Clavius method (1586)

(Fabica et usus instrumenti ad horologiorum descriptionem.) Rome Italy.

The Clavius method looks at a quarter of the dial. It views the horizontal and the perpendicular plane to the polar axis as two rectangles hinged around the top edge of both dials. the polar axis will be at φ degrees to the polar axis, and the hour lines will be equispaced on the polar plane an equitorial dial. (15°). Hour points on the polar plane will connect to the matching point on the horizontal plane. The horizontal hour lines are plotted to the origin.

• Draw the gnomomic triangle, lying on it hypotenuse.
• On the small side, draw a (equatorial) square, with 15° hour markings.
• The dial plate is constructed with compasses taking it sizes from the triangle.
• The hour lines 12, 3, and 6 are known. The hour lines 1 and 2 are taken from the side of the square.
• A diagonal is taken from 12 to 6, and lines parallel to this drawn through 1 and 2, giving 5 and 4
• The morning dial is a reflection of this.