Fig. L. I. II. III. IV. 2. Let the Position made by any direct Significator, or by the Promissor to which the Retrograde is Directed, be called the Horizon of a Star: And it is either a right one, passing through both the Poles, as the Meridian; or an Oblique one, having One of the Poles elevated. 3. The Oblique one is, sometimes, the fame as the Horizon of the Place; and confequently, the Elevation of the Pole is the same: But, when it is different (which most commonly happens) you must first enquire how much One of the Poles is Elevated above the Horizon of the Star: But if a Star be In the Triangle POS, or PHS, for the Situation of the Star above or below: There is Given, 1. The Side PO, or P H, the Elevation of the Pole at London, 51 d. 30 m. 2. The Side PS, the Complement of the Star's Declination. 3. The Angle SPO, comprehended between them. (whose Measure is the Arch of the Æquator, which is intercepted between the Sides PO (PH) PS: One of which being produced, shews the Right AScenfion of the Star; the other, the Right Afcenfion of Imum Cæli. Required, The Angle P OS, or PHS. By Cafe III. of R. A. S. T. Again, In the Triangle RPO, or RPH, (which are in different Hemispheres, when O or H (before found) are greater than a Quadrant or 90 d.) There is Given, (1. POor PH, the Elevation of the Pole. befides the Right Angle at R, { 2. The Angle O or H, before found, (which if it exceeds a Quadrant, is Complement to 180 d. To find R P, The Elevation of the Pole above the Horizon of the Star. By Cafe III. of R. A. S. T. 4. Having found the Elevation (by the Third beforegoing) then look Oriental, the Afc. Fig. L. when the Horizon hath any Star that is Occidental, the Obl. I. II. III. IV. both of the Significator and Promiffor.. 5. Having Significators Dired, found out the Promiffor, to whom the Afcension or Defcenfion Retrograde is Directed, for the Horizon of the Star: Let the Right one, or the Oblique one, be substracted from the like Afcenfion of Descension of the other Star (adding 360 d. if Need be) the Remainder is the Ark of Direction fought for. P.ROB. III. ; The Ark of Direction of any Significator being given; To find how far it will reach. ; THIS is but the Converse of the foregoing: Therefore look for the Elevation of the Pole above the Horizon of a Direct Significator, as before; and at that Elevation you will get (by the 3d.) the Oblique {Denon of the fame Significator to which S Afcenfion Oriental, 2 Occidental, S add the given Ark of Direction, fo will Afcenfion you get the Oblique To which find what Degree of the Ecliptick answers (being counted from the Elevation of the Pole above the Horizon of the Significator) which is the very Place to which the Ark is Directed, and to which the Significator will come. But substract the Ark of Direction given, from the Right Afcen- fion of the Retrograde Significator, and there will remain the Degree of the Æquator, which is found out by the Retrograde Significator, by Direction, tending to the Promiffor: The Circle of Position paffing through this Degree (which ought well to be observed) will be the Horizon of the Promiffor: Above which, find the Elevation of the Pole, as before: For, if that Degree fall on the Part of Heaven, the the North, Fig. I. 2 SEaftern Significator inclining unto Westerns For Fig. L. For the Situation of the Degree observed, whether Above or Below. From the given Angles, as above, (the Angle P being counted in the Æquator, not from the Right Afcenfion of the Significator, but from that Degree which hath, oftentimes, been taken notice of, as that at the Medium or Imum Cæli) I seek for the Angle O or H. And moreover, in the other Triangle, RP, the very Elevation of the Pole above the Horizon of the Promiffor: At this Elevation of the Significator, if you observe that Degree Oriental Occidental you you will gain the Oblique Bernion} Afcenfion. cenfion From which take the given Ark of Direction, and the Remainder will be the The End of the Astronomical Problems. A N |