PPOBLEM XXXVI. Given the Latitude of the Place, the Depression below the Horizon, and the Time of a Star's Achronical Setting, to find the Time of its Heliacal Setting. Practice. I demand the Heliacal Setting of the Star Fomabant at Chichester, Lat. 50° 56', where he setteth Achronically when the Sun is in no 12° 22', and the Altitude of the Nonagesima Degree is 52° oo'? Having duly prepared the Scheme P by drawing all the requisite Circles, there will be confti. Υ tuted the Right-angled Triangle ABD, H in which there is known the Side BD = 12000'; the Angle B AD=52° 00'; to find the Side AD, the Diftance of the Sun from its Place at the Achronical Setting of the Star. The Analogy; 9.8965321 9.3178789 10.0000000 9.4213468 Then 1 22 18 15 Then from the Achronical Place 27 04 To which Place the Sun doth approach about the fixth Day of January, and then will the Visibility of this Star be over at his Setting. These Poetical Risings and Settings of the Stars, viz. the Cosmical, Achronical, and Heliacal, serve only to shew us the Times of the Year, when they are to be seen by us, that so we may make our Obfervations on them ; though anciently they served other Purposes in adjusting the Times appointed for Civil and Religious Uses. Thus I have presented the Reader with an ample Collection of the more useful and requisite Problems of Spherical Astronomy, which, together with those in the first Volume, may perhaps prove sufficient for those who intend to acquire but a competent Knowledge of this noble Art ; to that End, I have all along endeavoured to adapt my Schemes to the Nature of the Things they are design'd to represent, that so they might be as demonstrative of the Manner and Truth thereof, as the Nature of Projections in Plano will permit. The Want of such a Property in the Figures and Schemes in many other Books, I question not but many, beside my self, have experienced, at the Expence of no little Time, Pains, and Perplexity, when they first began to tread those lonesome thorny Paths, without a living Guide. CH A P. CH A P. II. Spherical Trigonometry applied to Astro logy, shewing how to erect a Cælestial Scheme, or Figure of the Heavens, for any given Time and Place. А STROLOGERS divide their pretended Art into two Parts ; the First they term Mathe matical, as being altogether wrought by the Doctrine of Spherical Trigonometry, and this is the Construction of a Figure (as they term it ) of the Heavens, and distinguishing it into twelve Houses ( as their Jargon is, ) placing in each of them the Planet and Constellations belonging thereto for the given Time. The Second Part of Astrology they call Judiciary ; as being a Kind of Divination, made from an Inspection of the aforesaid Scheme or Figure of the Heavens, of Matters and Things to Futurity; as the Revolutions of Kingdoms, the Fortunes of particular Persons from their Nativities, and Things loft, and who are the Thieves, &c. in abundance. The most notable Authors, who have been infatuated with this most idle and impious Piece of Vanity, among the Ancients are 1. Ptolony, 2. Alcabilius, 3. Campanus, and 4 Regiomontanus ; whose several Methods for erecting a Scheme, or dividing the Heavens into 12 Pore tions, which they call Houses, by Domifying Circles, or Circles of Position, are as follows. 1. Ptolomy 0 1. Ptolomy divided the Heavens in P to twelve Houses by Circles of Position drawn through the Poles of the Ecliptic, and through every 30 Degrees thereof; beginning to reckon at the Alcendant, and count Q ing every 30 De S grees of the Ecliptic for the Space of one House ; A Scheme of this Sort is here annexed. 3 2. Alcabitius would have the twelve Houses in the Heaven to be determined by do. mifying Circles, or Circles of Position H drawn through the Poles of the World, and every 30 De. grees of the Equinoctial ; and where S these Circles interfect the Ecliptic, are the Cusps of the twelve Houses ; as they are marked in the Figure adjoined. Note, You must count the 30 Degrees on the Equinoctial, from that Point therein, where the Meridian passing through the Ascendant doth interfect it. 3. Cam, 3. Campanus divides the Heavens P into twelve Houses, Æ by Circles of the Points of Intersecti. on of the Horizon with the general Me. H ridian, and through every 30 Degrees of the Prime Vertical Circle, or Azimuth of East and Weft ; and where those Cir N clet interfect the Ecliptic, are the Cusps of the twelve Houses ; as in the Diagram hereto annexed. e Р 4. Regiomontanus Z divides the Celestial Houses by Circles of Position, passing thro' the Intersection of the Meridian and Horizon, and cut- H ting the Equinoctial in every 30 Degrees from the Ascendant; and the Points where they cut the Ecliptic, S are the Cusps of the several Houses ; as ( in the Figure in the Margin ) does appear by the Numbers. Of all these four Ways the Astrologers of these latter Times chuse to practise by the last ; and from an absurd Opinion they have of it, presume to call it, The Q N |