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LAY a Ruler to the angular Point, and the extremity of the Sides containing the Angle, they being continued to Quadrants; and note where the Ruler cuts the Meri∣dian or outward Circle; at both which places make marks up∣on the Meridian: the distance between those two marks, being measured upon your Line of Chords, shall give you the quan∣tity of the Angle required.
IN the Triangle P ☉ O, in the Projection, let it be requi∣red to find the quantity of the Angle ☉ P O.—First, lay a Ruler upon the angular Point P, and to the extreme ends of the Sides P ☉ and P O, they being extended to Quadrants, which is, to that Circle which measures that Angle: (as the Aequinoctial measures all the Angles at P, the Pole of the World; the Horizon all the Angles at Z, the Zenith, &c.) So the Ru∣ler laid from P to ae, will cut the Meridian in ae; and being laid from P to B, it will cut the Meridian in the Point b. The distance b ae, being taken in your Compasses and measured upon your Line of Chords, will be found to contain 62 degr. 46 min. which is the quantity of the Angle ☉ P O.—But if upon the Point P you were to project an Angle to contain 62 degr. 46 min. then take 90 degr. of your Chords, and set them from P to ae, and through the Centre A draw the Line AE A ae; then take 62 degr. 46 m. out of your Line of Chords, and set them from ae to b; and laying a Ruler from P to b, it will cut AE A ae in the Point B: the Circle P B S being drawn, the Angle at P will contain 62 degr. 46 min.
LET it be required to find the quantity of the Angle Z E P.—Lay a Ruler to ☉, the Pole of the Circle Z E N, and the Point E, it will cut the Meridian Circle in M; from M set 90 degr. to z; a Ruler laid from ☉ to z will cut the Circle Z E N (it being extended beyond the Zenith Z) at the Point δ.
Again, Lay a Ruler upon Y, the Pole of the Circle P E S, and it will cut the Meridian Circle in v; set 90 degr. from v
to x upon the Meridian; a Ruler laid from Y to x will cut the Circle P E S in y.
This done, lay a Ruler from E to δ, and it will cut the Me∣ridian in θ; also lay the Ruler from E to y, it will cut the Me∣ridian in λ: the distance θ λ, being taken in your Compasses and applied to your Line of Chords, will be found to contain 21 degr. 45 min. And such is the quantity of the Angle Z E P.
These two sorts of Angles are the most troublesome to find their quantities, and therefore I have instanced in them. There are other Angles in the Projection which render their measures to the eye, without farther Instructions for finding their quan∣tities.