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. III. How to draw the Hour-lines on a Meridian Plane, which is an East, or West Dial.

A Meridian Plane stands upright directly in the Meridian, and hath two Faces, one to∣wards the East, and the other towards the West.

Now admit it be required to make a direct East Dial, in the Latitude of 51° 32': let A, B,* 1.1 C, D, be a Dial-plane, on which you would de∣scribe a Direct East Dial, on the point D, de∣scribe

an obscure Arch HG, with the Radius of ••our line of Chords, then take 38° 28', the Complement of your Latitude, place it from G to L; then draw DL quite through the Plane; Then to proportion your Stile unto your Plane, so that all the Hours may be placed thereon, from Sun-rising to 11 a Clock. Assume two* 1.2 points in the line LD, as K, for 11; and I for the 6 a Clock Hour lines; then draw 6, 16, and 11, K 11, Perpendiculur to LD. This done, with the Radius of your line of Chords on L, strike the Arch OP, and from P, to O, place 15° 00'; and draw OK, to cut 6 I 6, in M, so shall IM be the height of the Stile proportioned unto this Plane; which may be a Plate of Brass, whose breadth must be equal to the distance between the Hour-lines of 6, and 9, which must be placed Perpendicular to the Plane, on the line 6, I 6, whose shadow of the upper edge, shall shew the Hour of the day. Now to draw the Hour-lines, with the Radius of your line of Chords, on M strike the Arch QN, which divide into 5 equal parts in the points •, •, •, &c. Then lay a Ruler from M un∣to each of those points, and it will cut the line JK in the points *, *, *, &c. through which points (by prop. 4. § 1. chap. 4.) draw Parallels to 6 I 6, as the lines 77, 88, &c. which shall be the true Hour-lines of an East Plane, from 6* 1.3 in the Morning, till 11 before Noon. Then for the Hour-lines of 4, and 5, you must prick off 5 as far from 6, as 6 is from 7; and 4, as far as 6 is from 8; and draw the Hour-lines 55, and 44, as before. Thus is your Dial compleat∣ed, and in the forming of which, you have 〈1 page duplicate〉〈1 page duplicate〉

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made both an East, and a West Dial; which is the same in all respects, only whereas the Arch H G, through which the Equinoctial passed in the East Dial, was described on the right hand of the Plane, in the West it must be drawn on the left hand, and the Hour-lines 4, 5, 6, 7, 8, 9, 10, and 11, in the Forenoon in the East Dial, must be 8, 7, 6, 5, 4, 3, 2, and 1, in the West in* 1.4 the Afternoon; as in the Figure plainly appear∣eth: Now you may find the distance of the Hour-lines from the Substile, by this Analogy or Proportion.

As the Radius,

To the Height of the Stile.

So is the Tangent of any Hours distance from 6,

To the distance thereof from the Substile.

Notes

• * 1.1

  Fig. 66.
• * 1.2

  Fig. 66.
• * 1.3

  Fig. 66.
• * 1.4

  Fig. 67.