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Let ABCD be the boundary lines; the base AC 64.4 perches; the perpendicular Bb. 13.6, and Dd 27.2 perches; the first perpendicular from A 18 perches, the 2d from C 14 perches. . . - .

TULE.

Draw AC equal to 64.4 perches: then 18 perches from A, raise a perpendicular equal to 13.6 perches; and 14 perches from C, raise a perpendicular equal to 27.2 perches, on the opposite side of the base AC; join the several boundary lines, as in the figure, and it is done.

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GEOMETRICAL PROBLEMS. 39

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To divide a given line, as AB, into any number of equal parts, suppose 7. ' * •

RULE.

From the point A, draw the line Ac, making any all

gle with the line AB, and from the point B, draw BD, parallel to AC; then with any convenient distance in the

compasses, on the lines AC and BD, and from the angu

lar points, turn over on each as many times, less One, than the divisions; join the several points, and the line is divided as proposed. -

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PROJECTION

of THE LINEs of . . " SINES, TANGENTs, AND SECANTS,

oN THE PLANE scALE.

1. WITH any convenient radius, describe a semicircle ADBC, and upon the centre C, raise the perpen- dicular CD, which will divide the semicircle into two quadrants AD, BD ; continue CD to S: and upon B raise the perpendicular BT ; then draw the lines BD and AD. . . . . -

2. Divide the quadrant BD, into 9 equal parts; then will each of these be 10 degrees, which may be subdi-, vided into single degrees and minutes, if the radius be large enough to admit. -

3. Set one foot of the compasses in B, and transfer each of the divisions in the quadrant BD, to the right line BD; then is BD a line of chords. -

4. From the points 10, 20, 30, &e, in the quadrant BD, draw lines parallel to CD, till they cut the radius CB; then is the line CB, divided into a line of Sines.

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5. From the centre C, through the several divisions of the quadrant BD, draw lines till they cut the tangent BT; so will the line BT become a line of tangents.

6. Set one foot of the compasses in C, extend the other to the several divisions 10, 20, 30, &c. in the tangent line BT, and transfer these extents, severally, into the lines CS; then will the line CS be a line of secants.

7. Right lines drawn from A to the several divisions 10, 20, 30, &c. in the quadrant BD, will divide the . radius CD into a line of sines.

8. Divide the quadrant AD, into 9 equal parts; and from A transfer these divisions, severally, into the line AD; then is AD a line of chords.

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