Therefore the horizon is a great circle; and its centre is the same as that of the ecliptic, as far as appearance goes; although nevertheless the line passing through the centre of the Earth and the line touching to the surface are necessarily different; but on account of their immensity in comparison with the Earth they are like parallel lines, which on account of the great distance between the termini appear to be one line, when the space contained between them is in no perceptible ratio to their length, as has been shown in optics. Whence even Plutarch in speaking of the revolving solar year says, "So far the movement of the stars has overcome the ingenuity of the mathematicians."
But when a revoiution has taken place and the beginning of Capricorn arises at B, then the setting of Cancer will be visible at D, and BED will be a straight line and a diameter of the ecliptic. Mathematics is written for mathematicians; and among them, if I am not mistaken, my labours will be seen to contribute something to the ecclesiastical commonwealth, the principate of which Your Holiness now holds. As a matter of fact, Philolaus the Pythagorean--no ordinary mathematician, whom Plato's biographers say Plato went to Italy for the sake of seeing--is supposed to have held that the Earth moved in a circle and wandered in some other movements and was one of the planets. But if someone opines that the Earth revolves, he will also say that the movement is natural and not violent.
And I think that is enough as regards the first part of the question. Conversely, for people who travel southward, the second group of stars becomes higher in the sky; while those become lower which for us are high up.
I myself think that gravity or heaviness is nothing except a certain natural appetency implanted in the parts by the divine providence of the universal Artisan, in order that they should unite with one another in their oneness and wholeness and come together in the form of a globe. For the daily revolution appears to carry the whole universe along, with the exception of the Earth and the things around it. For Aristotle says that the movement of a body which is one and simple is simple, and the simple movements are the rectilinear and the circular. And I think that is enough as regards the first part of the question. But on a sphere, if a circle bisects one of the great circles, then the circle bisecting is a great circle. For movement is the most powerful reason wherewith they try to conclude that the universe is finite. For if the annual revolution were changed from being solar to being terrestrial, and immobility were granted to the sun, the risings and settings of the signs and of the fixed stars--whereby they become morning or evening stars--will appear in the same way; and it will be seen that the stoppings, retrogressions, and progressions of the wandering stars are not their own, but are a movement of the Earth and that they borrow the appearances of this movement.
For even this earthly fire feeds principally on earthly matter; and they define flame as glowing smoke.
And conversely we note that this earthly fire--and we have experience of no other--when carried high up immediately dies down, as if through the acknowledged agency of the violence of earthly matter. It is clearer than daylight how false that is; for there would necessarily always be noon at one place and midnight at another, and so the daily risings and settings could not take place, since the movement of the whole and the part would be one and inseparable. And those things which are borne toward the centre seem to follow along in order to be at rest at the centre. Now it is necessary that the land and the surrounding waters have the figure which the shadow of the Earth casts, for it eclipses the moon by projecting a perfect circle upon it. The Movement of the Celestial Bodies is Regular, Circular, and Everlasting--or Else Compounded of Circular Movements After this we will recall that the movement of the celestial bodies is circular. Therefore, said Ptolemy of Alexandria, if the Earth moved, even if only by its daily rotation, the contrary of what was said above would necessarily take place. For the farther the movement is borne upward by the vehement force, the faster will the movement be, on account of the ever-increasing circumference which must be traversed every twenty-four hours: and conversely, the immensity of the sky would increase with the increase in movement. It is not yet clear whether the Earth draws near to them and moves away or they draw near to the Earth and move away And so it would not be very surprising if someone attributed some other movement to the earth in addition to the daily revolution. But it is not perceived straightway to be a perfect sphere, on account of the great height of its mountains and the lowness of its valleys though they modify its universal roundness to only a very small extent. Nicolaus Copernicus, On The Revolutions of the Heavenly Spheres: Book I Among the many and varied literary and artistic studies upon which the natural talents of man are nourished, I think that those above all should be embraced and pursued with the most loving care which have to do with things that are very beautiful and very worthy of knowledge. %%EOF And nevertheless the revolution of the whole brings them round in equal times but not over equal spaces. Accordingly it was necessary for there to be less water than land, so as not to have the whole earth soaked with water-- since both of them tend toward the same centre on account of their weight-- and so as to leave some portions of land--such as the islands discernible here and there--for the preservation of living creatures. So it is as regards the place of the earth; for although It is not at the centre of the world, nevertheless the distance is as nothing, particularly in comparison with the sphere of the fixed stars. And Italy sees the last star of Fluvius, which is not visible to this region situated in a more frigid zone. Therefore, since there are many centres, it is not foolhardy to doubt whether the centre of gravity of the Earth rather than some other is the centre of the world. As regards things which move downward on account of their weight because they have very much earth in them, doubtless their parts possess the same nature as the whole, and it is for the same reason that fiery bodies are drawn upward with force. But when a revoiution has taken place and the beginning of Capricorn arises at B, then the setting of Cancer will be visible at D, and BED will be a straight line and a diameter of the ecliptic. Hence the air which is nearest to the Earth and the things floating in it will appear tranquil, unless they are driven to and fro by the wind or some other force, as happens. Surely if this reasoning were tenable, the magnitude of the heavens would extend infinitely. From this argument it is certainly clear enough that the heavens are immense in comparison with the Earth and present the aspect of an infinite magnitude, and that in the judgment of sense-perception the Earth is to the heavens as a point to a body and as a finite to an infinite magnitude. Rectilinear movement, however, is added to those bodies which journey away from their natural place or are shoved out of it or are outside it somehow. But on a sphere, if a circle bisects one of the great circles, then the circle bisecting is a great circle. For spheres are to one another as the cubes of their diameters. And in order that the unlearned as well as the learned might see that I was not seeking to flee from the judgment of any man, I preferred to dedicate these results of my nocturnal study to Your Holiness rather than to anyone else; because, even in this remote corner of the earth where I live, you are held to be most eminent both in the dignity of your order and in your love of letters and even of mathematics; hence, by the authority of your judgment you can easily provide a guard against the bites of slanderers, despite the proverb that there is no medicine for the bite of a sycophant. Now it is a property of fire to make that which it invades to expand; and it does this with such force that it can be stopped by no means or contrivance from breaking prison and aolapleting its job. Whether Many Movements can be Attributed to The Earth, and Concerning the Centre Of the World Therefore, since nothing hinders the mobility of the Earth, I think we should now see whether more than one movement belongs to it, so that it can be rergarded as one of the wandering stars. In this way the sun gives us the year, the moon the months--the most common periods of time; and each of the other five planets follows its own cycle. For the apparent irregular movement of the planets and their variable distances from the Earth--which cannot be understood as occurring in circles homocentric with the Earth--make it clear that the Earth is not the centre of their circular movements. Therefore, since there are many centres, it is not foolhardy to doubt whether the centre of gravity of the Earth rather than some other is the centre of the world. For that would have to take place either on account of the inconstancy of the motor virtue--whether by reason of an extrinsic cause or its intrinsic nature-- or on account of the inequlity between it and the moved body.
Therefore, since AEC is in a straight line with the dioptra, it is clear that this line is a diameter of the ecliptic, because the six signs bound a semicircle, whose centre E is the same as that of the horizon. Add to this the fact that the inhabitants of the East do not perceive the evening eclipses of the sun and moon; nor the inhabitants of the West, the morning eclipses; while of those who live in the middle region--some see them earlier and some later. 9.
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