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 II.

Shewing the making of a direct Verticall Diall for an Oblique Sphear, that is, a direct North or South Diall plane.

EVery plane hath a Verticall point, and for the making of a Verticall Diall for the Latitude of London, out of the theoricall demonstrati∣on Chap. 7. Praecog. Astron▪ take the semidia∣meter of the Verticall, and with that, as with the semidiameter of the Horizon, describe a Quadrant, & draw the tangent line FG, and with the semidiameter of the Aequator finish all as in the Horizontall: the Style must proceed from the center A, and be elevated from the Meridian line AF, so much as is the complement of the E∣levation of the Pole, and must point toward the invisible Pole, viz. the South Pole, and hath but 12 houres on it.

The Arithmeticall Calculation.

As the Radius,

Is to the tangent of the Aequinoctiall distance of the houre from the Meridian;

So is the Co-sine, that is, the complement sine of the elevation, to the tangent of the houre distance from the Me∣ridian required.