Epitome Astronomiae Copernicanae: Liber IV, part 3
You say it is nearly three times that quantity which the ancients assigned to the greatest distance of the Sun from the Earth, since they set it at less than 1200 semidiameters of the Earth, and twenty times, you say, in the proportion of the bodies, since they made the Sun only 166 times greater than the Earth: do you not fear the astronomical observations? Not at all. For the ancients made the Sun so near that it ought to have a parallax of three minutes. Whence Tycho Brahe reasoned that the parallax of Mars, when it becomes nearer to the Earth than the Sun is, ought to be observed much greater than three minutes. But I have observed that the parallax of Mars is by no means sensible. The distance of Mars, therefore, even when it comes nearest, is greater, and the distance of the Sun also greater, than 1200 semidiameters.
The diameters of Mars and Venus can be observed, both with the ancient instruments and also with that recent Belgian telescope, and are found to be of very few minutes. If, then, the Sun is as near as the ancients said, these planets also, each in its own proportion, will become as near as Tycho Brahe said from Copernicus. If Mars is so near, it will under its visible diameter be also smaller. Mars will therefore be smaller than the Earth, the upper, that is, smaller than the lower; so that there would be no analogy of magnitude of the bodies to their order, which is not consonant with the adornment of the world.
The greater the distance of the Sun is set, the less the parallax of the Sun becomes; the less the parallax of the Sun, the greater the parallax of the Moon from the Sun, if the simple parallax of the Moon be assumed from its own principles: which admirably serves the doctrine of eclipses to be emended. The great magnitude of the interval of the Sun is therefore rather confirmed than refuted by astronomical observations. Physically, moreover, it is according to wish that the body of the Sun, which imparts motion to all the other planets, should be in very many parts greater than all the movable bodies fused into one.
The determination of what body follows next after the determination of the Earth? That of the Moon, a secondary planet. 1) Because this star is peculiarly assigned to the Earth, both to aid the growth of earthly creatures, and to be observed by the contemplative creature on the Earth, and as that from which the observation of the stars should begin. 2) Because the reasons of the proportion to be established are almost the same.
Set forth the foundations of the proportion between the Moon and the Earth, both in respect of the body and in respect of the interval. 1) Here again the Moon at its greatest distance from the Earth had to occupy with its visible diameter the 720th part of the circle, both on account of the number itself as before, and also on account of the eclipses of the Sun, a spectacle ordained by the Creator that the contemplative creature might be taught by it concerning the course of the stars; which was done most rightly if the semidiameters of the Sun and Moon at the greatest distance of each appeared equal: so that the Moon could exactly cover the Sun in this condition of both stars, if it were given, and so both Moon and Sun would constitute the same angle on the Earth.
2) It was fitting also that the proportion of the bodies of the Earth and Moon should stand to the proportion of the interval of the Moon and the semidiameter of the Earth as before the proportion of the bodies of the Sun and Earth stood to the proportion of the solar interval and the semidiameter of the Earth: namely that of the two proportions the same analogy should hold on both sides. For the Moon, an earthly and secondary planet, made for obscuring the Sun, had also to follow the example of the proportions of the orb of the Sun or of the Earth.
What follows from this? Two things follow from the two axioms laid down, each of which by itself, by a wonderful consent of probabilities, even if it did not follow from what precedes, could be used in place of an axiom, since they are in themselves most worthy of belief. The first is this, that since the analogy of the proportions on the side of the Sun is the proportion of equality itself, that is, as the body of the Earth is contained in the greater body of the Sun as many times as the semidiameter of the Earth is contained in the distance or semidiameter of the orb of the Earth or Sun, and not oftener the one than the other, so also the body of the Earth will contain the Moon’s body, which is smaller and narrower than itself, as many times as the semidiameter of the Earth is contained in the distance or semidiameter of the orb of the Moon, and not more rarely the one than the other. This very thing, used as an axiom, has its dignity from this, that the Earth is the dwelling of the measuring creature, wherefore she measures also with her body the smaller body of the Moon, as before she measured the body of the Sun greater than herself; and with her semidiameter measures the semidiameter of the orb of the Moon, both under the ratio of equality, for this reason, that the orb of the Moon alone is situated around the Earth, as the orb of the Earth around the Sun: so the measuring of the orb and body of the Moon, in preference to the bodies of the other planets, is proper to the Earth, no less than before the measuring of the orb and body of the Sun. In a proper measuring, however, it is fitting to hold the ratio of equality as first and chief, if nothing hinders.
The second, which follows from the premises by a long circuit of demonstration, to be seen in my Hipparchus, is this: that in this way the semidiameter of the orbit of the Moon, or the distance, becomes a mean proportional between the distance or semidiameter of the orb of the Earth and the semidiameter of the body of the Earth: so that as the semidiameter of the Earth is to the semidiameter of the orb of the Moon, so this is to the semidiameter of the orb of the Earth or of the Sun. Here again there is some equality of both proportions, probable also in itself, because what the orb of the Earth, placed around the Sun, is to the Sun, that the orb of the Moon, placed around the Earth, is to the Earth.
Do the observations also bear witness to this interval of the Moon and the Earth? Entirely, to a hair: for Brahe found the distance of the Moon at perigee from the Earth a little less than 54 semidiameters of the Earth in the quadratures, at apogee in the same quadratures greater than 59 and a little less than 60, whereas from these principles that is made 54 and this 59.
How now from the axioms laid down and the conclusions that rival the axioms is the quantity of the semidiameter of the Moon to be drawn out? 1) The semidiameter of the Moon being set at 100000 parts, so that the interval of the centres of the Moon and the Earth is 22918166 such parts: the cube of 100000, that is 1000000000000000, is to be multiplied by the number of the interval 22918166, and the fourth root of the product is to be extracted, which will be 389085, showing the quantity of the semidiameter of the Earth in the same parts. For as 389085, the semidiameter of the Earth, is contained in 22918166, the interval of the Moon, 59 times, a little less, so also the cube of 389085 will contain the cube of 100000 59 times, a little less, and so also the globe of the Earth the globe of the Moon. So the semidiameter of the body of the Earth will contain the semidiameter of the body of the Moon less than four times.
2) Otherwise and more simply, from the latter conclusion: let the square root be sought of 3469 and a third, namely of the interval of the Sun, which will be 59, a little less; so great is the distance of the Moon, in such parts as the semidiameter of the Earth is 1. The cube of the semidiameter of the Earth, 1, being divided by 59 and the cube root of the quotient taken, the semidiameter of the body of the Moon is obtained in the same measure.
What proportion of the diameters of the Sun and Moon is built up hence? The same as that of the orb of the Sun to the orb of the Moon, or of this to the body of the Earth, namely that which is between the numbers 59, a little less, and 1. So the body of the Sun contains more than two hundred thousand bodies of the Moon.
What is the mutual proportion of the planetary globes among themselves? Nothing is more consonant with nature than that the order of the magnitudes should be the same as that of the spheres, so that of the six primary planets Mercury should be the least in body, because it is innermost and holds the narrowest orb; Venus the next greater, but still less than the Earth, because she goes round in a narrower orb than this, a wider however than Mercury; next greater than the Earth the globe of Mars, because his orb is now outer and wider, yet the lowest of the upper; again greater the globe of Jupiter, the middle of the upper, and finally the greatest of the movables the globe of Saturn, because he is the highest.
Since, however, there are three dimensions of bodies, either according to diameters, or according to surfaces, or according to the spaces contained by the surfaces, that is, the corpulence, and the proportion of the diameters is simple, that of the surfaces duplicate, that of the bodies triplicate: it is consonant that to the proportion of the intervals one of these three of the globes should be accommodated. For example, since Saturn is almost ten times higher from the Sun than the Earth: either the diameter of Saturn will be ten times the diameter of the Earth, the surface a hundred times the surface of the Earth, the body a thousand times the body of the Earth; or the surface of Saturn will be ten times the surface of the Earth, so that the proportion of the bodies becomes the sesquialter of the proportion of the intervals, and Saturn is thirty times greater than the Earth, as he is also thirty times slower, while the proportion of the diameters becomes at least half the proportion of the intervals, namely threefold, a little more; or finally the bodies themselves have the proportion of the intervals, so that Saturn is at least ten times greater than the Earth, as he is also ten times higher, while in the surfaces two thirds of the proportion of the intervals is kept, in the diameters one third, and so the diameter of the body of Saturn is a little more than double the diameter of the body of the Earth.
Of these three modes the first is repudiated beyond controversy both by the archetypal reasons and by the observations of the diameters made with the Belgian telescope; the second I have hitherto held, the third John Remus Quietanus approves. For me the archetypal reasons seemed better, for Remus the observations stand, but in so great scrupulousness I feared that they were not beyond all exception. I yield the place, however, to Remus and to the observations. For Jupiter acronychal at the perigee of the eccentric has often seemed to me to occupy about 50 seconds; Saturn Remus judges to occupy 30 seconds; Mars acronychal and at perigee in Aquarius appears indeed greater than Jupiter, yet not much. Indeed a body equal to the Earth, if it were seen from the interval which we assign to the Sun, 3469 semidiameters of the Earth, would appear with a diameter of 2 minutes. But now, from the nearness of Mars, that same body, equal to the Earth, would be seen to occupy more than 5 minutes and so equal six Jupiters; the more, therefore, the diameter of the globe of Mars is greater than the diameter of the Earth, the greater will be its appearance. We ought not, therefore, to make the diameter of the globe of Mars greater than the diameter of the Earth by more than perhaps a sixth part, which is done in the third mode.
From the archetypal reasons, however, this will perhaps not unfitly serve: that as before we made the proportion of the bodies themselves of the Sun and Earth, of the Earth and Moon, the same as was between the semidiameter of the Earth and the semidiameters of the spheres, so now also the proportion of the planetary bodies is set the same as that between the semidiameters of the orbs. Thus Saturn in mass of body will be a little less than ten times greater than the Earth, Jupiter more than five times, Mars one and a half times, while Venus is a little less than three quarters of the body of the Earth, Mercury a little more than a third of it.
Ought not the bodies of all the planets also, as that of the Earth, to have been tempered to the body of the Sun by the same laws as the Earth? By no means. For if we followed this, the bodies of the planets would become great in the contrary order of the spheres; Mercury, namely, the greatest, Saturn the least, with a diameter smaller than a third of the diameter of the Earth. This is repugnant both to the reasons stated and to the observations of the diameters. For Saturn acronychal, when he is nine times higher than the Sun, occupies about 30 seconds; he would therefore occupy, if he stood in the neighbourhood of the Sun, about 4 minutes 30 seconds, whereas the Earth from so great an interval would occupy 2 minutes. So the diameter of Saturn is more than twice as great as the diameter of the Earth. And this is what I said at once at the beginning of this place: that it becomes most evident from the things themselves that the beginning of the proportions to be established was made from the Earth. For the observations of the Moon and of eclipses bear witness to the equality of two proportions, of which one is between the bodies of the Moon and Earth, the other between the diameters of the Earth and of the orb of the Moon; against this certainty of the observations we can by no means contend. Now it was most probable that by the same laws the Earth also should be tempered to the Sun: which when we had established, we had also here observations agreeing from afar, because they do not bear a nearness of the Sun of 1200 semidiameters of the Earth, but require double or triple, and this tempering plainly demanded triple. The Earth, then, is certainly the measure both of the bodies of the Sun and Moon and of the spheres. But thus the body of Saturn or of any other planet can by no means become the measure of both; of which again we have brought as witnesses the certain observations of the diameters. The Earth alone, therefore, is such a measure; and nature demands that from the measure of dimensions the beginning of the conformation be made.
What is to be held concerning the rarity and density of these six globes? First, it is not consonant that the density of matter should be the same in all. For where some multitude of bodies is necessary, there also a variety of conditions had to be employed for distinction, that they might be truly many. The chief condition of bodies, as bodies, is the internal disposition of the parts. For the inequality of masses befalls bodies in a manner on account of the surfaces defining the mass, nor does the internal part of one body differ from the part of another by this circumscription of mass. The chief argument, however, of the dissimilarity of the matters is drawn from the contemplation of the periodic times, which does not proceed if we make the density of the globes the same, as we shall hear below.
Secondly, it is consonant that the nearer each body is to the Sun, the denser it should be. For the Sun himself is the densest of all the bodies of the whole world, of which thing the immense manifold force bears witness, which cannot be without a proportionate subject; and the places themselves, near the centre, bear a certain idea of narrowness, such as is in the condensation of much matter into a narrow place.
Thirdly: the rarity, however, is not to be measured out proportionally to the magnitude of the bodies, nor the density to their smallness. For example, the distance and at the same time the amplitude of the globe of Saturn above is to the distance and amplitude of the globe of Jupiter as 10 to 5 nearly. I say that the density of the matter in the globe of Saturn to the density in the globe of Jupiter is not to be set in that proportion which is between 5 and 10. For if anyone followed this, he would offend against another law of variety, introducing an abundance of matter not unequal but the same through all the planets. For the mass of Saturn, 10, multiplied by the density 5, would give an abundance of matter 50, just as much as if you multiplied the mass of Jupiter, 5, by his density, 10. But it seems more excellent and more ornate that neither the masses themselves of globes of different density be equal among themselves, nor the density in the masses of unequal globes be the same, nor yet the abundance of matter be distributed in equal portions through all the globes distinguished by mass and density of matter: rather that all things vary, so that in the same order in which the movable globes succeed one another from the centre, in the same (in the order, I say, not in the proportion) we measure out to them not only the spaces of the bodies and in them the rarity, but the very abundance of matter: as if Saturn had an abundance of matter 50, there should be left to Jupiter less indeed than 50, yet more than the half, 25, say perhaps 36: for so the bodies will be as 50 to 25, the abundance of matter as 50 to 36, the rarity as 50 to 36 or 36 to 25, or the contrary, the density, as 25 to 36 or 36 to 50.
Moreover, since before this I had followed the equality of material abundance, I was compelled to transfer to the magnitude of the bodies the proportion of the periodic times themselves, so that as Saturn has 30 years, Jupiter 12, so also the amplitude of the globes of Saturn to that of Jupiter should be as 30 to 12. This proportion, however, as excessive, the observations of the diameters, mine and Remus’s, have refuted.
Fourthly: that the proportion of the material abundance is to be set precisely half the proportion of the masses or amplitudes (and so sesquialter of the diameters in the globes and three quarters of the surfaces) these things persuade. For first it will come about that both this proportion of abundance and that of density will each be half the proportion of the intervals from the Sun, and so they meet each other in equal portions of that proportion, here a greater abundance of matter, there a lesser density in the same great body, which is the best mediation of all. Saturn, that is, will be twice as high as Jupiter, one and a half times heavier, and one and a half times rarer, or Jupiter one and a half times denser; and by comparison of the proportions of one with the other, Saturn will be twice as high as heavy, and twice as ample as rare.
The same half of the proportion of the intervals is also established by this geometrical fitness: that as above between the intervals of two planets from the Sun (for example let them be 1 to 64, for ease of numbers) two mean proportionals, 4 and 16, had to be set, to form the two remaining dimensions of the bodies, so that the bodies themselves of the movable globes should be among themselves as 1 to 64, the surfaces of the globes as 1 to 16, or 4 to 64, the diameters of the same as 1 to 4, or 4 to 16, or 16 to 64: so now between the intervals of the same two planets from the Sun, 1 to 64, one mean proportional, 8, is set, to form physically the matter within the bodies, which is a single thing; so that again the spaces themselves of the globes are as 1 to 64, while the abundance of matter, and together with it the rarity, in the smaller to that in the greater is as 1 to 8 or 8 to 64: or the contrary, the density, as 8 to 1 or 64 to 8. For in this account it matters nothing at all what the mode is by which some corpulence is condensed or rarefied, whether in length only, or also in breadth, or finally in all three dimensions. For the proportion introduced prescribes some abundance of the thing to be condensed, to which those diverse modes of condensation befall, the abundance remaining always the same. From these principles, therefore, if we compute the densities of the planetary bodies, seeking always the mean proportional between the intervals of each pair from the Sun, or more accurately between the diameters of two spheres or orbits, and finally comparing and reducing all numbers to some common round number: there come out the numbers which follow in the table, with which I have found earthly materials set beside them agreeing in proportion as nearly as possible: as may be seen in my book in the German language, which I wrote in the year 1616 on weights and measures. (Compare Vol. V, p. 609.)
Saturn 324, hardest gems. Jupiter 438, lodestone.
Gold, whose density in this proportion is 1800 or 1900, let us reserve for the Sun.
What proportion of magnitude, finally, do you set between these three chief regions of the world: between the space in which the Sun is, the space or region of the movables, and the space of the whole world, or the region bounded by the sphere of the fixed stars? Although to determine the altitude of the fixed stars not even the reasons of Copernicus reach by observation, so that it seems like the infinite, since in comparison with it the whole interval between the Sun and the Earth, which in the judgment of the ancients embraces 1200, in our reckonings 3469, semidiameters of the globe of the Earth, is insensible: yet reason, following the tracks begun, opens a path of penetrating even so far.
And at the outset we must look to the example of the Earth and the orbs of the Moon and Sun, because the proportions of the whole world are derived from the proper proportions of the Earth, and the region described from these three bodies and their courses is a kind of small world. For what the Sun is in the region of the fixed stars for Copernicus, that the Earth is, to appearance, in the sphere or region of the Sun, and for Tycho also in the truth of the thing. And as the Sun is in the centre of the fixed stars, himself immovable in an immovable dwelling, so also, with respect to the motions of the Moon, the Earth is immovable in the centre of the sphere of the Sun, as it were immovable. For as the region of the movables is ordered around the Sun, so also the orb of the Moon is led around the Earth: there the fixed stars are the limit for the planets, here the Sun himself is the limit for the Moon, to which she returns when the month and all the phases are completed. It is consonant, therefore, that as the orb of the Moon has been made a mean proportional, by necessary reasons, between the apparent orb of the Sun and the body of the Earth in its centre, so also the region of the movables, or the outermost circuit of Saturn, should be a mean proportional between the outermost sphere of the fixed stars and the body of the Sun in the centre of the world.
Again, the same is concluded also, without regard to the small world, from the consideration of the great world itself. For since the movables on the one hand affect the immobility of the surrounding body, which gives place, while they resist motion so that they are not moved with so great a speed as the mover affects, and on the other hand receive motion from the mover to some extent, so that in the movables there is in a manner mingled the motion from the mover and the rest from the body that gives place: therefore, if it be allowed to state a physical matter in mathematical words, the movables can most aptly be called a mean proportional between the body which is the fountain of motion and the immovable body which affords place. Since this is true both physically and as to place (for the fountain is within, the one that gives place without, the movables in the middle), nothing is more probable than that geometrically also the semidiameter of the region of the movables is a mean proportional between the semidiameter of the body of the Sun and the semidiameter of the sphere of the fixed stars, so that as the globe of the Sun stands to the spherical system of all the planets, so this stands to the spherical body of the whole world, bounded by the region of the fixed stars.
How do we know the proportion of the diameter of the body of the Sun to the diameter of the region of the movables? From the angle which the body of the Sun itself occupies in our sight, aided by mathematical instruments. For since this is very nearly half a degree, it follows that it is distant from the sight 229 of its own semidiameters. But the sight is on the Earth, and the diameter of the orb of the Earth, placed around the Sun, is a little more than a tenth part of the orb of Saturn: therefore the outermost orb of the movables, that is of Saturn, contains almost ten times as many diameters of the Sun, that is about 2000.
How great, by this reckoning, does the sphere of the fixed stars turn out? As the diameter of Saturn, the outermost sphere of the movables, contains in itself the diameter of the solar body about two thousand times, so also the diameter of the sphere of the fixed stars would contain the diameter of Saturn in itself almost two thousand times. So the diameter of the fixed stars will contain in itself about four thousand myriads of diameters of the solar body, and of diameters of the Earth (according to the proportion of the bodies of the Sun and the Earth believed by the ancients) five times and more, that is more than two thousand myriads, and according to our reckonings three times that, namely six thousand myriads.
But this amplitude of the sphere of the fixed stars is incredible, which you make two thousand times greater than the sphere of Saturn, whereas among the ancients it stands immediately above Saturn. On the contrary, far more incredible among the ancients is the swiftness of the fixed stars and of Saturn; of which, since it is necessary to affirm one or the other, it is more probable that the sphere of the fixed stars is two thousand or a thousand times more ample than the ancients said, than that it is twenty-four thousand times swifter, as Copernicus established. For there, in a most ample subject and one like the infinite, no motion is present; here, in the modest orb of Saturn, a motion like the infinite would be established. In itself, however, so great an amplitude is neither repugnant to the observations of Brahe, nor dissonant from reason, that things at rest should be distant from the movables by an immense interval.
How do you know that so great an amplitude is not repugnant to the observations of Brahe? He observed the greatest altitude of the polar star, which at this time is in 7° of Aries, in the year 1586 at midnight after the autumnal equinox, and it was 58° 51′. He observed the same also about the winter solstice, on 26 December in the evening about the sixth hour, and found again 58° 51′. So there was no difference; although in the month of September the horizon cut the sphere of the fixed stars almost the whole semidiameter of the orb in which the Earth is carried round lower than on 26 December, since there the Sun appeared in Libra, here in Capricorn. The same happened also when the least altitude was observed at midnight after the vernal equinox and after the winter solstice in the morning at the sixth hour, for on both sides 52° 59′ and a half was found, although in the month of March the horizon cut the fixed stars almost the whole semidiameter of the orb in which the Earth is, higher than in December. Therefore that diameter of the orb in which the Earth is carried round is not sensible by the instruments of Brahe.
Since, then, it does not make one minute in the sphere of the fixed stars, it is not therefore the three thousand five hundredth part of the semidiameter of the fixed stars. The semidiameter, therefore, of the orb of Saturn, which is almost ten times the semidiameter of the orb of the Earth, does not equal the three hundred and fiftieth, nor the four hundredth part of the semidiameter of the fixed stars. Whether, then, it makes the two thousandth part of it, that is whether the altitudes of the polar star mentioned above differ by a fifth part of one minute or 12 seconds, can much less be discerned, since the diameter of the polar star seems to equal at least one minute, nor is the diligence of craftsmen to be trusted as to a fifth part of one minute.
Saturn is distant from the centre of the Earth, according to Brahe, 12300 semidiameters of the Earth. His diurnal circle, therefore, when he is in the equator, contains 77314 semidiameters of the Earth, that is 66420000 German miles, which divided into 24 hours make the portion of one hour 2767500, of which sum 240 miles (for so many Saturn, according to Copernicus, accomplishes in one hour) are about the twelve-thousandth part.
But according to Ptolemy, through the corrections of Copernicus, the proportion of the orbs would be this: the Moon from the Earth 64, 10 semidiameters.
This is more than double that which Brahe has; and 240 miles, the hourly motion of Saturn in Copernicus, are a portion less than the twenty-four thousandth part of the hourly motion of Saturn in Ptolemy.
What proportion of density do you think there is among the bodies of the Sun, of the ethereal air permeating the whole universe, and of the sphere of the fixed stars, enclosing all from without? Since these three bodies are analogous to the centre, the spherical surface, and the interval, three symbols of the three persons in the Holy Trinity, it is credible that there is as much matter in one as in either of the other two; so that a third part of the matter of the whole universe is compacted into the body of the Sun, although this is, with respect to the amplitude of the world, most narrow; a third part likewise of the matter is rarefied and unfolded through the immense space of the world, so that the Sun possesses within his body as much matter as he has obtained outside himself, to be illuminated by the most powerful virtue of his light and permeated by his rays; and finally a third part of the matter is spread out into an orb and cast about the world on the outside as walls. And that we may in some measure adumbrate the proportion by a known similar thing, although we by no means equal it, let us imagine the body of the Sun to be wholly golden, the orb of the fixed stars watery, glassy or crystalline, and the space within full of air. Whence it is given to understand in some measure what divine Moses signified by the firmament (raqia, which properly sounds expansion, that is, the blowing in of ethereal air), and likewise by the waters above the heavens. For so also children play at a certain idea of creation, raising bubbles from water and soap, blowing in air: the difference is this, that God kept a drop of water, so to speak, within in the centre, whereas with children the drop of water, on account of its weight, does not remain in the centre, nor is it divided from the surface by the blowing, but sticks at the bottom of the bubble.
What thickness do you set, or distance of the inner surface of the fixed stars from the outer? Since we have given it as much matter as is in the whole space of the world which it embraces, excepting that matter which is in the most narrow globe of the Sun, and since the matter of the orb of the fixed stars is by no means to be set of the same density as the matter of the space of the movables, but of a density in proportion intermediate between the density of the ethereal air and the density of the matter in the body of the Sun: therefore the space also due to it will be in proportion intermediate between the space of the body of the Sun and the space of the ethereal air. Now above, the proportion of the diameters of the Sun and the ethereal air was that of 1 to 4000000, that of the spaces themselves therefore the triplicate, that is 1 to 64000000000000000000. Between these numbers the mean proportional is 8000000000; so many spaces of the body of the Sun, therefore, did the space between the concave and convex surface of the orb of the fixed stars equal. So the whole world, joined together of three members, is represented by this number, 64000000008000000001, whose cube root, 4000000 and one six-thousandth, shows that the orb, with a thickness of one six-thousandth part of the semidiameter of the solar body, cast around the ethereal air, embraces in its body spaces 8000000000 times the capacity of the solar body. This, then, is that skin of the world, or tunic, or crystalline orb above the heavens, of such subtlety on account of the amplitude of the expansion: which, if it were coagulated into one spherical mass, would have a semidiameter 2000 times greater than the semidiameter of the solar body, whereas now it is not thicker than one six-thousandth of a semidiameter of the solar body, or a little over two German miles.
How great will be the appearance of the Sun if you imagine the eye placed in one of the fixed stars? The four-thousand-hundred-thousandth part of the semidiameter of the fixed stars subtends about the twentieth part of one second: the body of the Sun, therefore, appears with a diameter of 6 third minutes, or the six-hundredth part of one first minute, a great circle containing it 1296 myriads of times; or the appearance of the diameter of the Sun among the fixed stars is the eighteen-thousandth part of its appearance on the Earth.
How great, in turn, do the fixed stars appear from the Earth? Skilled craftsmen deny that any quantity, as of a round body, is detected by inspection through the telescope; rather, the more perfect the instrument, the more the fixed stars are represented as mere points, from which bright rays go out in the manner of hairs and are dispersed.
Each of the fixed stars seems, therefore, to be such a body as the Sun is, and the Sun in turn seems likely to appear among the fixed stars as great and of such sort as each of the fixed stars. I do not think so: for these observations do not at all prevent the Sun from being of greater mass of body than the fixed stars are. Moreover the sight of the Sun from so great an interval would be brighter than any of the fixed stars. For if you pierce a wall with only a needle, so that the Sun can shine through the hole, a greater brightness is diffused from that radiation than all the fixed stars together shining in the open air produce. Nor is the eye hurt by any of the fixed stars, yet it does not tolerate the aspect of the Sun, not even when he approaches from afar.