PROBLEM xxix.

To defcribe a circle, about a
about a given Square,

ABCD.

A

E

B

D

Draw the two diagonals, A C, and B D.

The interfection E is the centre, and the lines A E, BE, CE and DE are radii, with which draw the circle.

NOTE. The centres of all regular Polygons, may be found by bifecting two adjoining fides, or two angles with two lines, which will interfect each other in the

PROBLEM XXX.

To defcribe a Square, about a given circle.

Draw two diameters A B and C D, at right angles.
Through the point A, draw a line parallel to CD.
Do the fame at B.

Through the point C, draw a line parallel to A B.
Do the fame at D.

These lines will interfect in the points EF and GH, and form a fquare.

PROBLEM XXXI.

To defcribe any regular Polygon about a circle.

Infcribe a polygon, with the given number of fides in

the circle.

Draw tangents to the circle at the angular points, which will interfect each other, and form the Polygon required.

PROBLEM XXXII.

To make a regular Pentagon, on a given line

A B.

E

B

A

Draw B C perpendicular to A B, and equal to half of it.

Draw A C, and produce it till CD is equal to CB. With the radius B D, and A as a centre, defcribe an

arc.

With the fame radius, and B as a centre, cross the first arc in E.

With the radius EA or EB, and E as a centre, defcribe a circle.

Apply the given line five times round the circumference of the circle, and the Pentagon will be formed.

PROBLEM XXXIII.

To make a regular Hexagon on a given line

AB.

A

B

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

arc.

With the fame radius, and B as a centre, cross the firft arc in C.

With the radius C A or CB, and C as a centre, defcribe a circle.

Carry the line fix times round the circumference of the circle, and the Hexagon will be made.

PROBLEM XXXIV.

To draw an Heptagon, whofe fide fhall be equal to a given line A.

Infcribe an Heptagon in a circle, larger than the one required.

Draw the radius C F.

Take half the difference of the two fides A and CD, and fet off from C to E.

Erect a perpendicular at E, which will cut CF in G. With the radius GF, and F as a centre, describe a circle, which will admit the line A being carried feven times round it.

NOTE-This rule will do for any other regular polygon.