RULE.

Draw the line BC, equal to 105, from a scale of equal parts; take CD, 50 in the compasses, and with one foot on C, describe an arch at D; then take BD, 85, in the compasses, and with one foot on B, intersect the arch at D, join BD and CD; then the angle at B, being measured on a chord of 60 degrees, will be 28° 4, and at C 53° 7'; consequently the angle at D, 98° 49′, by position 3.

To describe a circle about a triangle ABC, or through any three points not in a direct line.

RULE.

Bisect any two of the triangle's sides, at right angles, and where the bisecting lines intersect, is the centre of the circle, as at D, the distance from which, to one point of the triangle, and carried round, will be the circle required.

F

With any radius, and one foot in the circle, as at A, describe an arch, as CBD; then with the same radius, and where the arch cuts the circle, describe another arch, as CAD, and through the points of intersection, draw the line CDG; in like manner draw another line as EFG, which will intersect the other line in the centre of the circle; for each of these lines, if continued, will be a diameter to the circle.

B

a

PROBLEM XX.

To make a right angled parallelogram, whether a square, or an oblong.

EXAMPLE.

The sides AB and CD, each 7 chains 20 links; the perpendiculars AC and BD, each 5 chains 40 links.

RULE.

Draw AB equal to 7.2 chains, from a scale of equal parts; on B erect a perpendicular equal to 5.4 chains; then with AB in the compasses, and one foot on D, de

scribe an arch at C, and with BD in the compasses, with one foot on A, intersect the former arch at C; join CA and CD, and it is done.

Let each side of the Rhombus be 6 chains, 35 links, and perpendicular height 5 chains, 80 links.

RULE.

Draw AB and CD parallel, at the distance of 5 chains, 80 links; then take 6.35 chains in the compasses, lay it from C to D, with one foot in D; let the other fall in the line AB at B; turn over to A, join the several corners

Let the lines AB and CD, be each 7 chains, 64 links; AC and BD, each 5 chains, 25 links; perpendicular height 4.85 chains.

RULE.

Draw AB and CD, parallel, at the distance of 4.85 ehains; take 7.64 chains in the compasses, and set it from C to D; take 5.25 chains in the compasses, and lay it from D to B; make BA equal to CD; join the several corners by lines, as in the figure, and it is done.