_The Method of finding the Distances of the Sun, Moon, and Planets._
[Sidenote: PLATE IV.]
190. Those who have not learnt how to take the [47]Altitude of any
Celestial Phenomenon by a common Quadrant, nor know any thing of Plain
Trigonometry, may pass over the first Article of this short Chapter, and
take the Astronomer’s word for it, that the distances of the Sun and
Planets are as stated in the first Chapter of this Book. But, to every
one who knows how to take the Altitude of the Sun, the Moon, or a Star,
and can solve a plain right-angled Triangle, the following method of
finding the distances of the Sun and Moon will be easily understood.
[Sidenote: Fig I.]
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.