Complete Works, Volume Four

...tium; or rather, there is no fire under the Moon with a thickness of more than seventy thousand leagues. Instead, following the thick and terrestrial air, there is the purest ether, or as they now call it, the ethereal breeze original: "aura Ætherea", all the way to the Moon. Therefore, there is no need for us to invent anything here regarding that air or fire.

We should rather note the Axis by which that little globe [the Earth] is supported in the middle of this space. The Earth is not supported by any visible axis ending at the Heaven itself. Instead, we understand an indivisible line passing through its center and the center of the World. Extended from here to the First Mover original: "Primum Mobile," the outermost moving sphere in the Ptolemaic system, it ends in two points called the Poles, or the Hinges of the World. Thus, the Poles of the World are nothing other than the ends of the Axis.

We have already said that one of these poles is the Boreal, or Northern, and the other is the Austral, or Southern. The former is also commonly called Arctic from its proximity to the twin Bears, which the Greeks call arktos (the bear). As we have already said, the star located at the end of the tail of the Little Bear is reciprocally called the Polar Star because of its proximity to it. At this time, it is two and three-fifths degrees away from the pole itself. The latter is called Antarctic because it is in the opposite region to the Arctic.

They are called Poles, or the Hinges of the World, because the principal part of the World—namely the Machine of the Heavens—turns daily upon them (polein means "to turn" in Greek) and completes a full rotation from East to West. It is known that they were also called Vertices in Latin, from "turning" original: "vertendo". For this reason, the Poet expressed the Arctic visible to us and the Antarctic invisible to us thus:

This Vertex is always high above us; but the other,
beneath our feet, black Styx sees, and the deep Spirits of the dead.
A quote from Virgil's Georgics, describing the two poles of the celestial sphere.

Furthermore, they are called Poles of the World (and also of the First Mover) to distinguish them from the Poles of the Zodiac. It is upon these latter poles that the specific rotations of the Second Movers the planets and lower celestial spheres or lower heavens occur. These movements tend obliquely from West to East. This applies especially to the Sun itself. Because the Sun moves continuously along the line called the Ecliptic, the Poles of the Ecliptic are both prominent and more frequently named.

Hence, that is called the Axis of the World which ends at the Poles of the World, and around which the entire Machine of the Heavens is understood to turn in that daily motion. Meanwhile, the Axis of the Zodiac is that which, also understood to pass through the Earth, ends at the lower heavens. We conceive the specific rotation of each body to happen around it. For this reason, in certain spheres armillary spheres or physical models of the cosmos, both circles and portions of axes are usually included to represent, to some extent, the heavens and the axes of the Sun and Moon.

Although every axis is conceived as passing through the middle of the Earth, none besides the World Axis is fixed. Therefore, this axis alone—at the parts where it emerges, as it were, from the Earth on both sides—marks two points on the Earth. Because these are directly beneath the Celestial Poles, they are also called Poles (specifically, of the Earth itself). One is similarly called Arctic or Boreal, and the other Antarctic or Southern.

CHAPTER V.

Concerning the Horizon.

Regarding the Circles, that one is called the Horizon which is outermost on the Sphere and surrounds the others.

In the World, it represents that circle which appears to us as a kind of seam between Heaven and Earth when we are on a level plain and look around. For this reason, it is called horizon (the limiting) in Greek and Finiens or Finitor (the finisher) in Latin, because it defines whatever we see from the Earth. It also separates the visible part of Heaven from the unseen, and distinguishes the two Hemispheres which they call the Upper and Lower.

It is above this that the emerging stars are said to rise, and below it the sinking stars are said to set.

Although the Horizon is immobile with respect to any specific place on Earth, it must be conceived as universally changeable. As we change our location on Earth, we also change our Horizon.

The Horizon of a physical sphere an armillary sphere model can represent this variety. Even if it does not move around the rest of the Sphere, the rest of the Sphere is movable within it. It makes no difference which of the two moves; the same change appears to be created.

Furthermore, this change is created because of the convexity of the Earth's surface, and specifically of that portion which we look around at. Even if a surface is leveled original: "libellata," measured with a level, although it appears flat to the senses, it is in fact slightly sloped. Therefore, while we move, something of it is lost on one side and something is gained on the opposite side.

When I say that the surface of the Earth is not flat even when leveled, but sloped, this is understood even from the sea itself. The sea, naturally arranging itself according to a level, simultaneously arranges itself into a circular shape. However much it may seem flat or straight to the senses in a small space, it is for this reason commonly used for leveling or for proving whether any area is flat.

A diagram shows a circular arc representing the surface of the Earth. Several vertical plumb lines converge toward a central point below the surface. This illustrates that vertical lines are not parallel to each other but are radial, pointing toward the Earth's center.

From this, it is understood in passing that no two perpendicular lines are truly parallel. Consequently, not even two neighboring walls built to a perpendicular are parallel, however much they appear to be so to the senses. This is because all perpendicular lines...