i6o

Plate

LVII.Fig. io.

A

S T R o N O M Yi

f of

¥

anomalous; and this Anomaly or IrregularsPlanet’s Motion is in itself very irregular a

ry

sometimes more, and sometimes less than alAnd in order to explain this, it will be requifA® jW.pare it with an equal and uniform Motion ° a .moving in a Circle. Let therefore the Elbpl®be the Orbit of a Planet, whose Focus is S, lts F‘ ' ‘ " On the Centre

P°rrft

between A K and O Kthe Circle C E GF. The Area of thisequal to the Area of the Ellipse, as I havemy Elements of Geometry,

Axis A B, and lesser O t

with the Distance S E (which is a mean

, the two Semi-Axes

an iy

j

48. In this Circle let us suppose a Point to

an uniform or equal Motion through the Perip** . ^GF, in the fame Time that the Planet deM' fa AEllipse ; and when the Planet is in its Aphtlf j fl 1the circulating Point be in C, and the Motifs 0 (VPoint will represent the equal or meanPlanet; and the Point Will describe round Sportional to the Times, and equal to the elbp ^the Planet at the same time describes.

49. Let now the equal Motion or angfl^ p e l l ll £tin the Circle be C S M, and take the Area A ^ pjiAto the Sector C S M ; and then the Place ■

in its Orbit will be P ; and the Angle M S P’„ a ji

ference between the true Motion of the ^

mean Motion, is the Equation, and is call 1

. ,at "%fk

d

antI is

ihaphœrests, from its being added to ormean Motion, to obtain the true or equated

50. Hence the Area ACDP will be ■*' j(,Sector D S M, and therefore proportional *° ■tbaphtgrefs ; and consequently where this Ai^ athere the Prosthapbærefis or Equation will £ |;

or a Maximum ; which, evidently happ eIlS , , l£ OPlanet arrives at E, where the Ellipse anti ^ fi>Fcut each other. For when the Planet < ^' cer ' l j 1 e P'r)to R, the Equation becomes proportional t° Arence of the Areas A C E and m E R,

GBRm; for when the Planet is at Rbe at V, and the Sector CSV will be

, th®,

liptic Area A S R, that is,,A C E -J- C E R^

«Vd-Afit

3 r\dA,fish