On the Revolutions of the Heavenly Spheres

...remain unmoved original: "maneat immotum" — this concludes the previous chapter's argument about the relative motion of the Earth and the center of the universe., and those things which are closest to the center would be carried most slowly.

On the Immensity of the Heavens in Relation to the Size of the Earth. Chapter VI.

That the great bulk of the Earth has no significant scale original: "aestimationem" — here meaning comparative value or measurable size compared to the magnitude of the heavens can be understood from the following fact. The "boundary circles"—for this is the meaning of the Greek term horizons original: ὁρίζοντας (horizontas)—cut the entire celestial sphere into two equal halves. This could not happen if the size of the Earth were significant when compared to the heavens, or if its distance from the center of the world were notable. For a circle that cuts a sphere into two equal halves must pass through the center of that sphere, and it is the largest of the circles that can be drawn around it.

Let the circle ABCD be the horizon, and let the Earth, from which our vision originates, be at E, which is the center of the horizon that separates the things that are visible from those that are not. Let there be observed through a sighting-tube Dioptra: an ancient Greek surveying instrument used for measuring angles and altitudes, or a "horoscope" here referring to a sighting instrument for determining the ascendant, not a modern birth chart, or a water-level Chorobates: a long wooden tool (about 20 feet long) used by Roman engineers for leveling, similar to a modern spirit level placed at E, the beginning of Cancer rising at point C; at that same moment, the beginning of Capricorn is seen to set at A. Since AEC forms a straight line through the sighting-tube, it is clear that this line is the diameter of the zodiac Signifer: literally "the sign-bearer," the Latin term for the belt of the zodiac, because six signs [of the twelve] define a semicircle, and the center E is the same as the center of the horizon.

Again, when the revolution has changed so that the beginning of Capricorn rises at B, the setting of Cancer will then also be seen at D. BED will be a straight line and itself a diameter of the zodiac. Now, since it has already appeared that AEC is also a diameter of the same circle, it is evident that their intersection at E is the center. Thus, the circle of the horizon always divides the zodiac—which is the greatest circle of the sphere—into two equal halves.

But in a sphere, if a circle cuts through the middle of any of the "great circles," the cutting circle itself must also be a "great circle." Therefore, the horizon is one of the "great circles," and its center appears to be the same as the center of the zodiac. This remains true even though a line drawn from the surface of the Earth must necessarily be different from one drawn from its center. Yet, because of the immensity of the heavens in respect to the Earth, these lines become, in a way, like parallel lines which, due to the excessive distance of their endpoint, appear to be a single line; for when the space that contains original: "continet" — the text continues onto the next page...

A geometric diagram of a circle representing the celestial horizon, labeled ABCD. A horizontal line AC and a vertical line BD intersect at the center point E. Point E represents the Earth or the observer's position. The diagram illustrates how the horizon divides the celestial sphere into two equal halves, indicating the insignificance of the Earth's size compared to the heavens.