Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath.

To resolve this Probleme by the Projection.

That which is most intricate and difficult to perform by Numbers, is by Projection effected with the same ease as any of the rest. As in this Proposition, it is the Angle E Z P which is required.—Lay a Ruler upon the Zenith-point Z, and to the Point G, upon the Horizon; the Ruler thus laid will cut the Meridian Circle in the Point g. So the di∣stance g O, being taken in your Compasses and measured up∣on your Line of Chords, will be found to contain 146 degr. which is the Sun's Azimuth from O, the North part of the Me∣ridian.—But if you measure the distance between the g and H, it will contain 34 degr. which is the Azimuth from H, the South part of the Meridian.—And if you measure the distance g N upon your Chord-Line, you shall find that to contain 56 degr. and so much is the Sun's Azimuth from A, the East and West Points of the Horizon.

This Example of finding the Azimuth was taken when the Sun had 20 degr. of South Declination. I will now farther exemplifie this Proposition by finding the Azimuth when the Sun hath North Declination.—As let the Latitude be as before 51 d. 30 min. the Sun's Altitude 12 degr. and the Declination 20 d. North.

To work this by the Canon of Sines differeth nothing from the former, for the Analogie or Proportion is general in all Cases.

Upon the Projection it is resolved (though the same way, yet) upon another Triangle, namely, the Triangle Z P a, in which is given (1.) Z P, the Complement of the Latitude 38 d. 30 min. (2.) Z a, the Complement of the Altitude 78 degr. (3.) the Complement of the Sun's Declination North 70 degr. and you are to find the Angle P Z a, the Sun's Azimuth from the North.

Lay a Ruler upon Z unto the Point a, it will cut the Meri∣dian Circle in the Point s; the distance s O, being taken in your Compasses and applied to your Line of Chords, will there give you 72 degr. 52 m. And such is the Sun's Azimuth from the North.

If you subtract this Azimuth from the North 72 degr. 52 m. from 180 degr. the remainer 107 degr. 8 min. will give you the Azimuth from the South, which upon the Projection is the di∣stance s H.—And if from this Azimuth from the South 107 d. 8 min. you take 90 degr. the remainer 17 degr. 8 min. is the Azimuth from the East or West, which in the Projection is the di∣stance N s.