Epitome Astronomiae Copernicanae: Liber II, part 1
Book II. On the Sphere and Its Circles
You have said that for the demonstration of the first motion a material sphere is needed. What, then, is a material sphere, and why is it so called? It is called a sphere from its globular figure, for a globe is called sphaira by the Greeks; material, because it is made of some matter, as of paper, wood or metal. It consists of certain circles, outlining one spherical surface, in the middle of which a little globe is hung from an axis passing through the middle of the sphere; and this, so put together, is an image of the world such as our sight imagines it to itself, prepared for this, that by it, as by an instrument, the reasons of the first motion and of the things that depend upon the first motion can be shown to the eye.
What is represented by the surface of the sphere? The heaven and the stars in it.
What by the innermost globe? The globe of the Earth.
But you said that it is not known where the outermost surface of the world is; how, then, can it be represented? As in geometry a circle is drawn about any point in a plane by geometrical licence, so also in the science of optics every eye imagines to itself some spherical surface placed around it, whether it passes through the middle of the fixed stars, or is above them, or below them. And the image of such a surface, at least an imaginary one, is the surface of the sphere.
You supposed above that the Earth is insensible in comparison with the heaven; that little globe in the sphere is necessarily sensible, and is not therefore its image. That globe represents not the magnitude of the Earth, but only the Earth itself in itself. For neither could it be seen, nor made, nor its parts distinguished, if it also corresponded in proportion to the smallness of the Earth.
You denied above that the Earth is in the centre of the world; why, then, is its image in the centre of the sphere? Because the Earth, which that globe represents, is the dwelling place of the eyes, and indeed any eye builds up about itself in imagination a sphere, placing itself in the centre.
But since the eyes are so many and the imaginary spheres as many, why is there only this one little globe, the index of the eye of the Earth, and one sphere? Because all the imaginary spheres are like one another and therefore also equal, that is, one sphere. For although the eyes are many and therefore the centres of that sphere many, both on account of the multitude of eyes over the whole circuit of the Earth and on account of the different positions of the Earth in the greatest circle about the Sun, of which in the theoretical doctrine: yet all that distance of the centres, or of the eyes, compared with the amplitude of the sphere of the fixed stars, wholly vanishes.
How many circles has the material sphere? Ordinarily ten. 1) The horizon. 2) The meridian. 3) The equinoctial. 4) The zodiac. 5, 6) The two tropics. 7, 8) The two polar circles. 9, 10) The two colures.
Which of them is first? The horizon, or limiter, because it is constituted in the simplest manner, namely by sight alone and by the reasoning that follows sight.
Whence has the horizon its name? In Greek it is called horizon, in Latin finitor, because it bounds or limits vision, dividing the upper and visible part of the world from the lower, which is not seen, so that all things above can be seen as far as this boundary, or horos, but those that lie below it are no longer seen, and a star falling on this circle either begins to be seen by rising or ceases by setting.
What, then, of the world is represented by the horizon circle of the sphere? No certain and constant part of the world, but that rim of the heaven, in whatever position it be, in which the visible hemisphere ends, that is, upon which fall all the straight lines drawn from the eye of the spectator to the farthest parts of the visible globe of the Earth, say, to the summits of the mountains and the swelling of the sea.
The stars are not on the same spherical surface; therefore the limit of the things that are seen is not the rim of one surface, but is a plane surface running out from the eye into the depth of the world. The former answer must be repeated; for although it is true that the stars are not on the same spherical surface, sight nevertheless imagines them all to stand on the same spherical surface, because in those bodies which are beyond the farthest mountains sight lacks the aid of distinguishing between near and remote. The material sphere, however, is an image of the imagination of sight. And the horizon therefore will represent the limit of the things that are seen, so far as sight imagines it to itself as a line, without regard to which seen thing is nearer to the eye or more remote from it.
Prove that the horizon is a circle. When any surface of a sphere is cut by a plane, the section is a circle. Now the figure of the world, by reason of vision, is a spherical surface, and the mundane horizon is conceived as a plane cutting the sphere, sight being the judge, as was said at the beginning; it is therefore a circle.
But that prospect, the limit of sight, is not a perfect circle, but is a winding rim, running through the summits of the farthest mountains, since they are not of the same height. And the lines of sight drawn through them are not ordered in the same plane. That is indeed true. Yet because this inequality of the height of mountains is different in different places, and in some places, as in the midst of the ocean, none at all, reason persuaded us to express in the material image some mean, to which the parts of the world that swell up or sink down might be compared.
What distinction of horizons arises from this? The horizon is either visible or rational.
What is the visible horizon? In geography the visible horizon is taken for so great a portion of the earthly surface, or region, as comes into view at once in a single turning of the eyes, which is narrow if the eye is in a valley, wider if on some very high mountain; see the table at folio 130; such a horizon would not exist at all if the Earth were perfectly round and the point of sight in the very surface of the Earth. Therefore where there is a broad plain the horizon is usually called free, where mountains stand in the way, impeded, and for one standing on some very high mountain or promontory and looking out along the course of a river or to the farthest part of the sea, the horizon is said to gape open. These are the epithets of the visible mundane horizon as compared with the rational.
How does reason constitute the rational horizon, if for this matter it is deprived of sight? It is not wholly deprived of sight, but uses it and helps it with the instrument of the dioptra. For the line of the dioptra, when it makes a right angle with the line of the plumb, directs the eye to the rational horizon and, being turned round, describes the plane of the rational horizon. Therefore the rational horizon is everywhere a quadrant of a great circle distant from the plumb line, and the visual ray passing out through the dioptra, where it falls upon earthly parts or mountains, judges them to stand above the rational horizon; but where it falls upon the clear sky, the Earth sinking, there it judges that it itself stands elevated with respect to that depressed quarter.
What are the poles of the rational horizon? The vertical point, in Arabic zenith, and its opposite, called the nadir.
What is the vertical point? It is the point of the visible sphere upon which falls the line of the plumb, that is, the straight line drawn in imagination from the centre of the Earth through the eye of the spectator. For a line from the centre of a globe necessarily falls at right angles on the surface of a perfect globe, and is therefore perpendicular to it, that is, to the plane of the rational limiter.
Whence is it called vertical? Because the body of man stands erect on the line of the plumb by reason of weight; the end, therefore, of the plumb line continued hangs over the vertex, or head, of the man.
Prove that the vertical point is the pole of the horizon. A straight line drawn perpendicularly from the centre of a circle of the sphere passes through the poles of that circle, as the geometers teach. Such a circle is the horizon, such a straight line the plumb line, as has already been shown from the definition. It passes, therefore, through the pole of the horizon, but it is drawn through the zenith; therefore the zenith is the pole of the horizon.
Whence does it happen to the eyes that they think the plane of the Earth cohering with the heaven itself and so cutting the sphere, though the heaven and the Earth are removed from each other by so great an interval? Because, since distance is not a primary object of sight, as the opticians teach, but is comprehended by reasoning from the multitude of visible bodies lying between, and between the heaven and the farthest visible parts of the Earth nothing is interposed, sight is therefore deprived of the aid of recognising this distance.
Since, then, the material sphere is an image of the world as it falls upon the eyes, the circle of the horizon in it ought not to be one thing and the globe of the Earth in the middle of the sphere another, but a continuous plane passing through the very centre, that vision might be represented. It ought indeed to be so, but this could not be done if the plane of the horizon had been entire, so that the sphere might be moved in it. Therefore the plane of the horizon is represented on the outside, but within it is pierced through, to give room to the sphere. Since, then, the horizon so expressed none the less represents the apparent section of the sphere into two hemispheres, and the inner parts of this plane, being taken away, are of no further use, the sphere could easily do without them.
The little globe of the Earth, however, is nevertheless hung in the middle, both for the sake of geography and in some measure to remind us of the origin of the horizon and of the despised smallness of the Earth. But whoever wishes may draw, on a flat circle fitted to the internal amplitude of the sphere, the visible horizon of the place in which he dwells, that is, the region, and make it, fixed in the sphere, correspond to the centre and to the horizon placed outside around it.
What kind of circle is the horizon with respect to the spherical surface? A circle, one of the greatest of the sphere, because it passes through the centre of the spherical surface.
What centre has the circle of the mundane horizon? As in the material sphere the centre of the sphere and of the horizon is the same, so the eye of the observer, which this centre represents, is the same centre both of his mundane horizon and of the whole imagined sphere.
There will then be many mundane horizons, because there are innumerable points over the surface of the Earth at which an eye can be placed? In truth there are innumerable mundane horizons, distinct in position, most of which cut one another; only those of any two opposite points of the Earth are parallel to each other. A far greater number of horizons arises if we transfer our thoughts also to the annual motion of the Earth about the Sun, of which in the theoretical doctrine.
Why, then, is there only one horizon in the sphere? Because any sphere in any one of its positions is the image of some certain and single vision of the heaven. Next, because that one in the sphere can in turn be adapted to all the horizons in the world.
If the two mundane horizons of two opposite places of the Earth (or even of the revolution of the Earth about the Sun) differ from each other, and are everywhere distant from each other by the whole diameter of the Earth (or even of the orbit of the Earth about the Sun), the whole heaven will not be divided by them into two visible hemispheres, but a rim of heaven will be left in the middle, of the breadth of this diameter, which will be assigned to neither hemisphere. It is true, but that celestial rim, on account of the immense distance from the eye, vanishes before its utterly contemptible smallness, since it appears narrower from afar than one of the fixed stars, as was proved above in book I, folio 161. Wherefore in this place too a single horizon suffices in the material sphere, taken for two parallels distant from each other, just as if both, drawn through the same centre, wholly coincided.
I grant that one horizon suffices for the fixed stars; but what of the planets, which are not so far removed from us as the fixed stars? In the first motion we consider the planets only so far as we imagine them, with sight for our guide, placed among the fixed stars themselves; nay more, we do not consider the planet itself in its remoteness from the Earth, but in place of the planet its apparent place among the fixed stars. And for the most part we suppose the planet immovable at some one point through a whole daily revolution, or 24 hours. For that within one day it slightly changes that place by a motion either its own or accidental and apparent, the causes of this we do not fetch from the first motion, nor demonstrate in the material sphere, but take over from the theoretical doctrine.
The axis and the poles.
How were the axis and poles introduced into the sphere? The Earth is moved like a globe on a lathe, two opposite points of which remain fixed with respect to the first motion; the rest of the body revolves about those immovable points. Those two points are called the poles of the Earth; the line connecting them, which also passes through the centre of the Earth, is called the axis of the Earth.
Now we imagine that the axis of the Earth is continued on both sides to the extremity of the surface of the fixed stars; where, then, the surface of the fixed stars is cut by this line, there are the poles of the world; this line itself continued is called the axis of the world and is represented by the axis of the sphere, from which the middle little globe is hung; and its extremities in the world are represented by the poles of the sphere.
In figure 28 the line BAC is the axis, B and C the poles.
Where are the poles of the Earth? One is from here beyond the frozen sea, which lies behind Denmark, Norway, Muscovy, Lapland and Tartary, in an unknown place, of which it is not established whether it is covered with waters or has continuous land or islands. The other is in the midst of the Magellanic land, far less known, whose shores have not yet been discovered and explored all round, much less do we know whether it is continuous within or divided by seas.
You said in the first book that the axis and poles of the Earth are fixed forever in the same parts of the Earth: I ask how you prove this. From the altitude of the pole of the sphere. For if the poles of the Earth wandered over the surface of the Earth, the zeniths of places would not keep the same circular distance from the poles of the sphere, since they are the zeniths of the poles of the Earth; and so the pole of the sphere would not always be elevated by an equal arc at any certain place of the Earth. Since, then, the altitude of the pole of the sphere remains invariable, as will be said in book III, the poles of the Earth also must be fixed in the same places of the Earth.
Where are the poles of the world or of the sphere? They pass from one place of the fixed stars to another in the course of the centuries, and today the one which always appears to us in Europe is very near the end of the tail of the Little Bear; the other we never see in Europe, Asia, America and a great part of Africa; and it is borne in a place of the heaven empty of notable fixed stars.
How is the pole visible to us called? Arctic, from the Little Bear, called in Greek arktos; and septentrional, because the stars of the Bear are called by the Latins the seven oxen, or triones. Aquilonar also, from the north wind aquilo, which blows from that quarter; so boreal, from the wind boreas.
How is the invisible pole called? Antarctic, as being opposite to the Arctic, and meridional, because for us dwelling in this half of the globe of the Earth the Sun at midday inclines toward that quarter, toward which this pole lies hidden beneath the Earth; also austral, because the wind coming to us from that quarter is called auster.
But why is the material sphere revolvable about this its axis and poles, while the middle globe fixed to it is immovable, when you have said above that the sphere of the fixed stars stands still, but the Earth, of which that little globe is the image, is turned? Although what was said above is true, yet because sight judges otherwise, namely in the popular way, that the Earth stands and the heaven turns, therefore this is so expressed in the material sphere adapted to one place of the Earth. For the sphere is an image of the world such as our sight imagines it to itself, as was said above.
But how can the true causes of the things that happen in the heavens be delivered by an instrument that partakes of falsity? This deception of sight, even carried over into the instrument, does not hinder us from drawing out the true causes. For most of the circles in the heaven and on the Earth are the same and subordinated to one another by the line drawn from the centre of the Earth into the heaven. Now it is certain that the parts of the tract of the heaven are separated from the subjacent parts of the tract of the Earth, through which tracts these circles pass, by the daily motion, and, the circuit being completed, return to their first correspondence, whether the heaven moves while the Earth is at rest, or the Earth moves while the heaven is at rest, upon the axis of the world: either of which can be represented in the material sphere.
But why, of two things that effect the same, namely the motion of the heaven and of the Earth, is not that rather expressed in the material sphere which is true, namely the motion of the Earth? 1) Because it is the astronomer’s office to tell the causes why our sight imagines this and that to itself, for example why the Sun seems to rise now at this, now at that place of the horizon, for in truth it is not moved. Now these causes cannot be explained otherwise unless we also explain the first elements which sight imagines to itself, and on which sight afterwards rests in judging, namely the apparent or imagined conformation of the world and of its motions, and therefore express them also by the instrument of the material sphere.
2) The sphere could surely be made external and immovable, and the horizon and meridian with the vertical point movable within; but not only learners, but even adults, would be confused: for they would always imagine themselves falling, whenever the zenith, with respect to the position of the sphere on the table, pointed downward.
On what principles is the meridian constituted? We imagine on the Earth a circle passing through the place of our dwelling and through the poles of the Earth, and among the fixed stars a circle drawn through the vertical point of each place and its opposite, or nadir, and through the poles of the sphere.
In this figure F is the zenith, G the nadir, B and C the poles.
What kind of circle is the meridian? It is one of the greatest, for it is drawn through both poles, and so its plane passes through the axis and through the eye, which is the centre of the sphere, and cuts the sphere in two.
Whence is it called meridian? From midday: for since it stands perpendicularly erect upon the horizon, it cuts the visible hemisphere into two equal parts, wherefore the Sun, coming to it by the daily motion, makes midday in the place whose meridian it is; for meridies is used for medidies, or middle day, when the part of the day that is past is equal to the remainder. Hence also the stars, when they have come to this circle, are said to be at mid-heaven.
Into what parts is the sphere divided by the meridian? Into two hemispheres, or into the halves of the hemispheres constituted by the horizon, or the eastern and western quarters of the heaven, or the rising and the falling. For since both the pole and the zenith are in the meridian, and the stars go round the pole in circles, they come nearer to the zenith, that is, are higher, nowhere but in the meridian.
How many meridians are there? In the material sphere there is one meridian, since any sphere by the very manner of its placing represents some one place of the Earth. But with respect to the Earth, since the horizon and the vertical point of sight constitute the meridian, there are as many meridians as there are places in one circle of the Earth having their vertical points in the surface of the world, that is, innumerable; yet the single meridian of the sphere satisfies all these meridians (as the single sphere does all the places). Geographers fix a certain number in place of the innumerable, namely 180, by which they divide the surface of the Earth into 360 equal parts.
How are these distinguished from one another? They are distinguished by numbers from one to 180. After the 180th, the places of the Earth next following are referred again to the first meridian, namely to its lower semicircle, or the numbering of the semicircles is continued to 360.
Whence does this numbering begin? By ancient custom, the meridian which passes through the Canary Islands in the Atlantic Ocean was numbered first, because these were the last places of the Earth among those known to the ancients, and because there nature herself had set the beginning of Europe and Africa, the ocean having what lies beyond. Present-day geographers, however, and the Arabs also before these centuries, each take some liberty here, some beginning from Cadiz, some from the westernmost parts of Portugal, others from those islands where the magnetic needle points exactly to the pole of the world, which islands are called Corvo and the Cape Verde promontory, and lie some degrees west of the Canaries.
In what direction is the numbering made? From the quarter of the west toward the east, because the parts of the zodiac and of the celestial equator also are numbered in that direction, for causes explained in them.
How is the equinoctial of the material sphere constituted? Since the Earth has two poles upon which it is moved, it will also have a middle circle, equally distant from the poles. Now a straight line is imagined drawn from the centre of the Earth through any point of this middle circle as far as the fixed stars, and this line, carried round with the Earth, will describe a circle among the fixed stars, which we call the equinoctial. And this is represented by the circle of the Earth midway between its poles.
In figures 28 and 29 DMEN is the equinoctial, its poles B and C.
What kind of circle is the equator? It is one of the greatest, because it is equidistant from the poles of the sphere.
What is the reason of the names? By the Greeks it is called isemerinos, as if equal-day, by the Latins aequinoctialis, because when the Sun comes to it the days are equal to the nights; but it has the name equator both from this office and also from equalling, examining and measuring in the whole of the first motion. Sailors of today call it the Line, because it is expressed in their plane charts in the form of a straight line.
What places of the Earth receive the equator? The equator passes through the island of St. Thomas in the great gulf of Africa, which is called the Ethiopic Ocean, and, having traversed Ethiopia, a part of Africa, passes over the city of Arin, celebrated by the astrologers of the Jews and Saracens as the middle of the world; thence it crosses the Indian Ocean and in it the island of Taprobane, the Golden Chersonese and the innumerable scattered islands of the eastern ocean; then, passing from afar the shores of the Magellanic land, where it receives the name of New Guinea, it traverses the southern ocean in an immense stretch and at last falls upon Peru, and passes through it by the Guajanan lake and the city of Manoa, and, entering again the Atlantic Ocean, completes the remainder of the circle as far as the shores of Africa.
How are the parts of the sphere which the equator constitutes called? They are called the northern and southern hemisphere, or boreal and meridional, of which names below.
How did it come about that they constituted a zodiac in the material sphere? The Sun, Moon and planets seem to mark a certain tract of the starry heaven by their motions or appearances, which tract girdles on every side the middle of the sphere of the fixed stars, as it is seen by us, so that we are in its plane. For the part of that tract holding the east and the part holding the west are always seen by us in one and the same straight line, and the two parts are never seen on the same side. The image of this tract, which is called the zodiac, in the material sphere is that broad rim oblique to the equinoctial.
In figure 29 and the rest LMQN is the zodiac and its poles O and P, in this instance.
Why does this alone of the circles of the material sphere have so great a breadth? Because the Sun alone is found to describe with its centre the middle line of it and to wander perpetually in it, while the other planets seldom fall into it, but for the most part run out to its sides, at most through so great a space as is fixed for the breadth of this rim in the material sphere.
How great is this breadth? The ancients, looking chiefly to the motion of the Moon, made it twelve degrees. But if the wanderings of all the planets, even of Mars and Venus, are to be reached by half its breadth, since that of Mars is seven and that of Venus ten degrees, the zodiac will have a breadth of 14 or 20 degrees.
Tell the true origin of this middle line, since the Sun is not truly moved, but only seems to be moved. Our Earth, besides being turned by the daily motion, is also one of the number of the planets, and goes round the Sun in the middle place between Mars and Venus, and also with a middle measure of time, as we shall hear in the theoretical doctrine. Now imagine a straight line drawn from the centre of the Sun through the centre of the Earth as far as the fixed stars and carried round with the Earth by the annual motion beneath the fixed stars: that line will then describe the middle path of the zodiac, so that the Sun always seems, to those looking from the Earth, to stick in the part opposite to that toward which the Earth looks.
How is this middle line called? Ecliptic, because the Earth carries the cone of its shadow, being in the line just now imagined, beneath it, and whenever the Moon falls into this shadow she suffers eclipse; by the Greeks kyklos heliakos, because this is the perpetual orbit of the Sun, and also kyklos dia mesou ton zodion, the circle through the middle of the signs, because it divides the breadth of the zodiac through the middle into two rims.
What, then, is the ecliptic? It is the common section of the plane drawn through the centre of the Sun and of the Earth, in every position of it, with the concave of the sphere of the fixed stars.
Where are the poles of the ecliptic? The pole of the ecliptic which we see is in the middle bend of Helice or the Dragon, in a dark place of the heaven, on the line erected from the quadrilateral of the Great Bear through the quadrilateral of the Little Bear, between the Little Bear and the neck of the Swan, and so between the Crown and Cassiopeia. The other, invisible pole is said to be held by the constellation of the Fish, called in Spanish Dorado, within the ship Argo; it has the greater cloud near it.
Are the poles of the ecliptic, and so the ecliptic itself, always found with these fixed stars? Throughout all the centuries in which astronomy has flourished, the ecliptic has receded from the former fixed stars either not at all or so little, in the confines of Cancer and Capricorn, that it is accepted by astronomers not without doubt; of which motion more in book VII.
What kind of circle is the ecliptic? It is one of the greatest, because the Sun is found to exhibit it at places opposite from the centre of the equator, and because the Sun in opposite places of the ecliptic is equally distant from the equator toward contrary quarters. But when a circle bisects a greatest circle, or is equidistant from a greatest circle in opposite places, it is itself a greatest circle.
Whence is this broad circle called the zodiac? Zodia, a Greek word, signifies in Latin signs, in German images, that is, images of men and animals. Zodiakos is therefore in Latin signifer, in German the circle of images. It has this name from the fixed stars which fall in this tract of the heaven, and from their disposition. For the ancients, seeing that twelve full moons occur in one year, and sometimes thirteen, distinguished the region of the zodiac also into twelve parts by the help of the different disposition of the fixed stars, and diligently observed in which sign or part each lunation, with the Moon full or half, was completed.
What are those twelve signs, and what is the cause or aid of imagining each? The position of the fixed stars suggested to the first observers certain members of animals. Aries was so called chiefly from the two horns, one of them curved, and from the body beneath; Taurus from the face of a bull and the eyes and the two horns; Gemini from two heads, four arms as it were, knees and feet; Cancer from the cloudy eyes and the multitude of feet about the body; Leo from the open jaws and four great stars arranged in the form of the animal; Virgo from two wings, the head and the border of the trailing robe. Libra is a sign of a different kind, since it is not an animal, nor does the disposition of the stars afford any other argument for imagining a balance, except that two great stars stand for two scales. Those stars, however, are reckoned with the following sign and are called the claws of the Scorpion. Libra, then, is so called from the equilibrium of day and night, and so from what happens in this sign, not from what appears to the eyes of the fixed stars; Scorpio from the joints of the curved tail and the sting, the vertebrae of the body, the brow and the outstretched claws; Sagittarius from the bow and arrow and the horse-form beneath; Capricorn from the horns, face and belly; Aquarius from the head, shoulders, arm, body, urn and long stream; Pisces from the bodies of the fishes, the cords and the knot of the cord, expressed by the position of the stars. About these there are well-worn verses to help the memory: