Let _BAG_ be one half of the Earth, _AC_ it’s semi-diameter, _S_ the Sun, _m_ the Moon, and _EKOL_ a quarter of the Circle described by the Moon in revolving from the Meridian to the Meridian again. Let _CRS_ be the rational Horizon of an observer at _A_, extended to the Sun in the Heavens, and _HAO_ his sensible Horizon; extended to the Moon’s Orbit. _ALC_ is the Angle under which the Earth’s semi-diameter _AC_ is seen from the Moon at _L_, which is equal to the Angle _OAL_, because the right lines _AO_ and _CL_ which include both these Angles are parallel. _ASC_ is the Angle under which the Earth’s semi-diameter _AC_ is seen from the Sun at _S_, and is equal to the Angle _OAf_ because the lines _AO_ and _CRS_ are parallel. Now, it is found by observation, that the Angle _OAL_ is much greater than the Angle _OAf_; but _OAL_ is equal to _ALC_, and _OAf_ is equal to _ASC_. Now, as _ASC_ is much less than _ALC_, it proves that the Earth’s semi-diameter _AC_ appears much greater as seen from the Moon at _L_ than from the Sun at _S_: and therefore the Earth is much farther from the Sun than from the Moon[48]. The Quantities of these Angles are determined by observation in the following manner. [Sidenote: The Moon’s horizontal Parallax, what. The Moon’s distance determined.] Let a graduated instrument as _DAE_, (the larger the better) having a moveable Index and Sight-holes, be fixed in such a manner, that it’s plane surface may be parallel to the Plan of the Equator, and it’s edge _AD_ in the Meridian: so that when the Moon is in the Equinoctial, and on the Meridian at _E_, she may be seen through the sight-holes when the edge of the moveable index cuts the beginning of the divisions at o, on the graduated limb _DE_; and when she is so seen, let the _precise_ time be noted. Now, as the Moon revolves about the Earth from the Meridian to the Meridian again in 24 hours 48 minutes, she will go a fourth part round it in a fourth part of that time, _viz._ in 6 hours 12 minutes, as seen from _C_, that is, from the Earth’s center or Pole. But as seen from _A_, the observer’s place on the Earth’s surface, the Moon will seem to have gone a quarter round the Earth when she comes to the sensible Horizon at _O_; for the Index through the sights of which she is then viewed will be at _d_, 90 degrees from _D_, where it was when she was seen at _E_. Now, let the exact moment when the Moon is seen at _O_ (which will be when she is in or near the sensible Horizon) be carefully noted[49], that it may be known in what time she has gone from _E_ to _O_; which time subtracted from 6 hours 12 minutes (the time of her going from _E_ to _L_) leaves the time of her going from _O_ to _L_, and affords an easy method for finding the Angle _OAL_ (called _the Moon’s horizontal Parallax_, which is equal to the Angle _ALC_) by the following Analogy: As the time of the Moon’s describing the arc _EO_ is