Chap. V
Containing such Astronomical Propositions as are of ordinary use in the practice of Navigation.

1. To find the Altitude of the Sun by the shadows of a Gnomon set Perpendicular to the Horizon.

• As the parts of the shadow, are to the parts of the Gnomon:
• So the Tangent of 45 gr. to the Tangent of the Altitude.

Extend the Compasses in the Line of Numbers, from the parts of the shadow to the parts of the Gnomon; the same extent will give the distance from the Tangent of 45 gr. to the Tangent of the Suns Altitude.

So the Gnomon being 36, and the shadow 27, the Altitude will be found to be 36 gr. 52 m. Or the Gnomon being 27, and the shadow 36 the Altitude will be found to be 53 gr. 8 m. Or the shadow being 20, and the Gnomon 9, the Altitude will be found to be 24 gr. 14 m. as in the eighth Proposition of the use of the Tangent-line.

If the Gnomon be 22. and the shadow 135, the Altitude is 9 gr. 15 m. as I shewed before.

2. Having the distance of the Sun, from the next Equinoctial point, to find his declination.

• As the Radius is in proportion, to the Sine of the Suns greatest declination:
• So the Sine of the Suns distance from the next Equinoctial point, to the Sine of the Declination required.

Extend the Compasses in the Line of Sines, from 90 gr. to 23 gr. 30 m. the same extent will give the distance from the Suns place unto his Decination.

So the Sun being either 29 gr. of Taurus, or 1 gr. of Aquarius, or 1 gr. of Leo, or 29 gr. of Scorpio, that is 59 gr. distant from the next Equinoctial Point, the Declination will be found about 20 gr.

If the Sun be so near the Equinoctial Point, that his Declination fall to be under 1 gr. it may be found by the Line of Numbers. As if the Sun were in 2 gr. 5 m. of Aries, that is 125 m. from the Euqinoctial Point, the former extent of the Compasses from the Sine of 90 gr. to the Sine of 23 gr. 30 m. will reach in the Line of Numbers from 125 unto 50, which shews the Declination to be about 50 m.