Operation. As the Sine of half the Sum 820 12'C. A. 0.0040361 Is to the Sine of half the Differ. 58° 43' 9.9317679 So is the Tangent of half the Side 25° 22' 9.6758902 To the Tangent of the Diffe 22° 14' 9.6116942 rence of the other two Sides } Then say again, As the Co-line of half Sum 82° 12' C. A. O 8673703 Is to the Co-fine of half the Differ. 58° 43' 9.7153937 So is the Tangent of half the Side 25° 22' 9.6758902 To the Tangent of half the Sum_61° 08'10.2586542 of the other two Sides 22 14 Then to the half Sum of the Sides 61 08 7 That is in the Ecliptic 2 23 2 2 Substract from There remains 9 06 38 = the Cusp of the first House, viz. in vs 06 38 = the oppo. site Point to which is in Cancer 06 38 = the Cusp of the 7th House, or Descendant. I 2 00 00 PROBLEM VI. To find the Cufps of the 2d and 8th Houses. Practice. In the Oblique Triangle 2 DY, there is given the Angle at Y = 23° 29', the Angle at D = HBC = 136 521, by Prob. 3, and the Side included Dr 200 44' the Complement of the Oblique Ascension of the ad House, to the whole Circle; to find the Side 2 Y, the Distance of the Cusp of the 2d House from Aries. 1 the Sum of the Angles is 160 21 113 23 56 42 80 10 10 22 Now say; As the Sine of half Sum 80° 10' Co. Ar. 0.0064277 Is to the Sine of half Difference 56° 42'9.9221062 So is the Tangent of half the Side 10° 22' 9.2622921 To Tang. of Dif. of other 2 Sides 89 49'9.1908260 8 49 Then say again ; 1 S 12 00 00 there remains 10 20 44 = the Cusp of the 2d House in Aquarius m 20 44 ; whose opposite Point in the Ecliptic is a 20 44 = the Cusp of the 8th House, as required. PRO I 09 16 PROBLEM VII. To find the Cusps of the 3d and 9th Houses. PraEtice. In the Oblique Triangle Y E 3, there is given the Angle Y= 23° 29'; the Angle at E=/ AC = 121° 38' (by Prob. 2 ;) and the included Side TE =9° 16' to find the Side r 3 the Distance of the Cusp of the 3d House from Aries. ܪ . Then the half Sum of the given Angles is 72 33 the half Difference thereof is 49 05 the half of the given Side 4 38 Now fay; As the Sine of half Sum 72° 33' Co. Ar. 0.0204612 Is to the Sine of half Difference 49°05' 9.8783281 So is the Tangent of half the Side 4° 38' 8.9087190 To Tang. of Dif. of other 2 Sides 3° 40' 8.8075183 Then fay again ; As Co-sine of the half Sum 72° 331 C. Ar. 0.5230610 To the Co-sine of half Difference 49°05' 9.8162152 So is the Tangent of half the Side 4° 38' 8.9087190 To Tang. of Sum of other 2 Sides 10° 02'9.2479952 IO 02 Then to the half Sum of the two Sides add their half Difference 3 40 The Sum is the greater Side fought Y3 = 13 42 That is in the Sine r 13° 42' = the Cusp of the 3d House ; whose opposite Point 4 13° 42' = the Cusp of the gth House ; as required. PRO ference of the other two Sides 48° 54' 10.0594918 PROBLEM. VIII. PraEtice. In the Oblique Triangle 11 AY, there is given the Angle at Y = 239 29' ; the Angle A 121° 38'; and the included Side AY = 110° 44', the Supplement of the Oblique Ascension of the 11th House to a whole Circle ; to find the Side 11 Y, in the Ecliptic. the half Sum of the given Angles 72 33 Then their half Difference 49 05 the Half of their given Side Now fay; As the Sine of half the Sum 72° 33'C. A. 0.0204612 Is to the Sine of half the Difference 49°05'9.8783281 So is the Tangent of half the Side 55° 22' 10.1607025 To the Tangent of half the Dif. { 55 22 ; } Then fay again ; As the Co-line of the Sum 72° 33'C. A..0.5230610 Is to the Co-sine of half the Differ. 49°05' 9.8162152 So the Tangent of half the Side 55° 22' 10.1607025 To the Tangent of half the Sum? of the other two Sides }72° 27' 10.4999787 Now to the Half Sum of the Sides 72 27 Add the Half Difference 48 54 The Sum is the greater Side 11. Y = 121 21 S This in the Ecliptic is 4 OT 21 Which take from 12 00 00 There remains 728 39 VOL. II. Do Which Which is in the Sign Scorpio M 28° 39'= Cusp of the rith House, and its opposite Point 8 280 39', is the Cusp of the 5th House, as required. PROBLEM IX. To find the Cufps of the 12th and 6th Houses. Practice. In the Oblique Triangle 12 BY, there is given the Angle at Y = 23° 29'; the Angle at B = 136° 52'; and the included Side B Y = 80 44'; to find the Side 121, in the Ecliptic. Then the half Sum of the Angles given 80 10 the half Difference thereof 56 42 the half of the given Side 40 22 Now fay; 9.9294516 As the Sine of half the Sum 80° 10' C. A. O 0064277 35° 47' 9.8579855 of half of the other two Sides Then to the half Sum of the two Sides 69 49 Add their half Difference 35 47 The Sum is the greater Side 105 36 |