much thereabouts: His Centre being an immoveable Point; to which the Revolutions of the other Planets are referred..

Secondly, The Planets are moved about the Sum, from Weft to Eaft, in feveral Orbs, which return into themselves, every Planet in Time proportionable to the Magnitude of his Orb and Distance from the Sun; the Motions of the Primary Planets, h, 4, 8, 9, and, being uniform, perpetually conftant, and regular..

The Figure of the System.

Fig. The Circle BCD, denotes the Way and Revolution of the LXX. Planet Mercury, about the Sun, in 88 Days - The Circle & E FG2, the Revolution of Venus in 225 Days--The Circle H IK, the Revolution of the Earth, with the Moon in one Year---The Circle & LMN 8, the Revolution of Mars - The Circle OPQV, the Revolution of Jupiter, with his four Companions (or Satellities) in twelve Years - The Circle RST, the Revolution of Saturn, with his Ring and Moon, in Thirty Years.The Moon also moves round the Earth, every Month ters four Companions, move about him according to their Diftances from him. The First (and nearest to him) in One Day and 18 Hours. The Second, in Three Days and 13 Hours The Third, in Seven Days and 4 Hours. The Fourth, in 26 Days and 5 Hours Saturn's Moon moveth about him in Sixteen Days: And all of them from West to East, according to their Planets Revolution about the Sun.

Jupi

These Planets, whose Revolutions respect the Sun only, as Saturn Jupiter, Mars, the Earth, Venus and Mercury, are called Primary Planets: The other that move about Saturn, Jupiter and the Earthy Secondary Planets.

The Secondary Planets, are all of thein much Less in Magnitude than their Primary; and all the Planets together, much Lej's than the Sun, from whom they receive their Light, Motion, &e.

CHAP. CHAP. Η.

Of the Theory of the Sun and the other Primary Planets.

T

HAT the Motion of the Primary Planets about the Sun were Elliptical, was first discovered by the learned Kepler, which he deduced from the acurate Observations of the Noble Dane Tychobra. And therefore, in such an Elliptical Figure, may be defcribed all fuck Points, Lines, Arches, &c. as are requifite to be known, and to inform the Fancy in the Trigonometrical Calculation of the Planets Places. But before I proceed fo far, I must thew,

How to describe an Ellipsis.

Concerning the Definition of this Figure, only that it is one of the Sections of a Cone, and the many ways that it may be Artificially described, I shall say nothing, referring the Reader to Midorges, and others that have largely written of the Sections of a Cone. But to Describe fuch a Figure Mechanically. Thus:

About any Two Right-Lines Given, for the Two Diameters of

the Ellipsis, to describe such an Ellipsis,

Fig. LXX.

Let the Line PY be the Longer, and RM the Shorter Diameter Fig. given: Let them cross one another at Right-angles in B. This LXXI. done, Take half of the Longest Diameter BP or BY, in your Compasses, and setting one foot in Ror M, the other will reach upon the Longest Diameter to the Points Z and S, which will be the Centres upon which the Ellipfis PRYM must be described. Wherefore,

In the two Points Z and S, Fix two Pins, Nails, or the like; and about them put a String fo long, that being doubled it may reach from the Pinat S, to the end of the Diameter at P; or from the Pin at Z to the end. Y; so then the whole length of the String, will be twice as long as the Distance SP or ZY; which String at that length, joyn at both ends: Then, putting this String over the two Pins, at Z and S, with a Third Pin (which may be a Black-Lead Pencil, or fuch like) move the String about upon the two Fixed Pins Z and S; and it will by its Motion defcribe.an Ellipsis, fuch as is the Figure PCREYFMDP.

CHAP

1

CHAP. III.

Of the Motion of the Planets in the Ellipsis.

IN N this Elliptical Figure, the Line P Y is called the Transverse, (or Longer,) And RM, the Conjugate (or Shorter) Diameter of the Ellipsis.---- S the Lower, and Z the Upper Focus of the Ellip fis; upon which two Points the Elliptical Figure was described--And the Elliptical Figure it self PCREYFMDP be the Orbit of the Earth, or any other of the Primary Planets :---- S the Place of the Sun; (the common Node, and Centre of the Planitary Orbs, to which the true Motions of the Planets are referred,) in the Lower Focus of the Ellipfis.---- Now, a Planet moving in the Ellipsis; when it shall be in P, it is in Aphelion, or at its Greatest Distance from the Sun---- When in Y Peribelion, or at its Nearest Distance to the Sun--- About the upper Foci of the Ellipsis Z, the mean Motion of the Planet is regulated: B is the common Centre of the Figure: BZ or B S, the Excentricity: And SZ the double Excentricity.

The Figure thus described, the next thing to be known is, after what manner the true Place of a Planet may be determined

therein.

First, The mean Anomaly of a Planet, is its equal Distance from P, the Aphelion Point of that Planet: And this Anomaly is to be accounted from P, to Pagain. And here it is to be observed, that a Planet moving in the Elliptical Arch PRYM, upon the Focus Z, is as long time tracing the leffer Arch CPD, as he is the greater CYM; the Reason is, for that (the mean Motion being made upon Z) the Planet describeth equal Angles in equal Intervals of Time: And it is also evident, That if the Motion be equal upon one Focus Z, of the Ellipsis, it must be unequal upon the other S, in which the Sun is feated.

For inftance: Suppose the Planet to be in C, which is 90 deg. from the Aphelion Point P, then will the Angle of its mean Anomaly be PZC; but the Co-equated Anomaly will be the Angle P BC: And the Angle at the Sum PSC, which is the Angle to be found.

CHAP

CHAP. IV.

L

How to find the Angle that a Planet (in any part of the Fig.
Ellipsis) makes with the Sun; and also, the Planets true LXXII.
Place in the Ellipfis.

L

Et S

be the Sun, X the Centre of the Planets Mean Motion; the Points H, A, T, several Places of the Planet in its Orb, from the Aphelion point P, then will the feveral Angles PXH, PXA, PXT, represent the Anomaly of the Planet: And the Angles PSN, and PSM; the Angles at the Sun. Now these An-gles may be found as followeth.

Suppose the Mean Anomaly of the Earth being at H,to be 30 deg. thisis represented by the Angle PXH, whose Complement BXH, is 150 deg. By help whereof, with the Common Radius, and Excentricity, the true Place of the Planet may be found by Trigonometrical Calculation. For,

First, In the Triangle HXB, there is Given, (1) The Angle HXB, 150.00 d. the Complement of the Planets Mean Anomaly to 180 deg. (2) The Side BH, the Common Radius 100000. And (3) The Side B X, 1685, equal to half X S, the Excentricity. By which you may find the Angle B HX, By CASE I. of O. A. P. T. Then,

:

(1) As the Common Radius, BH, 100000 Parts
To XB (half the Excentricity) 1685 P.
So is the Sine of H XB, the Complement of
Anomaly HZP, 30 d. to 180 deg.

5.000000
3.226599

the 9.698970

:

12.925569

To the Sine of BH X 0.483 deg...

7

7.925569

And therefore the Angle XBH is 29.518 deg, the double

whereof, 59.036 deg. is the Anomaly of Variation.

(2) As the Radius, Sine 90 d.

Is to the Sine of the Greatest Variation

:

Then fay, Secondly,

10

>ХЛИ 5:6.594172

9.933210

6.527382

Now,

(which is) 0.24 deg.:

So is the Variation laft found, 59.034 d. 11

To the Sine of 0. 019 deg.

Which is the Variation required..

Fig. Now, forasmuch as the Planets are moved in Ellipses, and not LXXII. in perfect Circles, the next thing, therefore, to be enquired is, the Planets Place in the Ellipsis: And to that purpose, about Z, let there be defcribed a little Circle K ON, upon which, from K to N, I number the Anomaly of the Epicicle 59.034 deg. before found, and then will the Angle PBZ, be equal to the corrected Anomaly; and so is N the place of the Planet in the Ellipsis; and the Angle Z BN, the Equotion of the Epicicle; or (which is the same) the Difference between the Place of a Planet in the Circle, and in the Ellipfis: And may be found Trigonometrically, thus. For,

Thirdly, In the Triangle B ZN, you have given, (1) The Side B Z, the common Radius 100000 P. (2.) The Side ZN, 00008 P, the Semidiameter of the Epicicle. (3) The Angle BZN 120.98 Deg. by which you may find, the Angles BN Z and ZBN, (by CASE II. of O. A. R. T.) Thus,

The Angle N ZB being 120.98 deg. the Complement to 180 deg. is 59.02 deg. the half whereof is 29.51 deg. The Side BZ is 100000 P. the Side Z N 00008 P, their Sum 100008 P, their Difference 99992. Then,

(3) As the Sum of the Sides B Z and Z N, 10000৪

Is to their Difference 99992

5.000035

4-999965

So is the Tang. of half ZBN and ZNB 29.505 d.

9.752818

14-752783

To the Tang. of the half Difference 29.502 d.

9-752748

This half Difference, added to the half Sum, gives 59.007 deg.

for the Angla ZN B: And substracted from it, leaves 0.003 deg.

for the Angle NBZ.

From the AngleBPZ 29.502

Substract NBZ

005

There remains PBN 29.497 Whose Complement to 180

deg. is 150.503 deg. and is the Angle SBN.

Fourthly,