PROBLEM XXXV.

On a given line A B, to defcribe an Octagon.

On the ends of the given line A B, erect the indefinite perpendiculars A F and B E.

Produce A B both ways to m and n.

Bifect the angles m AF and n BE, with the lines AH and B C.

Make AH and B C each equal to A B.

Draw H G and CD, parallel to AF or B E.

Make HG and C D each equal to A B.

On the centre G, with the radius A B, cross the line AF in F.

On the centre D, with the fame radius, cross the line BE in E.

Draw the lines GF, FE, ED, which will complete the Octagon required.

PROBLEM XXXVI.

To make a triangle equal to a given trapezium,

Produce A B till it meets CE in E
Draw D E.

ADE will be the Triangle required.

This and the following problem are eafieft to be done by a protractor, for want of which draw the line AB.

Take the first 60 degrees from a fcale of chords as a radius, and with A as a centre, describe an arc B C. Take the propofed number of degrees from the fcale of chords, and set off from B to C.

Draw the lines A D, and the angle will be formed. NOTE. If the angle is to contain more than 90 degrees, it must be taken at twice.

PROBLEM XXXVIII.

To find the number of Degrees contained in an angle BAC.

With A for a centre, and a chord of 60 degrees for a radius, defcribe the arc B C.

Take the distance B C and apply to the fcale of chords, which will show the number of degrees.

E

PROBLEM XXXIX.

To draw an Oval, whofe two diameters fhall be equal to two given lines, A and B.

Draw two diameters equal to the two given lines, croffing each other in the middle at right angles.

Take two thirds of the difference of the diameters, and fet off from the point of interfection C, on each fide the longest line at D and E.

With the radius DE, and D or E as a centre, cross the fhorteft diameter in F and G.

With the radius DH, and D as a centre, describe a circle.

With the fame radius, and E as a centre, defcribe another circle.

With the radius GK, and G as a centre, describe the arc LM.

With the fame radius, and F as a centre describe the arc NO, which will complete the Oval required.