The greatest _Elongation_ of _Venus_ is found by observation to be about 48 degrees, which is the angle S T ♀; whence, by the known rules of Trigonometry, the proportion of S ♀, the mean distance of _Venus_ from the Sun to ST, the mean distance of the Earth from him may be easily found. After the same manner, in the right-angled triangle S T ☿, may be found the distance S ☿ of _Mercury_ from the Sun. And if the mean distance of the Earth from the Sun S T be made 1000, the mean distance of _Venus_ S ♀ from the Sun will be 723; and of _Mercury_ S ☿ 387: And if the Planets moved round the Sun in circles, having him for their center, the distances here found would be always their true distances: But as they move in Ellipses, their distances from the Sun will be sometimes greater, and sometimes less. Their _Excentricities_ are computed to be as follows, _viz._
{ _Mercury_ 80 } of the parts _Excent._ of { _Venus_ 5 } above-mentioned. { _Earth_ 169 }
[Sidenote: _Heliocentric_ and _Geocentric Place_, what.]
The distances of the superior Planets, _viz._ ♂, ♃, and ♄, are found by comparing their true places, as they are seen from the Sun, with their apparent places, as they are seen from the Earth. Let S be the Sun, the circle ABC the Earth’s orbit, AG a line touching the Earth’s orbit, in which we’ll suppose the superior Planets are seen from the Earth in the points of their orbits ♂, ♃, ♄; and let DEFGH be a portion of a great circle in the Heavens, at an infinite distance: Then the place of _Mars_ seen from the Sun is D, which is called his true, or _Heliocentric Place_; but from the Earth, he will be seen in G, which is called his apparent, or _Geocentric Place_. So likewise _Jupiter_ and _Saturn_ will be seen from the Sun in the points E and F, their Heliocentric places; but a spectator from the Earth will see them in the point of the Heavens G, which is their Geocentric place. The arches DG, EG, FG, the differences between the true and apparent places of the Superior Planets, are called the _Parallaxes_ of the Earth’s annual Orb, as seen from these Planets. If thro’ the Sun we draw SH parallel to AG, the angles A ♂ S, A ♃ S, A ♄ S, will be respectively equal to the angles D S H, E S H, and F S H; and the angle A G S is equal to the angle GSH, whose measure is the arch GH; which therefore will be the measure of the angle AGS, the angle under which the semidiameter A S of the Earth’s orbit, is seen from the Starry Heavens. But this semidiameter is nothing in respect of the immense distance of the Heavens or Fixed Stars; for from thence it would appear under no sensible angle, but look like a point. And therefore in the Heavens, the angle G S H, or the arch G H vanishes; and the Points G and H coincide; and the arches D H, E H, F H, may be considered as being of the same bigness with the arches D G, E G, and F G, which are the measures of the angles A ♂ S, A ♃ S, A ♄ S; which angles are nearly the greatest elongation of the Earth from the Sun, if the Earth be observed from the respective Planets, when the line G ♄ ♃ ♂ A, touches the Earth’s orbit in A. The nearer any of the superior Planets is to the Sun, the greater is the Parallax of the annual Orb, or the angle under which the semidiameter of the Earth’s orbit is seen from that Planet. In _Mars_ the angle ♂ S, (which is the visible elongation of the Earth seen from _Mars_, or the Parallax of the annual Orb seen from that Planet) is about 42 degrees, and therefore the Earth is always to the inhabitants of _Mars_ either their Morning or Evening Star, and is never seen by them so far distant from the Sun as we see _Venus_. The greatest elongation of the Earth seen from _Jupiter_, being nearly equal to the angle A ♃ S, is about 11 degrees. In _Saturn_ the angle A ♄ S is but 6 degrees, which is not much above ¼ part of the greatest elongation we observe in _Mercury_. And since _Mercury_ is so rarely seen by us, probably the astronomers of _Saturn_ (except they have better Optics than we have) have not yet discovered that there is such a body as our Earth in the Universe.