In one synodical month the Moon has all manner of aspects with the Sun and Earth, and because she is opaque, that face of hers will only appear bright which is towards the Sun, while the opposite remains in darkness. But the inhabitants of the Earth can only see that face of the Moon which is turned towards the Earth; and therefore, according to the various positions of the Moon, in respect of the Sun and Earth, we observe different portions of her illuminated face, and so a continual change in her[7]_Phases_. Let S be the Sun, RTV an arch of the Earth’s orbit, T the Earth, and the circle ABCD, _&c._ the Moon’s orbit, in which she turns round the Earth in the space of a month; and let A, B, C, _&c._ be the centers of the Moon in different parts of her orbit. Now if with the lines S A, S B, _&c._ we join the centers of the Sun and Moon, and at right angles to these draw the lines H O; the said lines H O will be the circles that separate the illuminated part of the Moon from the dark and obscure. Again, if we conceive another line I L to be drawn at right angles to the lines TA, TB, _&c._ passing from the center of the Earth to the Moon, the said line I L will divide the visible hemisphere of the Moon, or that which is turned towards us, from the invisible, or that which is turned from us; and this circle may be called the _Circle of Vision_. [Sidenote: _Full Moon._] [Sidenote: _Half Moon._] [Sidenote: _New Moon._] Now it is manifest, that whenever the Moon is in the position A, or in that point of her orbit which is opposite to the Sun, the circle of vision, and the circle bounding light and darkness, do coincide, and all the illuminated face of the Moon is turned towards the Earth, and is visible to us; and in this position the _Moon_ is said to be _full_. But when the Moon arrives to B, all her illuminated face is then not towards the Earth, there being a part of it, HBI, not to be seen by us; and then her visible face is deficient from a circle, and appears of a gibbous form, as in B. _Fig. 3_. Again when she arrives to C, the two forementioned circles cut each other at right angles, and then we observe a _half Moon_, as in C, _Fig. 3_. And again the illuminated face of the Moon is more and more turned from the Earth, until she comes to the Point E, where the circle of vision, and that bounding light and darkness, do again coincide. Here the Moon disappears, the illuminated part being wholly turned from the Earth; and she is now said to be in _Conjunction_ with the _Sun_, because she is in the same direction from the Earth that the Sun is in, which position we call a _New Moon_. When the Moon is arrived to F, she again assumes a horned figure, but her horns (which before the change were turned Westward) have now changed their position, and look Eastward. When she has arrived to a quadrate aspect at G, she will appear bissected, like a half Moon, afterwards she will still grow bigger, until at last she