Fig. XLVI. XLVII.

i. The Side ZP (the Distance of the Poles of the Æqua

tor, and Horizon of London) 38 d. 30 m.

2. The Side PS, the Complement of the Star's DeclinaGiven, tion (Cap. Andromeda) 62 d. 42 m.

3.

The Angle SPZ (the Time between the Time of Ob. Jervation, and the Time of the Stars next Culmination, viz. 8 h. 10 m) which is 122 d. 20m.

1. The Side Z S, (the Complement of the Star's Obser.
Required,

ved Altitude).
2. The Angle at Z (the Azimuth of the Star, from

the North Part of the Meridian.)
The Canons for Calculation. By Cafe IX. and Cafe I. of O, A.S.T.

1. For the Angle at Z.
(1.) As the Sine of half the Sum of the Sides ZP and ZS, sod.

36 m.
Is to the Sine of their half Difference, 12 d. 6 m.
So is the Co-tangent of half the Given Angle, ZPS, 61 d. rom.
To the Tangent of 8 d. 30 m. the half Difference of the Two

Angles, Ž and S.
(2.) As the Co-fine of half the Sum of the Given Sides, 50 de

36 m.
Is to the Co-fine of their balf Difference, 12 d. 6 m.
So is the Co-tangent of half the given Angle Z, 61 d. 10 m.
To the Tangent of 40 d. 22 m.

d. 22 m. Which is the half Sum of the
Two Angles.

2D. M:SD: M. For the S.
D. (.

52
Subftracted from gives 31 52

)
So that the Azimuth of the Star is 48 d. 52 m. from the North
Part of the Meridian.

2. For the Side Z S.
(3.) As the Sine of the Angle at Z, (last found) 48 d. 52 0.1
Ís to the Sine of the Side SP (the Complement of the Star's

Declination) 62 d. 42 m.
So is the Sine of the Angle at P, 122 d. 20m. (or 57 d. 40 m.)
To the Sine of 84 d. 36 m. for the Side Z s. Whofe Com-

plement, 5 d. 24 m. is the Altitude of the Star at the Time
of Observation.

Astrono.

Then 8 d. SAdded to

40 2234333} Angles.

30 m.

Astronomical Problems

Relating to

ASTROLOG Y.

INTRODUCTION.

Mathematical, as is the Astronomical Part; the other Judiciary, as is the Astrological Part.

The Mathematical Part teacheth how in a Scheme or Figure (as they call it) to represent the Face of the Heavens in Plano, for any Hour of the Day or Night, at all Times of the Year, and in all, Parts of the World.

The Astrological Part teacheth how (from the Sight of the said Pofition of the Scheme or Figure of the Heavens at the Time of its Ere&tion) to give a determinate Judgment of what was demanded upon that Erektion of the Scheme or Figure; as of Annual Revolutions, Elections, the Nativity of a Person, &c.

The principal Authors that have given their Opinions concerning the dividing of the Heavens into 12 Mansions or Houses, are, 1. Prolomy, 2. Alcabitius, 3. Campanus, and 4. Regiomontanus : Which last Way is now generally received and pra&ticed among the Astrologers of these Times, and by them termed the Rational Way of Regiomontanus.

Now, because (as I said before) that the Erection of a Figure of the Heavens is the Mathematical Part of Astrology, I shall therefore Thew how by the Globes to erect a Figure of the Heavens according to the Rational Way of Regiomontanus.

PROB

THE

PRO B. I.
How to Ered a Figure of the Heavens in the Latitude of London,

51 d. 30 m. N. for ihe 10th Day of March, at 49 m. after 9 in
the Forenoon; at which Time the Sun entred into the first Scru-
ple of Aries, in the Tear 1675.
HE Heavens are divided in XII Houses or Mansions, by 12

Semicircles of Position; for which Purpose, to fome Globes, there is made one of Brass, which is fixed in the Intersections of the Meridian and Horizon, by the Elevation of Depreffior whereof the Heavens may be divided into Parts or Houses through each Degree of the Ecliptick.

Of these XII Houses, or Mansions of Heaven, Four are called Cardinal, as, (1.) The Horoscope, or Ascendent, or Cufpis of the First House. (2.) The Medium Cæli

, or Angle of the South, or Cuspis of the Tenth House. (3.) The Descendent, or_Angle of the West, or the Cuspis of the Seventh House. (4.) The Imum Cæli, or the Angle of the North, or the Cuspis of the Fourth House.

Regiomontanus divides the Heavens into XII Houses according to his Way, by the Circle of Positions passing through every 30th Degree of the Æquino&tial, and cutting the Ecliptick at several Points, which are the Cufpises of the several Houses : -So that when the Globe is set to the Latitude, and the Hour-Wheel Redified and brought to the Given Hour, you have the Cuspises of the Four Cardinal Houses: For, The Degree (East Side of the Horizon, Gives (First of the E. South Part of the Meridian, the Tenth cliptick cut) Weft Side of the Horizon, Cufpis Seventh by the North Part of the Meridian,) of the (Fourth

The Cuspises of the other 8 Houses are found by the Motion of the Circle of Position, as shall be shewed by and by. The Houses are denominated by 1, 2, 3, 4, Sc. to 12,

ccfrom the Ascendent downwards to the Imum Cæli, up again to the Descendent, and again by Medium Cæli, down to the Afcendent. As in the following Scheme.

House.

A

t this fuffice for Definition, and now we will come to the
ice by the Globes.
ft, To the Day proposed, the roth of March, find (by the
Astronomical Problem) the Sun's Place in the Ecliprick at
1, which you shall find to be in o d. 5 m. of Aries.
condly, Set the Globe to the Latitude 51 d. 30 m.
irdly, Bring the Sun's Place at Noon (od. 5 m. of Aries) to
Meridian.
{rthly, Turn the Globe about till the Hour-Index point to
four given, viz. to 49 m. after 9 in the Morning.
Aly, The Globe teing fixed in this position, you shall find
hé East-Semicircle of the Horizon doth cut the Ecliptick in
29 m. of Cancer, which is the Sign then Ascending, and must
aced upon the Cuspis of the First House.
ien cast your Eye upon the Intersection of the South Part of
Meridian and the Ecliptick, and there you shall find the E-
ck cut by the Meridian in 25 d. of Aquarius, and that Point
e Ecliptick is then in the Medium Cæli, and must be set upon
ufpis of the Tenth House.
so, you find that the West Semicircle of the Horizon, cuts the
tick in oo d. 29 m. of Capricorn; which Point is then De-
ling, and must be placed upon the Cuspis of the Seventh House.

Lastly,

1

Lastly, You shall 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 Cuspis of the Fourth House. Thus have you found the Points of the Ecliptick, which do

occupy the Cuspises of the Four Cardinal Houses: Now for

the other Eight Houses. Let the Globe still rest in its former Position, and then,

First, Bring the Circle of Position to its Place on the East Side of the Horizon; and being there fixed, raise it upwards towards the Meridian, till 30 d. of the Aquino&tial be intercepted between the Horizon and the Circle of Position, and then you shall find that the Circle of Position will intersect the Ecliprick in 20 d. of Taurus ; which Degrees must be set upon the Cuspis of the Twelfth House.

Secondly, Move the Circle of Position yet higher towards the Meridian, till 30 d. more of the Æquinoctial be intercepted be. tween it and the Horizon, (in all 60 d.) and when in doth fo, you shall find the Circle of Position will cut the Ecliptick in 36d. of Pisces; which Point must be set upon the Cuspis of the Eleventh House. The Meridian gives the Cuspis of the Tentb House in 25 d.

of Aquarius, as before. Thirdly, Move the Semicircle of Pofition from the East Side of the Horizon to the West Side, and move it downwards from the. Meridian, till 30 d. of the Æquinoctial be intercepted between the Meridian and Circle of Position, and then you Thall find the Circle of Position will intersect the Ecliprick in 7 d. of Aquarius ; which Point must be set upon the Caspis of the Ninib House.

Fourthly, Move the Circle of Position yet lower by 30 d. i.e. 60 d. from the Meridian downwards, and then you shall find the Position-Circle to cut the Ecliptick in 21 d. of Capricorn ; which Point must be set upon the Cuspis of the Eighth Houfe. The Descendant or Cuspis of the Seventh House, is the In

terfeštion of the West Side of the Horizon and Ecliprick, 05. which is in oo d. 29 min. of Capricorn, as before.

And thus have you found the Cuspises of the Four Houfes Cabove the Horizon, beside the Ascendant and the Medium Cæ-H, viz. of the 12, 11, 9. and 8. Houses. Now the Cufpifes of

the