Horlogiographia optica. Dialling universall and particular: speculative and practicall. In a threefold præcognita, viz. geometricall, philosophicall, and astronomicall: and a threefold practise, viz. arithmeticall, geometricall, and instrumentall. With diverse propositions of the use and benefit of shadows, serving to prick down the signes, declination, and azimuths, on sun-dials, and diverse other benefits. Illustrated by diverse opticall conceits, taken out of Augilonius, Kercherius, Clavius, and others. Lastly, topothesia, or, a feigned description of the court of art. Full of benefit for the making of dials, use of the globes, difference of meridians, and most propositions of astronomie. Together with many usefull instruments and dials in brasse, made by Walter Hayes, at the Crosse Daggers in More Fields. / Written by Silvanus Morgan.

CHAP IV.

Shewing the making of the Prime Verticall planes, that is, a direct East or West Diall.

FOr the effecting of this Diall, first draw the line AD, on one end thereof draw the circle in the figure representing the Equator; then draw two touch lines to the Equator, parallel to the line AD, these are they on which the houres are marked: divide the Equator in the lower semi∣circle in 12 equall parts, then apply a ruler to the center, through each part, and where it touches the lines of con∣tingence make marks; from each touch point draw lines to the opposite touch point, which are the parallels of the houres, and at the end of those lines mark the Easterly houres from 6 to 11, and of the West from 1 to 6. These planes, as I told you, want the Meridian houre, because it is parallel to the Meridian. Now for the placing of the East Diall, number the elevation of the Axis, to wit, the arch DC, from the line of the Equator, to wit, the line AD: and in the West Diall number the elevation to B; fasten a plummet and thrid in the center A, and hold it so that the plummet may fall on the line AC for the East Diall, and AB for the West Diall, and then the line AD is parallel to the Equator, and the Dial in its right position. And thus the West as well as East, for according to the saying, Contrariorum eadem est doctrina, contraries have one manner of doctrine.

Here you may perceive the use of Tangent line, for it is evident that every houres distance is ••••t the Tangent of the Aequinoctiall distance.

The Arithmeticall Calculation.

1 Having drawn a line for the houre of 6, whether East or West, As the tangent of the houre distance, is to the Radius, so is the distance of the houre from 6, to the height of the Style.

2 As the Radius is to the height of the Style, so is the tangent of the houre distance from 6, to the distance of the same houre from the substyle.

The style must be equall in height to the semidiameter of the Equator, and fixed on the line of 6.