PROBLEM XXXVI. Given the Latitude of the Place, the Depreffion 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 fetteth Achronically when the Sun is in 12 22', and the Altitude of the Nonagefima Degree is 52° 00'? Having duly prepared the Scheme by drawing all the requifite Circles, there will be conftituted the Right-angled Triangle ABD, in which there is known the Side BD 12° 00'; the Angle B AD=52° oo; to find the Side AD, the Dif tance of the Sun from its Place at the Achronical Setting of the Star. Then from the Achronical Place Substract the Arch now found 12 22 00 15 18 Remains the Place fought in Capricorn vs 27 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. Thefe Poetical Rifings and Settings of the Stars, viz. the Cofmical, Achronical, and Heliacal, ferve only to fhew us the Times of the Year, when they are to be seen by us, that fo we may make our Observations on them; though anciently they served other Purposes in adjufting the Times appointed for Civil and Religious Ufes. Thus I have prefented the Reader with an ample Collection of the more useful and requifite Problems of Spherical Aftronomy, which, together with thofe in the first Volume, may perhaps prove fufficient 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 defign'd to reprefent, that fo they might be as demonstrative of the Manner and Truth thereof, as the Nature of Projections in Plano will permit. The Want of fuch a Property in the Figures and Schemes in many other Books, I queftion not but many, befide my felf, have experienced, at the Expence of no little Time, Pains, and Perplexity, when they firft began to tread thofe lonefome thorny Paths, without a living Guide. CHAP. CHA P. II. Spherical Trigonometry applied to Aftrology, fhewing how to erect a Cæleftial Scheme, or Figure of the Heavens, for any given Time and Place. A STROLOGERS divide their pretended Art into two Parts; the Firft they term Mathematical, as being altogether wrought by the Doctrine of Spherical Trigonometry, and this is the Conftruction of a Figure (as they term it) of the Heavens, and diftinguifhing it into twelve Houfes (as their Jargon is,) placing in each of them the Planet and Conftellations belonging thereto for the given Time. The Second Part of Aftrology they call Judiciary; as being a Kind of Divination, made from an Infpection of the aforefaid Scheme or Figure of the Heavens, of Matters and Things to Futurity; as the Revolutions of Kingdoms, the Fortunes of particular Perfons from their Nativities, and Things loft, and who are the Thieves, &c. in abundance. The most notable Authors, who have been infatuated with this moft idle and impious Piece of Vanity, among the Ancients are 1. Ptolomy, 2. Alcabitius, 3. Campanus, and 4 Regiomontanus; whofe feveral Methods for erecting a Scheme, or dividing the Heavens into 12 Portions, which they call Houfes, by Domifying Circles, or Circles of Pofition, are as follows. 1. Ptolomy 1. Ptolomy divided the Heavens into twelve Houses by Circles of Pofition drawn through the Poles of the Ecliptic, and through every 30 Degrees thereof; beginning to reckon at the Af cendant, and counting every 30 De grees of the Ecliptic for the Space of one Houfe; A Scheme of this Sort is here annexed. fect the Ecliptic, are the Cufps 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 paffing through the Afcendant doth interfect it. 3. Campanus di vides the Heavens and where thofe Cir clet interfect the E cliptic, are the Cufps of the twelve Houses; as in the Diagram hereto annexed. 4. Regiomontanus divides the Coeleftial Houses by Circles of Pofition, paffing thro' the Interfection of the Meridian and Horizon, and cut- H ting the Equinoctial in every 30 Degrees from the Afcendant; and the Points where they cut the Ecliptic, are the Cufps of the · feveral Houses; as e S (in the Figure in the Margin) does appear by the Numbers. Of all these four Ways the Aftrologers of these latter Times chufe to practise by the laft; and from an abfurd Opinion they have of it, prefume to call it, The |