Astronomy.

M S V ; consequently AGE ■«ER —v -~«RBG.

IVtu, • In the Perihelion the equal Motion and the trueCt o st0f the Planet coincide, because the Semicircles criK j and Semi-ellipse A E B are equal, and are de-ff 0l ^ €d ln the fame Time. As. the Planet descended

t-v» J

'''as n 6 ^phelium

^ ili~'ise

■°Wer,

A to the Perihcliitm B, its Motion

, , or less than the mean Motion; in which

hom e Equation or Projlhapbœresis is to be fubtrafled^e r ,A mean Motion, to get the true Motion and

k>,

^**»'*» f.r , avxw

J4 Planet.h r ‘her durin g the Ascent os the Planet from the^‘clce E t0 the -dphelium A, its Motion will bethe mean Motion, as might be shewn ina]] e -Wanner as above. In A the Velocity is leafth i s ’ e an d in B greatest, as we have strewn ; and in Et0 the mean Velocity in the Circle. Forc rea E planet is in E, let the Point be in m, and let thehni te ] S n and Sector m S i be described in the same in-^ch Jit a E Particle of Time, and therefore equal tob «t S p her ; for E h X S n - (E h X S E =) m i X triS ;

therefore E b — nli-i therefore the an-Ecit e Ecity E ST at E is equal so the angular Ve->■- *» which is the mean Velocity.

order therefore to find the equated or true

4$

a Li'n e (7 E°m the Mean, we are to find the Position ofh ' c h E that shall cut off the elliptic Area A S P, toj\° r ti 0ri e whole Area of the Ellipse has the fame Pro-^ the ^ t * le whole Periodical Time of the Planet has^ given in which the elliptic Sector was de-j°hger a . r AQB be a Semicircle described on the‘he § x ‘s of the Ellipse, we must draw from S thehicb tb- 5 w ^ich shall cut off the Area A S Q., toe hti Qr( ? Area °f the whole Circle is in the above-tk*' thepu- at ‘° > for then a perpendicular Q_H wille Hint• *^ e ‘ n E, so that the Line P S being drawn,I 6 bdio]e < V^ rea ASP will be to the Sector A S Q_asS Area of rhe Ellipse to that of the Circle, as

54. ^

^ th e jP cut an Ellipse or Circle in this Proportion, h is Problem long since proposed by Kepler ,

v ed as follows. Upon QC, produced ifM required,

III,

16 *

pl.LVII-Fig. it-