Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

PROP. II. How to draw the Hour-lines on a Polar Plane.

A Polar Plane is one that lies Parallel unto the Pole, and under the Equinoctial is an Hori∣zontal Dial: the way to make this Dial is thus. First draw the line AB, for the Horizontal line of the Plane; and cross it at the Middle at right angles, with the line 12, Q, 12, which is the* 1.1 Meridian or Hour line of 12; Then upon the line 12, Q 12, either above or below the point Q, assume any point as S, then setting one foot of your Compasses in S, describe the Semicircle CED, which divide into 12 Equal parts, in the points ☉, ☉, ☉, &c. Then lay a Ruler un∣to S, and unto the several points ☉, ☉, ☉, &c. and it will cross the line AB, in the points x, x, x, &c. Then through those points draw (by prop. 4. §. 1. chap. 4.) right lines all Parallel

unto 12 Q 12, and so is your Dial finished. Then according unto the breadth of the Plane, you may proportion* 1.2 your Stile,* 1.3 Whose height must be equal to the di∣stance between the two Hour-lines 12, and 9, or 12, and 3, and then will the shadow of the upper edge thereof shew the Hour of the day: The height of the Stile, is also found thus.

As the Tangent of the Hour-line 4 or 5,

To the Distance hereof from the Meridian.

So is the Radius,

To the Height of the Stile.

Then for the other Hour-line, say,

As the Radius,

To the Height of the Stile.

So is the Tangent of any other Hour-line,

To the Distance thereof from the Meridian line.

Notes

• * 1.1

  Fig. 65.
• * 1.2

  Fig. 65.
• * 1.3

  Which may be ei∣ther a Pin of the length of Q S, placed on Q, and Perpendicular unto the Plane, or it may be a piece of brass or elsewhat of the breadth of 12, to 3, or 9.