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kind of figures

NOTE. And thus any number of any may be added together.

PROBLEM L

To construct the lines of the Plane Scale.

The divisions on the Plane Scale are of two kinds

; one kind having relation merely to right lines, and the other to the circle and its properties. The former are called Lines, or Scales, of Equal Parts, and are either simple or diagonal,

By the Lines of the Plane Scale we here mean the follow ing Lines, most of which commonly, and all of them sometimes, are drawn on a Plane Scale.

2.

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1. A Line or Scale of Equal Parts, marked E. P. Chords

Cho, 3. Rhumbs

Rhu.
4.
Sives

Sin,
Tangents

Tan,

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I, To construct plane diagonal Scales. Draw any line, as A B, of any convenient length. Die pide it into 11 equal parts.* Complete these into rectang gles of a convenient height, by drawing parallel and perpendicular lines. Divide the altitude into 10 equal parts, if it be for a decimal scale for common numbers, or into 12 equal parts, if it be for feet and inches ; and through these points of division draw as many parallel lines, the whole length of the scale. Then divide the length of the first division AC into 10 equal parts, both above and below ; and connect these points of division by diagonal lines, and the scale is finished, after being numbered as you please,

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* Only 4 parts are here drawn for want of room.

Of the preceding three forms of scales for two figures the first is a decimal scale, for taking off common numbers consisting of two figures. The other two are duos decimal scales, and serve for feet and inches.

In order to construct the other lines, describe a circuma ference with any convenient radius, and draw the diameters A B, DE, at right angles to each other ; continue BA at pleasure toward F; through D draw DG parallel to BF; and draw the chords BD, BE, AD, AE. Circumscribe the circle with the square HMN, whose sides. HM, MN, shall be parallel to A B, ED,

2. To construct the Line of Chordse

Divide the arc AD into go cqual parts ; mark the 10th divisions with the figures 10, 20, 30, 49, 50, 60, 70, 80, 90; on D, as a centre, with the compasses, transfer the several divisions of the quadrantal arc, to the chord AD, which marked with the figures corresponding, will be a line of chords.

Note. In the construction of this and the following scales, only the primary divisions are drawn ; the intermediate ones are omitted, that the figure may not appear too much crowded.

3. To construct the Line of Rhumbs.

Divide the arc BE into 8 equal parts, which mark with the figures 1, 2, 3, 4, 5, 6, 7, 8; and divide each of

those

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those parts into quarters ; on B, as a centre, transfer the divisions of the arc to the chord B E, which, marked with the corresponding figures, will be a line of thumbs.

4. To construct the Line of Sines.*

Through each of the divisions of the arc AD draw tight lines parallel to the radius AC; and CD will be divided into a line of sines, which are to be numbered from C to D for the right sines; and from D to C for the versed sines. The versed sines may be continued to 180 degrees, by laying the divisions of the radius CD from C to E.

5. To construct the Line of Tangents.

A rule on C, and the several divisions of the arc AD, will intersect the line DG, which will become a line of tangents, and is to be figured from D to G with 10, 20, 30, 40, &c.

6. To construct the Line of Secants.

The distances from the centre C to the divisions on the line of tangents, being transferred to the line CF from the

centre

* For Definitions of Sines, Tangents and Secants, see PLANI TRIGONOMETRY; and for that of Rhumbs, see NAVIGATION.

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