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HAving resolved upon the figure which the Planets describe in their motions, we come now to shew you what lines must be drawn, and method used for the finding a planets true longitude from the Aphelion in
this figure; and in order thereunto, we will shew you first the order of the spheares in which the planets move, and how mechanically to draw this Ellipticall figure of their motions upon a plane. As to the Spheares, 1 We suppose that the Sun is placed in the middle of the world in or a∣bout the center of the Spheare of the fixed Starres, and hath no circular motion but centrall onely.
2 That the Earth is one of the planets, and with her annual motion a∣bout the Sun describeth her Orbe between the Orbs of Mars and Venus.
3 That the Moon is moved about the Earth, as her center, and so in her annuall motion hath respect both to the Earth, and to the center of the Earths orbe the Sun.
4 That the Orbe of Venus is next under the Orbe of the earth, and the Orbe of Mercury between the Sun & the Orbe of Venus. Next above the Orbe of the earth we suppose the orbe of Mars, the Orbe of Jupiter next above Mars, and the Orbe of Saturn next to the Orbe of the fixed Stars.
According to these supposed principles, we would have immediately shewed the method of calculation, but that the Mechanicall way of draw∣ing an Ellpsis, doth if not demostrate, yet at least illustrate that method.
An Ellipsis by the helpe of a thread may be mechanically made thus, first draw a right line to that length which you would have the greatest Diameter to be, which let be A P, and from the middle of this line at X, set off with your Compasses the equal distances X M and X H.
Then take a piece of thrid of the same length with the diameter AP, & fasten one end of the thrid in the point M, and the other at H, & with your pen extending the thread thus fastened to A, & from thence towards P, keep∣ing the thrid stiffe upon your pen, draw a line from P by B to A, the line so drawne shall be an Ellipsis, in which because the whole thread is equal to the Diameter A P therefore the two lines made by the thread in draw∣ing of the Ellipsis must in every point of the Ellipsis be also equal to the fame diameter A P, they that desire a demonstration thereof Geometri∣cally may consult with Apollonius Pergaeus, Claudius Mydorgius, o•• others, in their treatises of Conicall sections; for our present purpose this is sufficient, and from the equality of those two lines, with the Diameter, a brief Method of Calculation, is thus demonstrated by Dr. Warde.
Let the line M E be equal to A P, and draw the lines H B and H E, then in the plaine triangle M H E, having the sides M E equal to the Dia∣meter, and M H the distance of the umbilique points, with the angle H M E, the angles M E H and M H E shall be given also, but the angles B E H and B H E are equal, because the sides B H and B E are equal by construction, and therefore if you subtract the angle B E H from the angle M H E, there will remaine the angle at the Sun M H B, which is a planets true longitude from the Aphelion or the equated Anomaly.
And of these three things propounded to be given, the side M E is by construction made equal to the Diameter A P, how the angle H M E and the side M H must be had shall plainely appeare by that which fol∣lowes.