THE LIFE OF

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ter of the Earth E to the nearest Point of the representative Orbit æ, cutsthe Periphery of the Earth in «, measuring the Arch of the Earth G«= tothe Za EH = eAH its greatest apparent Latitude: and in like Manner theLine Ec piercing the Periphery FG in y, makes >G — ,/cEIf — eCH theleast Latitude of the Star.

If further, Lines be drawn from the Center of the Earth E, touching therepresentative Orbit in d and b y these will cut the Earth’s Periphery inp and §, and will give the greatest Diameter of the Curve; describe! in theSuperficies of the Earth, by Lines proceeding from its Center to the infinitePoints of the representative Orbit.

The shortest was found in the preceding Paragraph to be a y which Curve(because all the Points in the Orbit abed are conceiv’d to be in a Planeparallel to the Ecliptick, and Lines drawn from E to every one of themdescrib’d a Cone,) shall be an Ellipsis, whose Diameters are given.

1. Hence it follows that the longest or transverse Diameter of every Ellip-sis or Curve, expressing the Parallax of the Orb, shall lie parallel to thePlanes of the Ecliptick.

2 The conjugate or shortest at Right-angles to it, and the longer to theshorter, shall be as the Radius to the Co-fine of the Star’s Latitude.

3. The farther any Star is from the Earth or Sun, the lesser these Ellipsesor parallactick Curves shall be: and farther,

4. If a Star have no Latitude, then lying in the Plane os the Ecliptick,and the Earth moving always in the fame Plane, its Latitude cannot be alter’dby the Parallax, but its Parallax of Longitude will cast it sometimes in An-tecedence, sometimes in Consequence of its middle Place.

5. If a Star be conceiv’d also in the Pole of the Ecliptick at i, the Pa-rallax of Longitude shall cast it always into the fame Longitude with theSun, and its Latitude shall be always the Complement of half the intire Pa-rallax of the Orb; so that the Star with the Sun shall traverse all the Signsin the Space of one Year.

6. That from the Time of the first Quartile with the Sun, after its Emer-sion from his Rays, to the second Quartile, (whilst the Earth moves from Vby A to B, or the representative Point of the Star from d by a to b)the Star (suppos’d at H) appears to move always retrograde; from thenceby the Conjunction to the first Quartile Star (whilst the Earth moves froMB by C to D or the Star in its Representative from b by c to d) again conn'nually direct ; the Parallaxes of Longitude ceasing, and not changing its trueor middle Place, at the Conjunction and Opposition to the Sun, and beinggreatest in Antecedence at the first Quartile, in Consequence at the second.

These are the Affections of the Parallactick Curves or Ellipses, and th eProperties of the Parallaxes of the Orb at the fix’d Stars, dedue’d from tlu 5Figure ; we shall find more in the next Figure B.

Wherein let v 25 a v represent the Ecliptic, P its Pole, A the Pole of th*Earth, * the Æquator; conceive a Star plac’d in the first Point of

without Latitude, the Ellipsis that expresses its Parallax shall have no L^*'tude, and therefore will appear a straight Line, let it be represented byshort straight Line I v m coinciding with the Ecliptick : At the Conjunct*? 11with the o its primitive or middle Place is unaltered; from thence afterEmersion from the Sun it moves in Consequence towards m, at which Po^he arrives when he is in Quartile of it j and now ’tis evident by the Fig use 'that tho’ its Latitude be not chang’d, yet by the Parallax of Longitude it h aSgotten North Declination from the Equator equal to 4 of 4- the intire P*'rallax of Longitude I m C; when afterwards the Sun comes into V, and tu ePoint on which the Star appears to /; it has there as much South Declin 3 '