the parallel circle poh;

through h, the point where it intersects the primitive, draw the diameter hg, and bf perpendicular to it.

3. In the plate.

Draw the given leg AB, by Prob. VI. 3; and project the oblique circle xBz; through its pole m draw xmz; and reduce m to o. Set the complement of the angle C from o to pand q; and draw the parallel circle rls; through the point of intersection 1 draw the right circle ud; and through u, A, d, draw uCAd.

Calculation.

Z

The angle A is here ambiguous, or doubtful, as it does not appear from the data alone, whether BC, A and AC, be each greater or less than 90°; but the projection shews, that they are each less than 90°.

The side BC is ambiguous, as before observed.

Calculation.

1. To find the other leg BC.

RX sin. AB cot. A X tang. BC.

40° 30' 5" ar. co. 9'9315202

Cot. A

The side BC is of the same affection as the given

3. To find the hypotenuse AC.

RX cos. A tang. AB X cot. AC.

The hypotenuse AC is acute, because the given leg and

angle are alike.

A

CASE

CASE 5:

EXAMPLE. Given the two legs, namely, AB 47° 30 4, and BC=32° 12′; to find the rest.

Projection of the triangle.

1. At the circumference.

Set AB on the circumference, and draw the right circle BCx. Set BC from y to z; reduce z to m; y draw the quadrant mCn; and through C, where it intersects BCx, draw the oblique circle ACd.

2. At the centre.

Set AB from A to B, by Prob. VI. 2; through d, B, e, project the oblique circle dBe; on which set the other leg BC, by means of the parallel circle xCy.

B