygon round a Regular Polygon.

Let BCDEFG be the given Polygon, round which a like Polygon is to be circumfcribed.

Draw the Radiufes AL, AM, AN, AO.

Through the Middle of each Side.

Then draw the Sides of the exterior Polygon required thro'

the Sections

ILMNOP.

PRO

PROPOSITION VII.

To circumfcribe a Square round an Equilateral Triangle. A, B, C, is an Equilateral Triangle round which a Square is to be circumfcribed.

PROPOSITION VIII.

To circumfcribe a Pentagon round an Equilateral Tri

angle.

ABC is the given Triangle round which a Pentagon is to be circumfcribed.

PRACTICE.

From the Points or Angles

A,B,C.

And with the fame Opening of the Com-
paffes,

Describe at Difcretion the Arches DI,LP,HE.

PROPOSITION IX.

To circumscribe a Triangle round a Square, equiangular to a Triangle given.

Let DEFG be the Square, round which a Triangle is to be formed, like the Triangle ABC.

PRACTICE.

Make the Angle

B. 1. P. 8. Equal to the Angle

Make the Angle

Equal to the Angle

Prolong the Lines

Towards

EFM

A

MEF

B

ME, MF, DG.

I and H.

MIH will be the Triangle required, like the Triangle ABC. and circumfcribed round the given Square DEFG.

PROPOSITION X.

To circumfcribe a Pentagon round a Square.

ABCD is a Square, round which a Pentagon is to be cir

the Pentagon required.

SCT, SDT

VB, CT, to O.

OV.

will have

you