PROBLEM XXIII.

To infcribe an Heptagon in a given circle.

A

B

D

With the radius of the circle, and any point A in the circumference as a centre, defcribe the arc B C. Draw the line B C, and bifect it in D. DB or DC, is the fide of the Heptagon.

PROBLEM XXIV.

To inscribe an Octagon, in a given circle.

Draw two diameters A B and C D, at right angles.
Bifect the arc A C, in E.

Draw the line A E, which will be the fide of the Octagon.

PROBLEM XXV.

To infcribe a Nonagon, in a given circle.

With the radius of the circle, and A as a centre, defcribe the arc E F.

Divide the arc E A F, into three equal parts.

The chord of any of them will be the fide of a Nonagon.

PROBLEM XXVI.

To inferibe a Decagon, in a given circle.

Draw two diameters A B and CD, at right angles. With the radius of the circle, and A as a centre, defcribe the arc EF.

Draw the chord E F.

With the radius G C, and G as a centre, describe the arc C H.

The distance from H to the centre I, is the fide of a Decagon.

Draw the diameter A B, and divide it into as many equal parts as the Polygon is to have fides.

arc.

With the radius A B, and A as a centre, defcribe an

With the fame radius, and B as a centre, defcribe another arc croffing the first in C.

From the point C, through the fecond divifion of the diameter, draw the line CD.

The chord DA, will be the fide of the Polygon required.

PROBLEM XXVIII.

To defcribe a circle, about a given triangle

A BC.

A

D

B

Bifect any two fides with two lines at right angles, thefe lines will interfect in the point D, which will be the centre of the circle.

With the radius D A, D B, or DC, defcribe a circle.