Astronomia Britannica exhibiting the doctrine of the sphere, and theory of the planets decimally by trigonometry, and by tables : fitted for the meridian of London ... / by John Newton ...

CHAP. 4. How to find the Right Ascension of any point of the Ecliptique.

THe Ascension of the Sun or Starres is the degree of the Aequator that riseth with the same above the Horizno. And the Descension of it is the degree of the Aequator that goeth under the Horizon with the same, both these are either Right or Oblique. The Right Ascension or Descension is the degree of the Aequator that Ascendeth or Descendeth with the Sun or other starre in a Right Spheare, and the Oblique Ascension is the degree of the Aequator, that ascendeth or descendeth with the same in an ob∣lique spheare. The former of these is simple, and of one kind onely; be∣cause there can be but one position of a Right spheare, but the later is va∣rious and manifold according to the diverse inclination of the same. To find the Right Ascension of a planet in the Eclptique, There must be gi∣ven as in the first Chapter, the planets longitude or distance from the next Equinoctiall point: and the Suns greatest declination. Then in the Rect∣angle sphericall Triangle of the first chapter A B C, we have limi∣ted.

• 1 The angle B A C, the Suns greatest declination 23. 31. 30.
• 2 The Hypothenuse A C, the Suns distance from the next Equino∣ctiall point, whose place we will suppose to be in 10 degrees of Gemini, and consequently his distance from Aries is 70 degrees. Hence to find the base A B, the right Right Ascension the point sought, the proportion is.

As the Radius is to the tangent of the planets distance from the next Ae∣quinoctial

point: So is the Cosine of the Suns greatest declination▪ to the tangent of the Right Ascension of the point sought, Example.

As the Radius	90	10, 0000000
To tangent of A C	70.	10, 4389341
So is the Cosine of B A C	23. 5250	9, 9623154
To the tangent of A B	68. 34874	10, 4012495

which is the Right Ascension of the Sun or any other planet without lati∣tude, when they be in the the 10 degree of Gemini.

Note that if the Right Ascension of the point sought be in the second quadrant (is in Cancer, Leo, Virgo.) you must take the complement of the arch found to a semicircle: if in the third Quadrant (as in Libra, Scor∣pio, Sagitarius) you must add a semicircle to the arch found: if in the last quadrant (as in Capricorn, Aquarius, Pisces) you must substract the arch found from a whole circle or 360, and so shall you have the Right Ascension of any point of the Ecliptique, to make it plaine we will in each case add an Example.

In the second Quadrant.

Let the Right Ascension of the point sought be 10 degrees of Virgo, the distance thereof from Libra, which is the next Aequinoctiall point is 20 degrees, according therefore to the former Analogie, I say.

As the Radius	90.	10. 0000000
To the tangent of A C	20.	9. 5610658
So is the cosine of B A C	23. 5250	9. 9623154
To the tangent of A B	18. 45	9. 5233813

whose complement to a semicircle 161. 55 is the Right Ascension thereof.

In the third Quadrant.

Let the Right Ascension of the point sought be in 14 degrees of Scorpio, the distance thereof from Libra, the next Aequinoctiall point is 44 de∣grees. Therefore I say.

As the Radius	90.	10. 0000000
To the tangent of A C	44. deg.	9. 9848371
So is the Cosine of	23. 5250	9. 9623154
To the tangent of A B	4152	9. 9471525

to which if you adde a semicircle or 180 degrees the Right Ascension of of the point sought will be 221. 52.

In the last Quadrant.

Let the Right Ascension of the point sought, be 22 degrees of Aquarius; the distance thereof from Aries, which is the next Aequinoctiall point ••s 38 degrees. Therefore I say.

As the Raduis	90.	10. 000000
To the Tangent of A C	38.	9. 8928098
So is the Cosine of	23. 5250	9. 9623154
To the tangent of A B	35. 62	9. 8551252

which being subtracted from 360 there rests▪ 324. 38 for the Right Ascen∣sion of the point sought.