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 VII.

Being the fundamentall Diagram for the Geometricall projection of Dials.

THe Style being the representation of the Axis of the World, doth become the Gnomon or substance casting shadow on all Planes lying parallel to some Circle or other, as to circles of Azimuthes in all Verticall Dials.

So that the figure following is a representation of divers semidiameters, doth plainly shew the theoricall ground of the practick part hereof.

Where the line in the demonstration, noted the semidi∣ameter of the Horizon, signifies the Horizon, for so sup∣posing it to represent an Horizontall Diall, the style or Axis must be elevated above it, according to the Poles ele∣vation above the Horizon, and then the semidiameter or Axis of the World represents the style or Axis casting sha∣dow being the line AC.

The Geometricall projection of Dials.

[illustration]

Where note by the way, that if you set one foot of the Compasses in B, and with the Semidiameter of the Equa∣tor, fix the other foot in the line BC, keeping that last foot fast, and at that center draw a Quadrant divided into six parts, & a ruler from the center of the Equator through each division, shall divide the line AB as a contingent line, and if from C to these marks on the line AB you draw lines, it shall be the houre lines of a Verticall Diall.

But supposing a Diall to stand verticall, or upright to the Horizon AB, as the line BC, then that is represented by the semidiameter of the Verticall, and his style again represented by the semidiameter or Axis AC, being di∣stant

from the Verticall equall to the complement of the Poles elevation, and again, the Aequinoctiall crossing the Axis at right angles, the semidiameter thereof is represent∣ed by the line BD, the reason why the angle at A hath to his opposite angle at C, the complement of the angle at A, is grounded on this, the three angles of any right lined triangle are equall to two right angles, and a right angle consists of 90 degrees: now the angle at B is 90 degrees, being one right angle, and the angle at A being an angle of 51 degrees, which wants of 90 39 degrees, which is the angle at C, all which being added together doe make 180 degrees, being two right angles: here you see that having two angles, the third is the complement of 180 degrees.