PROB. I. How to Ered a Figure of the Heavens in the Latitude of London, 51. d. 30 m. N. for the 10th Day of March, at 49 m. after 9 in the Forenoon; at which Time the Sun entred into the firft Scru ple of Aries, in the Year 1675. HE Heavens are divided in XII Houfes or Manfions, by 12 Semicircles of Pofition; for which Purpose, to fome Globes, there is made one of Brafs, which is fixed in the Interfections of the Meridian and Horizon, by the Elevation or Depreffion whereof the Heavens may be divided into Parts or Houfes through each Degree of the Ecliptick. Of these XII Houfes, or Manfions of Heaven, Four are called Cardinal, as, (1.) The Horofcope, or Afcendent, or Cufpis of the Firft Houfe. (2.) The Medium Cali, or Angle of the South, or Cufpis of the Tenth Houfe. (3.) The Defcendent, or Angle of the Weft, or the Cufpis of the Seventh Houfe. (4.) The Imum Cæli, or the Angle of the North, or the Cufpis of the Fourth Houfe. Regiomontanus divides the Heavens into XII Houfes according to his Way, by the Circle of Pofitions paffing through every 30th Degree of the Equinoctial, and cutting the Ecliptick at feveral Points, which are the Cufpifes of the feveral Houses : -So that when the Globe is fet to the Latitude, and the Hour-Wheel Redified and brought to the Given Hour, you have the Cufpifes of the Four Cardinal Houfes: For, The Degree (Eaft Side of the Horizon, of the E cliptick cut by the Tenth Gives (Firft House. The Cufpifes of the other 8 Houfes are found by the Motion of the Circle of Pofition, as fhall be fhewed by and by. The Houses are denominated by 1, 2, 3, 4, &c. to 12, from the Afcendent downwards to the Imum Cali, up again to the Defcendent, and again by Medium Cæli, down to the Afcendent. As in the following Scheme. A Let this fuffice for Definition, and now we will come to the Practice by the Globes. Irft, To the Day propofed, the 10th of March, find (by the Aftronomical Problem) the Sun's Place in the Ecliptick at Noon, which you fhall find to be in o d. 5 m. of Aries. Secondly, Set the Globe to the Latitude 51 d. 30 m. Thirdly, Bring the Sun's Place at Noon (od. 5 m. of Aries) to the Meridian. Fourthly, Turn the Globe about till the Hour-Index point to the Hour given, viz. to 49 m. after 9 in the Morning. Laftly, The Globe being fixed in this Pofition, you fhall find that the Eaft-Semicircle of the Horizon doth cut the Ecliptick in o d. 29 m. of Cancer, which is the Sign then Afcending, and muft be placed upon the Cufpis of the First Houfe. Then caft your Eye upon the Interfection of the South Part of the Meridian and the Ecliptick, and there you fhall find the Ecliptick cut by the Meridian in 25 d. of Aquarius, and that Point of the Ecliptick is then in the Medium Cæli, and must be fet upon the Cufpis of the Tenth Houfe. Alfo, you find that the Weft Semicircle of the Horizon, cuts the Ecliptick in oo d. 29 m. of Capricorn; which Point is then Defcending, and muft be placed upon the Cufpis of the Seventh Houfe. Laftly, Laftly, You fhall find that the North Part of the Meridian doth cut the Ecliptick in the 25th O d. of Leo, which Point is then upon the Imum Cæli, and must be placed upon the Cufpis of the Fourth Houfe. Thus have you found the Points of the Ecliptick, which do Occupy the Cufpifes of the Four Cardinal Houfes: Now for the other Eight Houfes. Let the Globe ftill reft in its former Pofition, and then, First, Bring the Circle of Pofition to its Place on the Eaft Side of the Horizon, and being there fixed, raife it upwards towards the Meridian, till 30 d. of the Equinoctial be intercepted between the Horizon and the Circle of Pofition; and then you fhall find that the Circle of Pofition will interfect the Ecliptick in 20 d. of Taurus; which Degrees must be fet upon the Cufpis of the Twelfth Houfe. Secondly, Move the Circle of Pofition yet higher towards the Meridian, till 30 d. more of the quinolial be intercepted between it and the Horizon, (in all 60 d.) and when in doth fo, you fhall find the Circle of Pofition will cut the Ecliptick in 36 d. of Pifces; which Point muft be fet upon the Cufpis of the Eleventh Houfe. The Meridian gives the Cufpis of the Tenth House in 25 d. of Aquarius, as before. Thirdly, Move the Semicircle of Pofition from the East Side of the Horizon to the Weft Side, and move it downwards from the Meridian, till 30 d. of the Equinoctial be intercepted between the Meridian and Circle of Pofition, and then you fhall find the Circle of Pofition will interfect the Ecliptick in 7 d. of Aquarius; which Point must be set upon the Cufpis of the Ninth Houfe: Fourthly, Move the Circle of Pofition yet lower by 30 d. i.c. 60 d. from the Meridian downwards, and then you fhall find the Pofition Circle to cut the Ecliptick in 21 d. of Capricorn; which Point must be fet upon the Cufpis of the Eighth Houfe. The Defcendant or Cufpis of the Seventh Houfe, is the Interfection of the Weft Side of the Horizon and Ecliptick, Dog which is in oo d. 29 min. of Capricorn, as before. And thus have you found the Cufpifes of the Four Houfes above the Horizon, befide the Afcendant and the Medium Ca viz. of the 12, 11, 9 and 8 Houfes. Now the Cufpifes of the the Four other Houfes under the Earth have the fame Degrees of the oppofite Signs upon them. For, 20 d. 26 d. Being upon the 26 d. will be on the Houfe. 12 20 d. m Cufpis of the 21 d. y 8 21 d. n For the Six Signs Houfe. 6 5 Cufpis of the 3 2 Aries, Taurus, Gemini, Cancer, Leo, Virgo, are oppofite to Libra, Scorpio, Sagitt. Capric. Aquar. Pifces. And this is the manner how (by the Globe) to erect a Figure according to the (reputed) Rational Way of Regiomon tanus. Now if you would infert the Places of the Planets into your Figure, (for it is them that the Aftrologer principally giveth Fudgment by your beft Way will be to have Recourfe to fome good Ephemeris, or Calculate them from Aftronomical Tables), Having in the foregoing Precepts fhewed how to erect a Scheme (or Figure of the Heavens) by the Globe, I fhall now (to retain the fame Method throughout this whole Treatife) shew how to effect the fame Trigonometrically; the which I fhall do in the Three following PROBLEMS. PROB. I. The Time of the Day, and Latitude of the Place given: How to Place. By Trigonometrical Calculation. Ou must first find (either by Tables already Calculated, Fig. You or by the foregoing Aftronomical Problems) the true Place XLVIII. of the Sun in Longitude; and alfo, his Right Afcenfion, both for the Moment of Time given. Then turn the Time given, (counted from the preceding Noon) into Degrees and Minutes of the Equator; and add them (being fo turned into Degrees and Minutes) to the Right Afcenfion of the Sun before-found; the Agregate (cafting away 360 d. if Fig. need be) is the Right Afcenfion of the Mid-Heaven: To which XLVIII. you must find what Degree of the Ecliptick doth answer; for that will be the Sign of the Xth Houfe. Then, To the Right Afcenfion of the Mid-Heaven, add 30 d. then 60 d. again 90 d. and 120 d. and 150 d. And thus you will find the Oblique Afcenfion of the XIth, XIIth, and Ift House; or of the Ild and IIId Horofcope. By the Erection of the Circle of Pofition above the Horizon at every 30 Degrees, there are made feveral Spherical Triangles, as HE 11, &c. In which Triangle (befides the Right Angle at Æ,) there is Given, 2. The Side 11, 30 d. (and Æ 12, 60 d. &c. To find, The Angle of R. A..S. T. 11 H, -Æ 12 H, &c. By Cafe XIIL As the Tangent of H, 38 d. 30 m.. Is to the Radius: So is the Sine of E11, 30 d. To the Tangent of 32 d. 9 m. Whofe Complement 57 d. 51 m. is the Quantity of the H 11 Æ D. M. 57 51 32 gle H 2 to be 7.10 42 32 H 3 Æ Is equal, Thefe Angles being once found will be always in Ufe in the Latitude of 51 d. 30 m. For that they fhew the Quantity of the Angle, that the Ecliptick makes with every Circle of Pofition. Given, Moreover, In the Triangle 11 √ X, 12Y, &c. there is 1. The Angle X 11 r, which is a contiguous Angle to the before-found Angle H 11 Æ. 2. The Sider 11, the Complement of the Oblique Afcenfion of the XIth Heufe, to a whole Circle, or 360 d. 3. The Angle 11 r X, 23 d. 30 m.. Te |