The works of that late most excellent philosopher and astronomer, Sir George Wharton, bar. collected into one volume / by John Gadbvry ...

Of the Planetary Aspects, both Old and New, their Characters, and Aequa∣tions.

KEpler (the Lyncaeus of the last Age) defines an Aspect in this manner: Aspectus est Angulus à Radiis Luminosis binorum Planetarum in terra forma∣tus, efficax ad stimulandum naturam sublunarem.

It is (saith he) an Angle made in the Earth by the Luminous Beams of two Planets, of strength to stir up the vertue of all sublunary things.

The ancient Astrologers took notice but of five that were effectual, namely, the Conjunction, Opposi∣tion, Quartile, Trine, and Sextile: The first whereof, although it be not properly an Aspect, yet if the word Aspect be to be taken in a larger sense, the Conjuncti∣ons may be so term'd, for that in it the Planets have their vertues United: And as Sound is the Basis of Harmonical Proportion, and an Unit the beginning

of Number; so is the Conjunction the ground of the other Aspects.

But although the Ancients number'd no more that were effectual, yet surely all Aspects are so (more or less) which being multiplied in themselves beget others that are greater, even till they finish the whole Circle, and they are very many, indeed innumer∣able, because there are infinite Regular Figures to be expressed, or at least imagined, by the continual du∣plication made of their sides, whose efficacy or force emitted from above, some attribute to Pythagorical Numbers, (and therefore as many ways as an Aspect is found to be effectual, so many Numbers of the in∣tercepted Degrees are observed:) Others say, and believe, it depends only upon the Nature of the Signs; (and so every Configuration of an Opposite sign produces alteration:) And this is clear'd in the Crises of Diseases

Hence the Learned Kepler (after many praevious Meteorological observations) added more Aspects to the Old, whose formal cause is drawn from 7 Figures describ'd in a Circle, viz. a Triangle, a Quadrangle, a Pentagon, a Hexagon, an Octogon, a Decagon, and a Dodecagon; from whence arise these Aspects in Order.

Planetary Aspects, Old and New, and Characters, &c.
☌	Conjunction,	is distant in degrees	00
SS.	Semi-Sextile,	30
Dec.	Decile,	36
Sq.	Semiquadrate, or Octile,	45
✶.	Sextile,	60
Q.	Quintile,	72
□.	Quartile,	90
Td.	Tridecile,	108
△.	Trigon,	120
SSq.	Sesquiquadrate or Trioctile,	135
Bq.	Biquintile,	144
VC.	Quincunx,	150
☍.	Opposition,	180

For if the Semi-Sextile containing 30 degrees be multiplied by 6 it produces a greater Aspect of 180 degrees, viz. an Opposition. But if by the whole Zodiaque, or 12 Signs, the Factus is 360. (the num∣ber of degrees contained in the whole Circle) and so of others.

But because some Aspects are more Effectual than others, therefore are they (respectu graduum, Scientiae and Congruentiae, necnon Efficacitatis) thus to be Dis∣posed: viz. ☌. ☍. □. △. ✶. SS. Q. Bq. Vc. Dec. Td. Sq. SSq. whereunto are added (as in the last and low∣est degree of Dignity and Efficacy) the Quindecile, Hexadecile, Vigintile, and the Icositesseragonall, (or figure of 24. sides) which are only consider'd in Venus and Mercury with the Sun.

These Radiations or Aspects were diversly taken by Astrologers before Regiomontanus: for some ac∣c••unte•• the place of the Aspects in the Aequator,

others otherwise, as Regiomontanus himself observes, Tab. Dir. Probl. 31.

Now, as touching their Aequation there hath been, and yet is some difference depending amongst Astrolo∣gers: For a sort of Pretenders (very strangers to Mathematical Demonstrations) do wilfully neglect the latitude of the Planets in Direction: And all their Reason is, because (as they think) Ptolemy, 3. Qua∣dripart. does the like; which smells too rank of Igno∣rance: for if they rightly understood Ptolemy, they might plainly perceive his Examples there do suppose the Promissors and Significators within the Ecliptique, and therefore no Latitude to be consider'd; whereas Doubtless, if he had directed any of the Planets hav∣ing Latitude, he would have regarded their Latitude, very necessary to be known, as himself acknowledges, Cap. de Applicationibus, De bis, qui non nutriuntur in Figurâ aequicruria, and elsewhere. But these men are laught at.

The truth is, Ptolemy made question only whe∣ther or no it ought to be observed in the Sextil, and Trine Aspect; And if he had exploded it (which is not to be credited in so great and famous an Artist) 'twas possible Ptolemy, (being but a Man) might therein have err'd as well as in other things. How∣ever, such as say they follow him, do utterly reject it, affirming, that these Radiations are not to be con∣sider'd as they proceed from one Point of the Heavens to another, but according as they concur in the Center of the Earth, where they do Angulum Con∣stituere: which (say they) is always the same, what∣soever Point or place they proceed from, with La∣titude, or without.

Another sort there are (and they otherwise very Learned) who will have them Aequated bo••h in

respect of Longitude and Latitude, in which Num∣ber is Leovitius, and Johannes Blanchinus, the latter of which prying (as he thought) deeper into the matter, and making great account of a little space of time, (Neglected by Ptolemy) in taking these Aspects; assumes their Aequation for a great Circle passing by the Center of a Star having Latitude; and enclin'd beyond the Aequator; Proving that the Quartile Aspect ever falls within the Ecliptique, and is to be accounted without Latitude: that the Opposi∣tion always retains the same Latitude, which the Body of the Star doth, though of Contrary Denomination; the △ and ✶ half the Latitude (the ✶ of the same, the △ of a contrary Denomination) and shews that these Radiations cannot possibly make an Angle in the Center of the Earth, unless they first truly behold one another in the Heavens; whose configuration admits of variation in respect of Latitude. And to this Opi∣nion Argol freely subscribes, rejecting the Aequations of Regiomontanus and all others, as void of Demon∣stration, averring this most agreeable to observation, having had (as he saith) experience thereof in more than a 1000 Genitures.

But Oranigus (as great an Astrologer and Mathe∣matician as any of the other) although he denies not but that the Square and Opposite Aspects do always retain the same Point of the Zodiack, wherein they are made, and require no alteration thereof; so that the Latitude is not to be Changed, in the Quartiles (be¦cause they always terminate in the Ecliptique) howso∣ever it be in the Oppositions that (they terminating on the Contrary part) the Latitude admits of contrary Denomination; which the Diametrical Line passing by the Center and cutting the Plane of the Ecliptique de∣monstrates: yet (neglecting any Aequation of the Lati∣tude,

which indeed never ought to be regarded in the Aspects, as sufficiently appears by the Doctrine of Triangles, and the Dimension of the sides of these Aspects in the Globe) he Aequates them only in re∣spect of Longitude, which (in my Opinion) is a way the most exact and Rational of all others, and approved of by the most and best of Modern Mathe∣maticians, provided we consider them (as they do) in respect of the Ecliptique, not of the Aequator. How∣beit, it will merit the Pains if in Directions we ob∣serve both, (viz. that of Blanchinus, and this of Origanus) and by comparing severally the just time of every Accident; we shall quickly Discover, which of the two may best Challenge our Observance.

But because the Latter is most regarded, and con∣sidering how requisite it is to be known of all that Practise the Genethliacal part of Astrology, I shall here give you the Grounds, and manner of this Equa∣tion by the Diagram, and directions following.

[illustration]

The Diagram.

Wherein let the Point A. represent the Star Arctu∣rus (mention'd in the 9th. of Job,) whose Latitude from the Ecliptique, is 31 Degr. 2 Min. North, from which Point as from its Pole or Center, the Circle B. C. D. is described by the Interval of the Hexagon, or Sex∣tile Aspect, viz. A. D. 60 degrees. And let B. E. D. represent the Ecliptique, and A. E. the Latitude of the Star.

N••••, to determin how much is to be counted in the Ecliptique for the Sextile Aspect of the Star pro∣posed: In the Sphaerical Orthogon, A. E. D. we have given A. D. 60 degrees, A. E. 31 degrees, 2 Mi∣nutes, the Latitude of the Star, Ergò, E. D. shall be 54 degrees, 18 Min. by the following 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉.

As the Sine Compl. Lat. Star, — 58°. 58′. — 9932914.

To the Radius, —10000000.

So the Sine Compl. Basis, A.D. 30. 0. —9698970.

To the Sine Compl. E. D. —54. 18.— 9766056,

The Sextile Aspect, — Lat. 31°. 2′.

Next, to get the Longitude of the Trine Aspect, Substract the Arch of the ✶ 54°. 18′ from the Semi-Circle, and the remainder counted from the Place of the Stars Longitude limits the △ thereof: For look how much the ✶ Aspect wants of 60 degrees in the Ecliptique, by reason of the Stars Latitude, and just so much the △ exceeds 120 degrees.

Example.

The Sextile Aspect of the Star Arcturus is here found to be 54°. 18′. which is 5°. 42′. short of 60 degrees. Now if either 54°. 18′. be deduced from 180. or 5°. 42′. added to 120 degrees, the remain∣der, or Aggregate 125°. 42′. is the Trigonal Arch of

Arcturus: and that added to the place of the Star, gives the △ sinister thereof 25°. 4′. of ♒,

So likewise if you add the Hexagon Arch 54°. 18′. to the Longitude of the Star ♎ 19°. 22′. it gives you the place of the Sextile sinister of Arcturus ♐ 13°. 40′. whose Point opposite, ♊ 13°. 40′. is the Trine Dex∣ter of the same Star. But if you deduct the said Hexagon Arch, 54°. 18′. from the Longitude of the of the Star, the residue points out the ✶ Dexter there∣of, ♌ 25°. 4′.

In like manner, if you would know the Semi-Sextile Aspect of a Planet whose Lat. is 7 degrees, —Sub∣stract the Sine of the Compl. of the Latitude, from the Sine of the Complement of the given Aspect, and the Sine of the Complement of the Remainder is the Arch of the Ecliptique, or Distance of the given Aspect; as appears by the work.

SS. Aspect, 30d. Sine Complement	9.937531.
Lat, Planets, 7°. Sine Complement	9,996751.
Arch, 60°. 45′.	9,940780.
Sine of whose Complement 19°. 15′. is the Distance required.	9,688972

And from this ground is Calculated the following Table for Aequating the Aspects of the Planets and Stars, Extended to 60 degrees of Latitude from the Ecliptique (if in it you will reckon the Aspects, as do all Modern Astrologers) or of Declination from the Aequator, if you had rather side with Antiquity:) The use whereof is so Obvious by what I have said, Examples are Needless.

A Table for Aequating the Aspects of the Planets and Stars.
Degr. of Latit.Latitude from the Ecliptique, or Declination from the Aequator.	Sextile Arch, ✶ Degr. M.	Trigonal Arch, △ Deg. Min.
1	60	00	120	0
2	59	59	120	1
3	59	57	120	3
4	59	55	120	5
5	59	52	120	8
6	59	49	120	11
7	59	45	120	15
8	59	40	120	20
9	59	35	120	25
10	59	29	120	31
11	59	22	120	38
12	59	15	120	45
13	59	7	120	53
14	58	59	121	1
15	58	50	121	10
16	58	40	121	20
17	58	29	121	31
18	58	17	121	43
19	58	4	121	56
20	57	51	122	9
21	57	37	122	23
22	57	22	122	38
23	57	6	122	54
24	56	49	123	11
25	56	31	123	28
26	56	12	123	48
27	55	52	124	8
28	55	31	124	29
29	55	8	124	52
30	54	44	125	16
31	54	19	125	41
32	53	52	126	8
33	53	24	126	36
34	52	55	127	5
35	52	23	127	37
36	51	50	128	10
37	51	14	128	46
38	50	37	129	23
39	49	57	130	3
40	49	15	130	45
41	48	31	131	29
42	47	43	132	17
43	46	52	133	8
44	45	48	134	12
45	45	0	135	0
46	43	58	136	2
47	42	51	137	9
48	41	39	138	21
49	40	21	139	39
50	38	56	141	4
51	37	23	142	37
52	35	42	144	18
53	33	49	146	11
54	31	43	148	17
55	29	20	150	40
56	26	36	153	24
57	23	22	156	38
58	19	21	160	39
59	13	53	166	7
60	00	00	180	0