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IT appears plainly by the Scheme here before us, that the Shade (AB) being Radius, the Perpendicular (CB) is Tangent of (A v. g. 14.) the Degrees of the Suns height, as also that the Perpendicular (CB) being Radius, the Shade▪ (AB) is Tan∣gent
of the Complement of the said height; therefore if the Radius being 100, you mark from the Zenith to the Horizon each De∣gree of your Quadrant of Proportion with Figures according to the value of their respective Tangents, you must necessarily per∣form the late Operations, that give us the height of things, the hour of the Day, &c. For if your Bead be rectify'd (from the Horizon of your Globe) to (76) the Complement of the Suns height, it will be distant from the Zenith just as many Degrees as the Sun is high, to wit 14, and consequently being moved to the Quadrant of Proportion (which is figur'd we see, from the Zenith downwards) must lye there on 25, the Tangent of his said Height, therefore as the Radius 100 is to (25) this Tangent, so (80) the length of the Shade must be to the Perpendicular 20.
In the next Place if your Bead be rectify'd every hour to the Suns height, it must (when moved to the Quadrant) still lye on Tangent Complement of his said hourly height; Now the Shade being always as I told you the Tangent Complement of this height, the former little Tables must needs shew you the cor∣responding Hour, when we once know the value of the Shade, i. e. its proportion to the Stick. To conclude the Tangents of the first 10 Degrees are not exprest on the Quadrant▪ because when the Sun is no higher, we may easily guess at the hour, and besides (as we said) the Shade is then extremely long, and conse∣quently very troublesom to measure; nor need we go further than 62 Degrees, since his greatest Meridian Altitude exceeds not that value.