Ouranoskopia, or, The contemplation of the heavens, in a perpetual speculum, or general prognostication for ever wherein is succinctly demonstrated the names and natures of the signs, planets and aspects, terms of art, order of the spheres, the colours, magnitudes, motions, solid proportions and distances of the seven planets from the earth ... / by Iames Corss ...

CHAP. XXI. Containing several Propositions in Astronomy.

THese few Propositions which I intend here to deli∣ver, be such as are of ordinary and frequent use in the practice of the Mathematicks, and such as I hold fit and requisit for all them to know who shall make use of this Treatise.

Proposition 1. To find the Suns Declination.

As the Radius is to the sine of the Suns greatest Decli∣nation, so is the fine of his distance from the next Equi∣noctial Point, to the sine of his Declination required, which is North if the Sun be in Aries, Taurus, Gemini, Cancer, Leo and Virgo, and south when he is in Libra, Scorpio, Sagitary, Capricorn, Aquary and Pisces.

Proposition. 2. To find the Suns right Ascension.

As the Radius, is to the Tangent of the Suns Longi∣tude, so the Co-fine of his greatest Declination, to the Tangent of his right Ascension required.

Proposition 3. To find the Ascensional Difference.

As the Co-tangent of the Latitude, is to the Radius, so is the Tangent of his Declination, to the sine of his Ascen∣sional Difference.

Proposition 4. To find the Suns Amplitude.

As the Co-sine of the Latitude, is to the Radius, so is the sine of the Suns Declination, to the sine of the Am∣plitude required.

Proposition 5. To find the time when the Sun will be due East and West.

As the Tangent of the Latitude, is to the Radius, so the Tangent of the Declination, to the Co-sine of the hour from the Meridian, when he will be due East or West.

Proposition 6. To find the Suns Altitude when he is due East or West.

As the sine of the Latitude, is to the Radius, so is the sine of the Suns Declination, to the sine of his Altitude, when he is due East or West.

Proposition 7. To find the Suns Altitude at the hour of six.

As the Radius, is to the sine of the Latitude, so is the sine of the Suns Declination, to the sine of the Suns Alti∣tude, at the hour of six as was required.

Proposition 8. To find the Suns Altitude at any time assigned.

In this Proposition there be two cases; For,

1. If he be in the Aequator, say, — As the Radius, is to the Co-sine of his distance from the Meridian, so is the Co-sine of the Latitude, to the sine of his Altitude re∣quired.

2. When the Sun hath either North or South Declina∣tion: As the Radius, is to the Co-tangent of the Latitude, so the Co-sine of his distance from the Meridian, to the Tangent of ane Arch, which substracted from the Suns distance from the Pole, leaveth a second Arch. Then say,

As the Co-sine of the first Arch, is to the Cosine of the second Arch, so is the sine of the Latitude, to the sine of the Suns Altitude, as was required.

Proposition 9. To find the Suns Azimuth.

As the Co-sine of the Suns Altitude, is to the sine of his distance from the Meridian, so is the sine of his distance from the Pole, to the sine of his Azimuth re∣quired.

Proposition 10. To find the Declination, right Ascension and Ascen∣sional difference of the Planets or fixed Stars.

Suppose the place of any Planet be given in Longitude and Latitude: As suppose the Moon were the Planet pro∣posed her true place given, let be Leo, 20 d. 49 m. 53 s. and her Latitude 00 d. 22 m. 52 s. North (as at the time of that solar Eclipse, which will happen in July 1684.) which being given with the greatest obliquity of the Ecliptique, 23 d. 31 m. 30 s. we shall enquire for the Moons declination thus.

	d.	m.	s.
As the Radius,	90	00	00
Is to the s. of the Moons Longitude ab. Ariete,	110	49	53
So is the Tangent of the greatest obliq.	23	31	30
To the Tangent of an Arch.	22	8	24
Then from the Radius,	90	00	00
Substract the Moons latitude (because its North)	00	22	57
Rests distance of the Moon from the Pole	89	37	8
From which Substract the first Arch	22	8	24
Rests a second Arch	67	28	44
Then I say again;
As the Cosine of the first Arch	22	8	24
Is to the Cosine of the second Arch	67	28	44
So is the Cosine of the greatest obliq.	23	31	30
To the sine of the Moons declination required	22	16	50
2. To find the Moons right ascension, I say,
As the Cosine of the Moons declination	22	16	50
Is to the Cosine of the Moons longitude, ab Ariete	110	49	53
So is the sine of her distance from the Pole	89	37	8
To the sine of an Arch, viz.	22	36	2

Which added to 90 degrees, because the Moon is in the second Quadrant of the Ecliptique, (and to 180 deg. when in the third Quadrant, &c.) the Aggregate 112 deg. 36 min. 2 sec. is the right ascension of the Moon, as was required.

Lastly, Her ascensional difference is to be found accor∣ding to the third Proposition aforesaid.

Proposition 11. To find the oblique ascensions and descensions of the Planets and fixed Stars for any time assigned.

In this Proposition there be two Cases.

1. If the declination of the Planet or Star (given) be North, substract the ascensional difference from the right ascension, and the residue will be the Planets (or Stars) oblique ascension, but if you adde them, the aggregate will be his oblique descension.

2. If the Planets declination be South, add the ascen∣sional difference and right ascension together, the sum will be the Planets oblique ascension, but if you substract it, the remainder will be the Planets oblique descension.

As in the former Example, the right ascension of the Moon is 112 deg. 36 min. 2 sec. and her ascensional diffe∣rence 37 deg. 26 m. 31 sec. Now because the Moons de∣clination is North, I substract the ascensional difference from the right ascension, and the residue 75 deg. 9 min. 31 sec. is the Moons oblique ascension; Likewise, I add the ascensional difference to the right ascension, and the aggregate 150 deg. 2 min. 33 sec. is the Moons oblique descension as was required.