Operation.

As the Sine of half the Sum 82° 12' C. A. 0.0040361 Is to the Sine of half the Differ. 58° 431 9.9317679 So is the Tangent of half the Side 25° 22' 9.6758902 To the Tangent of the Diffe

}

rence of the other two Sides 22° 14′ 9.6116942

Then say again,

As the Co-fine 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 of the other two Sides

61° 08′ 10.2586542

Then to the half Sum of the Sides 61 08
Add the half Difference

22 14

The Sum is the greater Side 18322

That is in the Ecliptic

Subftract from

There remains

S

223 22

12 00 00

9 66 38

the Cufp =the oppo

06 38

of the firft Houfe, viz. in VS 06 38 fite Point to which is in Cancer

of the 7th House, or Defcendant.

PROBLEM VI.

To find the Cufps of the 2d and 8th Houfes.

Practice.

In the Oblique Triangle 2 DY, there is given the 239 29'; the Angle at DHB C

Angle at

=

=136° 52', by Prob. 3, and the Side included Dr 20° 44′ the Complement of the Oblique Afcenfion of the 2d House, to the whole Circle; to find the Side 2 Y, the Distance of the Cufp of the 2d House from Aries.

Now fay;

IO 22

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 8° 49' 9.1908260

Then say again;

As Cofine of half the Sum 80° 10' Co. Ar. 0.7675550 Is to the Co-fine of half the Differ. 56° 42′ 9.7395904 So is the Tangent of half the Side 10° 22' 9.2622921 To Tang. of Sum of other 2 Sides 30° 27′ 9.7694375

Then to the half Sum of the Sides 30 27
Add the half Difference

8 49

The Sum the gr. Side sought 2 Y = 39 16

That in the Ecliptic is

S

which take from

I 09
12 00 00

PROBLEM VII.

To find the Cufps of the 3d and 9th Houses.

Practice.

In the Oblique Triangle YE 3, there is given the Angle 23° 29'; the Angle at E = HAC = r= 121° 38' (by Prob. 2 ;) and the included Side TE = 9° 16' to find the Side 23 the Distance of the Cufp of the 3d House from Aries.

Then

the half Sum of the given Angles is 72 33
the half Difference thereof is
the half of the given Side

Now fay;

49 05

4 38

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-fine of the half Sum 72° 331 C. Ar. 0.5230610 To the Co-fine 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

Then to the half Sum of the two Sides add their half Difference

The Sum is the greater Side fought
That is in the Sine 13° 42' = the Cusp
House; whose oppofite Point

of the 9th Houfe; as required.

10 02

3 40

3

13 42

13° 42'

of the 3d the Cufp

PRO

PROBLEM VIII.

To find the Cufps of the 11th and 5th Houses.
Practice.

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 Afcenfion of the 11th Houfe to a whole Circle; to find the Side 11 7, in the Ecliptic.

Then

the half Sum of the given Angles 72 33 their half Difference

the Half of their given Side Now fay;

49 05.

55 22

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

ference of the other two Sides (48° 54′ 10.0594918 Then say again;

As the Co-fine of the Sum 72° 33' C. A. 0.5230610 Is to the Co-fine 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

Which is in the Sign Scorpio m 28° 39′ = Cufp of the 11th House, and its oppofite Point & 28° 39', is the Cufp of the 5th Houfe, 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 = 23° 29'; the Angle at B 136° 52′; r= and the included Side B Y = 80° 44'; to find the Side 12 2, in the Ecliptic.

Then

Now fay;

the half Sum of the Angles given 80 10 the half Difference thereof

the half of the given Side

56 42

40 22

As the Sine of half the Sum 80° 10' C. A. o 0064277 To the Sine of half the Difference 56° 42′ 9.9221062 So is the Tangent of half the Side 40° 22' 9.9294516

To the Tangent of half the Dif-7

ference of the other two Sides 35° 47' 9.8579855

Then say again;

As the Co-fine of the Sum 80° 10' C. A. 0.7675550 Is to the Co-fine of the Difference 56° 42' 9.7395904 So is the Tangent of half the Side 40° 22′

9.9294516

To the Tangent of half the Sum 69° 49′ 10.4365970

of the other two Sides

Then to the half Sum of the two Sides 69 49 Add their half Difference

The Sum is the greater Side

35 47

105 36