Lecture 28 — Proofs of the earth's sphericity from the angle of motion of its parts and from astronomy

399 But the spherical shape, necessitated by this argument, follows also from the fact that the motions of heavy bodies always make equal angles, and are not parallel. This would be the natural form of movement towards what is naturally spherical. Either then the earth is spherical or it is at least naturally spherical. And it is right to call anything that which nature intends it to be, and which belongs to it, rather than that which it is by constraint and contrary to nature.

400 The evidence of the senses further corroborates this. How else would eclipses of the moon show segments shaped as we see them? As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and concave—but in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth's surface, which is therefore spherical.

401 Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent. Hence one should not be too sure of the incredibility of the view of those who conceive that there is continuity between the parts about the pillars of Hercules and the parts about India, and that in this way the ocean is one. As further evidence in favour of this they quote the case of elephants, a species occurring in each of these extreme regions, suggesting that the common characteristic of these extremes is explained by their continuity.

402 Also, those mathematicians who try to calculate the size of the earth's circumference arrive at the figure 400,000 stades. This indicates not only that the earth's mass is spherical in shape, but also that as compared with the stars it is not of great size.

540. Having given an argument for the rotundity of the earth taken from the type of motion of its parts, he here adduces another argument for the same taken from the figure of the motion of the parts of earth. And he says (297b17) that all heavy bodies, from whatever region of the heaven, they are moved, are carried to the earth at like angles, i.e., according to right angles formed by the straight line of the body's motion with a line tangent to the earth (which is evident from the fact that heavy objects do not stand firmly on the earth unless they are perpendicular to it); but heavy bodies are not carried to the earth side by side, i.e., according to parallel lines. Now all this is ordered to the fact that the earth is naturally apt to be spherical: because heavy bodies have a like inclination to the place of earth no matter from what part of the heaven they are released. And so there is an aptitude for additions to the earth to be made in a like and equal manner on all sides, which makes it to be spherical in shape. But if the earth were naturally wide [flat] in its surface, as some claimed, the motions of heavy bodies from the heaven to earth would not be from all sides at similar angles. Therefore, the earth must either be spherical or be spherical by nature. He added this last phrase on account of the bulges of mountains and the depressions of valleys which seem to militate against a rotund earth. But such [deviations] arise from some accidental cause and not from what belongs or se to earth; nor does this amount to an appreciable quantity in relation to the whole earth, as has been said above. Now one must say each thing to be as it is according to its nature and not as it is by reason of some violent or preternatural cause. And therefore, although by accident the earth may not be perfectly spherical due to some chance happening, yet, because it is naturally apt to be spherical, it should, absolutely speaking, be called spherical.

541. Then, at the evidence of the senses (297b23), he proves that the earth is spherical with astronomical arguments, based on what appears according to sense. And he brings in three proofs.

The first of these is taken from the eclipse of the moon. And he says that it is further manifest by what appears according to sense, that the earth is spherical. For unless the earth were spherical, an eclipse of the moon would not always reveal circular segments; for we observe that whenever the moon is eclipsed, its dark and its shining portions are distinguished by a curved line. Now an eclipse of the moon results from its entering the earth's shadow—hence the earth's shadow appears to be round. From this it appears that the earth, which makes such a shadow, is round—for only a spherical body is apt always to cast a round shadow. For if the shining body, namely, the sun is larger than the earth, the earth must make a pyramidical shadow, whose cone is above and base on earth; if the sun should be smaller than the earth, it would likewise produce a shadow according to the figure of a round pyramid [i.e., a cone], but, conversely [the summit of] the cone of this pyramid would be on the earth and its base in the heaven; if the sun were equal to the earth, the shadow made would be cylindrical, i.e., columnar. Now, no matter which of these it should be, it would follow, on account of the earth's sphericity, that its shadow would cut the moon according to a circular line. Now someone could say that this circular section is not due to the earth's rotundity but to the moon's. But to exclude this he adds that in the monthly waxing and waning of the moon, the section of the moon takes all differences of shape—for sometimes it is divided by a straight line, as when it is divided through the center, for example, on the 7th and the 21st days; at other times, it is amphicurtos [gibbous], having a circular or arc-like section, namely from the 7th to the 21st; at still other times it is concave [crescent], as from the 1st to the 7th, and from the 21st to its total waning. All this happens according to its position in relation to the sun, as has been said above. But during eclipses the line dividing the moon is always gibbous, i.e., circular. Since, therefore, the moon is eclipsed by the interposition of the earth, the rotundity of the earth, since it is spherical, is the cause of such a shape with respect to the division of the moon.

542. The second proof is given at again, our observations of the stars (297b30) and is based on the appearance of the stars. And he says that from the difference in the appearance of the stars it appears that the earth is not only round, but also small in comparison with the heavenly bodies. For if we move a slight distance to the south or north, our horizon is noticeably changed. This change is particularly evident in two respects.

First, with respect to the horizon's pole, which is the point of the heaven above our head. This point markedly varies in proportion to a short distance, as is apparent from the fixed stars—since with a slight change of location on our part different stars appear overhead.

Secondly, a difference of horizon appears from the different cutting of the heaven by the horizon. And he shows this from the fact that, as one moves to the north or to the south, the same stars are not visible. To those who live in the oblique sphere, the north pole is above their horizon, and all the stars which are not farther from the pole than the elevation of the pole above the horizon are perpetually visible, while all the stars at an equal distance from the other pole are perpetually hidden. Since, therefore, because of the difference of horizon, in northern lands the north pole is higher, and the opposite pole is lower, it happens that certain stars which are near to the ant-arctic pole are not perpetually hidden, but are sometimes seen in lands more to the south, for example in Egypt and about Cyprus, which are never seen in the more northerly region. Conversely, certain stars are always visible in the more northern regions, which in more southern regions are hidden by setting. And from this it appears that the earth is rotund in shape especially according to its aspect at the two poles—for if it were flat, all those dwelling on the whole face of the earth to the south and north would have the same horizon and the very same stars would appear to them and be hidden from them, no impediment arising from the bulge of the earth. And with a similar argument it is proved that the earth is round toward the east and west—otherwise no star would rise any earlier for people in the east than for those in the west. For if the earth were concave, a rising star would appear first to people in the west; but if the earth were flat, it would appear to everyone at the same time. But it is evident that a rising star appears first to those in the east, if we consider a lunar eclipse. If such an eclipse appears in a more easterly region about midnight, it will appear before midnight in a more westerly region, depending on the amount of the distance. From this it is plain that the sun rises earlier and sets earlier in a more easterly region.

This also shows, as Aristotle says, that the earth's rotundity is of no great quantity. For if it were, in so small a distance there would not so soon be made a change in the appearance of the stars. And therefore, we would not consider as very absurd the view of those who wish to link, on the basis of similarity and nearness, the region situated in the far west about the pillars of Hercules (which Hercules set up as a memorial of his victory), and the region in the far east about the Indian Ocean, and who say there is one sea, the Ocean, bordering on both places. And they make a conjecture as to the similarity of both places from the elephants which arise in both places but are not found in the regions between them. This of course is a sign of the agreement of these places but not necessarily of their nearness to one another.

543. He adduces a third proof at also, those mathematicians (298a15), and it is based on measurements of the earth. And he says that whatever mathematicians have attempted to reason about the size of the earth's rotundity assert that its circumference reaches 40 myriads of stades, i.e., 40 times 10,000, which is 400,000 stades. Now a stadium is 1/8 of 1,000 paces. But 1/8 of the aforesaid number is 50,000. Therefore, according to this, the circumference of the earth will be 50,000 times a thousand paces. But according to the more careful measurent of present-day astronomers, the earth's circumference is much less, i.e., 20,000 times 1,000 paces and 400, as Al Fargani says; or 180,000 stades, as Simplicius says—which is about the same, since 20,000 is 1/8 of 160,000. Now astronomers were able to calculate this by considering how much space on earth makes for a difference of one degree in the heaven; and they found that it was 500 stadia according to Simplicius, or 56 2/3 times 1,000 paces according to Al Fargani. Hence, multiplying this number by 360, which is the number of degrees in the heaven, they found the size of the earth's circumference.

And so, from all of this, we can argue that the earth's quantity is not only spherical, but not large in comparison to the sizes of the other stars. For astronomers prove that the sun is 170 times greater than the earth, even though its distance from us makes it seem to be only a foot in diameter. He says, of the other stars, because of Pythagoras' opinion, who held that the earth is one of the stars. And with this is terminated the doctrine of book II.