The Rational Way of Regiomontanus; as if, forfooth, there were any Reafon for dividing the Heavens into twelve Parts this way, rather than by a thousand others we might invent. The four Schemes above are general, adapted to the Lat. 50° 56', the Horoscope in each being the first Min. of Libra; and confequently the Cufpides of the several Houses are eafily known by Calculation of a Right-angled Triangle in the three first Schemes; and of a Right and Oblique One in the laft. But in the following Problems, I fhall fhew how to find what Degree and Minute of the Ecliptic, conftitutes the Cufp of every House or Manfion in the Figure, for any particular Time and Place. PROBLEM I. Let it be required to erect a Scheme or Figure of the Heavens at Chichester, Lat. 50° 56′, for May the 12th Day, at 36' 40" paft 10 at Night, A. D. 1735, the apparent Time. In order to this, we must first find the Equation of Time, and thereby reduce the Apparent to the Equal or Mean Time. 2. The Place of the Sun must be found to the Mean Time precifely. 3. The Sun's Right Ascension at the fame Moment. 4. Time from Noon must be reduced to the Degrees and Minutes of the Equator, by which means we shall have the Right Afcenfion of Medium Cali or Cufp of the 10th House. 5. Laftly, by the continual Addition of 30 Degrees to the Cufp of the 10th Houfe, and the confequent Sums, we hall obtain the Oblique Afcenfion of the 11th, 12th, 1ft, 2d, 3d Houfes; and fo. this Work, according to the Time and Place in this Problem, will ftand in the following Order. VOL. II. Anno Dom. 1735, May Ob. Afc. of the 11th House Ob. Afc. of the 12th House Ob. Afc. of the Afcendant Ob. Afcenf. of the 2d Houfe Ob. Afcenf. of the 3d House. D. H. M. S. II 2 II 22 159 10 00 Having proceeded thus far, we may now construct the Scheme; and firft let it be according to the Method of Regiomontanus, as is here reprefented in the Margin. Wherein HZON is the Meridian of the Place; 2, the Equinoctial; whose Poles are P and S; 10 2 4, the Ecliptic; HAO, HBO, &c. are the Circles of Pofition; PFSL, the Elevation of the Pole above the Circles of Pofition of the 11th, 9th, 3d, and 5th Houfes, to which the Complement of the Angle HA Æ is equal; fo PG = S K is the Height of the Pole above the Circles of Pofition of the 12th, 8th, 2d, 6th Houses, which is equal to the Complement of the Angle HB E. Now we fhall eafily find the Elevation of the Pole above the Circles of the Houses, and the Cufps of the feveral Houses, by the following Problems. PROBLEM II. To find the Elevation of the Pole above the Circles of the 11th, 9th, 3d, and 5th Houses. Practice. In the Right-angled Triangle HÆ A, there is given H E 39° 04', the Co-Latitude; and E A = 30° 00', the Distance of the Circle of Pofition in the Equinoctial from the Meridian; to find the Angle at A, whofe Complement is the Arch P F, the Height of the Pole required. Whose Complement is 31° 38' = PFSL, the Elevation of the Pole above thofe Circles of Pofition, as required. PROBLEM III. 『་ To find the Elevation of the Pole above the Circles of the 12th, 8th, 2d, and 6th Houfes. VOL. II. Nn 2 Practice. Practice. In the Right-angled Triangle HB Æ, there is known HÆ 39° 04', E B 60° oo'; to find the Angle at B, whofe Complement is equal to P G the Height of the Pole required. The Proportion. As the Sine of В Æ = 60° 00' Is to Radius So is the Tangent of Æ H = 39° 04′ To the Tangent of HB = 43° 08′ 9.9375306 10.0000000 9.9094022 9.9718716 PG SK the Height of the Poles above the Circles of Pofition, as required, of the Pole above the Cir. II, 9, 3, 5 cles of Position of the feve-12, 8, 2, 6 ṛal Houses ftands thus | 1, 7, Note; Thefe Elevations will be the fame in every Scheme erected in the Latitude of Chichester 50° 56′ for any Time of the Year. Thus having found the Oblique Afcenfion of the Houses, and the Elevation of the Pole above their Circles of Pofition; we proceed now to find the Cufps of the Houses, as follows. PROBLEM IV. To find the Cufps of the 10th and 4th House. Practice. In the Right-angled Triangle 24, there is given the Side 2=39° 16', the Right Afcenfion of Imum Cali, as being the oppofite Point in the Equinoctial to 219° 16' the Right Afcenfion of Med. Cali; there is alfo given the Angle at Y= 23° 29', the Obliquity of the Ecliptic; to find the Side 24, the Longitude of the Cufp of the fourth House in the Ecliptic. The Proportion. As Radius So the Cufp of the is in the Sign Taurus to which is Scorpio m Houfe or Medium Cali; 10.0000000 9.9624527 10.0875019 10.0499546 fourth Houfe, or Imum Cali, 11° 43', the Oppofite Point 11° 43', the Cufp of the 10th as required. PROBLEM V. To find the Cufps of the 1ft House, Horoscope, or Ascendant; and of the 7th House, or Defcendant. Practice. In the Oblique Triangle 1 C Y, there is given the Angle at r=23° 29'; the Angle at C 140° 56'; and the Side included C Y= 50° 44', the Complement of the Oblique Afcenfion of the Horoscope to a whole Circle; to find the Side Y 1, in the Ecliptic. |