Question Two. Whether there is any Movable Heaven other than the Starry Heaven

25. Second, I ask about the motion of the heavens, whether there is any movable heaven other than the starry heaven.

26. That there is not:

In Genesis 1.17 it is said of the stars that ‘God placed them in the firmament of the heaven’; therefore all the stars are in one firmament.

27. Further, by reason:

“The continuous is that whose motion is one,” according to the Philosopher Metaphysics 5.6.1016a5-6; but the motion of any inferior heaven is one with the superior heaven, because every inferior heaven - if one be posited - is moved with a diurnal motion [sc. from East to West] and also with other motions proper to the superior heavens, if superior heavens are posited; therefore any inferior heaven, if it is posited, is continuous with the whole superior heaven.

28. Further, the whole heaven other than a star is of itself and in itself uniform;     therefore no other motion should be posited because of it, because one part when present does perhaps the same as another; no motion therefore is necessary save the motion of the stars. But the proper motion of the stars seems it can be accounted for in one heaven, just as can the many proper motions in water or air; therefore etc     .

29. To the opposite:

The stars are moved differently, so they have diverse heavens; because if not, a star would be moved with its own motion without the motion of the sphere, and so either there would be a vacuum in the heaven, or the sphere would be rent, or two bodies would be in the same place [n.31].

I. To the Question

30. To discern the number of the heavens we must first show what all the astronomers agree in, and secondly we must see what some of them disagree with others in.

A. All Astronomers Agree that there are at least Nine Heavens

31. Here the supposition must be made that no star [sc. planet] has a proper local motion, that is, that it is not moved with a motion other than with the motion of the sphere in which it is located; for if it left the part of the sphere where it is and moved to another part, either nothing would succeed to it (and so there would be a vacuum), or something else would succeed to it (and so the heavenly body would be made thinner or denser, or it could be rent and, when the rending body recedes, be again continuous), or if none of these is conceded, then the result is that a moved star is always in the same place as another moving body. - This is what Aristotle means in On the Heaven 2.8.290a29-35, “If nature had given a power of progress to the stars, etc.”

32. With this supposition it follows that all the stars that are not at the same distance from each other are not in the same heaven, for different distances at different times cannot be by a motion proper to the star but only by the motion of the heaven in which it is; and if one star is at different distances from another, then the heaven of the first is differently moved from the heaven of the second, and so the heaven of the first is other than that of the second.

33. Now seven stars [sc. the seven planets] are moved differently, so that they are not always at the same distance from the fixed stars, which are for this reason called fixed that they are always at the same distance from each other and keep the same place and local arrangement; and so there is no need to posit more than one heaven in respect of all the fixed stars. But the seven planets are not always at the same distance from each other.

34. These two points, about the varying distance of the planets from each other and from the other stars that are called fixed, are the supposition for the second consideration of the astronomers; for it is possible to be sure of the positions of the planets by means of instruments, one of which - namely armillary spheres - is dealt with by Ptolemy in the Almagest statement 5 ch.1.

35. And if it is objected that ‘the visual ray is refracted because of the diversity of the mediums, and so does not give certainty about the position of the stars’, then at least it will give certainly about the visible position of a star; and if the stars be at the same distance according to the visible position, then they are so also according to their true position, because their varying visible positions are disposed proportionally to their true positions (or at least they are not so disproportionally disposed that there could be so great a distance in their visible positions without some distance in their true positions), and this distance suffices for the matter at issue.

36. So, in addition to the sphere posited for all the fixed stars that are always at the same distance from each other, at least seven other spheres are posited proper to the seven planets that are moved differently both from the fixed stars and from each other; therefore there are eight heavens.

37. Further it is also commonly conceded that there is a ninth heaven higher than the starry heaven, because there is only one proper motion to one celestial body; but the diurnal motion is not proper to the motion of the starry heaven, since the starry heaven is moved by another motion, as has been proved by observations (for no fixed star is always at the same distance from the stationary poles, nor is it even at the same distance at the same times from the houses of Aries and Libra); therefore this diurnal motion will be proper to some other body - and only to a higher body, because the eighth heaven [sc. that of the fixed stars] is moved by this motion (but no heaven is moved by the motion proper to another unless that other is higher than it). There is therefore some movable body that is uniformly moved with a diurnal motion, higher than the starry heaven; Avicenna says this in his Metaphysics 9 ch.2 and Ptolemy in his Almagest statement 1 ch.8, statement 7 ch.3.

B. Astronomers Disagree whether there are more than Nine Heavens

38. On the second point [n.30], about what not all those who treat of this matter agree in, there is doubt whether each planet’s heaven is sufficient for it, and so whether only positing nine heavens is enough.

39. A threefold difference indeed appears in the motions of the planets:

One is in latitude, because the planets do not always appear at the same distance from the stationary poles.

40. Another is in longitude, because the planets pass along the zodiac in different ways and not the same way.

41. A third is in departure and approach, because the same planet sometimes comes closer to the center of the earth and sometimes is further away, as Ptolemy proves in his Almagest, statements 3-12, because there is a circle whose visual diameter is longer in a longer longitude and shorter in a shorter longitude. It is clear too about Mars which, when at the aux,For this term see the figure and footnote to n.49. ³¹ appears of a notably small size with respect to what it has when it is opposite the aux. It is also proved of the moon, because when it and the sun are equally near the tail and head of Draco, an eclipse of the moon does not last the same time but is sometimes longer and sometimes shorter; this is only possible because the moon sometimes enters more and sometimes less into the earth’s shadow, so that when the shadow passes across the diameter of the moon, it stays longer because of the fact the diameter of the shadow is longer there in the cone than it is elsewhere. Also, if this departure and approach of the sun and moon were universally denied, no difference in amount of shadow could be assigned either on the one part or on the other; for the shadow would always stretch to an equal depth and so would be of an equal quantity, and the moon, since it would always be at the same distance near the cone, would always be in equal proximity to the shadow. The supposition of departure and approach is based on these and other observations of Ptolemy.

42. One could perhaps, by attributing one heaven to a planet, save the first two differences (namely of longitude and latitude [nn.39-40]) with a displacement of the polls of the heaven, in the way that Alpetragius [al-Bitruji] tried to do in his book On the Quality of the Celestial Motions when, by positing that the polls of the starry heaven are displaced from the polls of the ninth heaven (and that, as a result, they describe small circles round those stationary polls), he posited that the eighth heaven revolves about its own polls (but not with a motion contrary to the motion of the ninth heaven, but in the same direction), and that the poll of the eighth heaven receives the influence less effectively than does the ninth heaven, and so its poll does not complete a circle when some point on the ninth heaven does complete a circle.

43. And the deficiency of the poll of the lower heaven in its completion of a circle he calls the first shortening which, according to him, supplies the lower heaven’s motion about the poll, and supplies it perfectly in the eighth heaven as far as longitude is concerned; but as far as latitude is concerned there is necessarily a difference, for poll is displaced from poll; for although the motion about the poll of the lower heaven completes that heaven’s motion about the poll of the higher heaven as to longitude, there cannot however truly be a circle to any star moved in the lower heaven but rather a spiral, because it does not return to the same point from which the motion began.

44. Thus by the diversity of the polls of some heavens from others, and by the first shortening and the supplying of it, and especially in the case of some stars because of their not being situated in the middle of their heaven, he tries to give bases for saving the differences of longitude and latitude in the motions of the planets, and this not by positing ad hoc that some lower heaven is moved contrary to the motion of a higher heaven, but by positing that a lower heaven is moved in the same direction as the higher one, but yet less efficaciously, because it is natural that a power received in things ordered relative to each other is more efficaciously received in the ones closer to it.

45. This tradition seems sufficiently to agree with natural principles, provided that through it all the appearances as to longitude and latitude can be saved; for perhaps through it the stoppings and retrogressions and processions of the planets can be saved in the way he in fact tries in his book to save them in the case of certain planets.

46. The third difference, however, namely of departure and approach [n.41], can only be saved by positing that all the heavens are eccentric, because if a planet does not in that case leave its heaven but only a part of its heaven, and that part of its heaven, however it is moved, is always equally distant from the center (because that whole heaven, being rotated in a circle, is concentric with the world), then, wherever the star is, its departure and approach will always be at the same distance with respect to its center. And though it would not be necessary to posit eccentric circles and epicycles (as Ptolemy and other astronomers do) because of the first two differences, yet it is necessary to do so because of the third difference.

47. And, on this supposition, the conclusion for the issue at hand is that a single heaven does not suffice for any planet in respect of its motion.

So, for example’s sake, let the heaven of Saturn be taken. If it is posited as eccentric to the world, let the heaven of Saturn be moved while the eighth heaven is concentric with the world; the aux of that heaven therefore succeeds to the opposite of the aux. If the aux of it did not penetrate the starry heaven (so that two bodies would be together in the same place) but only reached it, then the opposite of the aux, which is less distant from the center of the earth than the aux is, will not reach the concave surface of the starry heaven, and thus there would be a vacuum there.

48. So it is only possible to avoid an unacceptable result about bodies being rent and existing in the same place or about a vacuum by attributing to each planet at least three heavens circling the earth,See the figure at n.49. ³² the two limits of which heavens (namely the lower and higher) would have concentric ultimate surfaces, namely the superior being convex and the lower concave; but those two would have another two surfaces, namely the higher being concave and the lower convex, being eccentric to the world; and between these two surfaces [sc. the concave of the superior and the convex of the inferior] let there be a third sphere (which may be called the deferent), eccentric to those two deferent surfaces, so that when the two revolving heavens are moved to any part a vacuum does not follow; for the thicker part of one is against the less thick part of the other, and conversely.

49. Likewise, in whatever way the deferent is moved within the two revolving spheres (the higher and lower), no vacuum or rending follows from its motion because its surfaces are both concentric to the surfaces within which it is contained and moved; and thus the star [planet], fixed at one part of the deferent will sometimes be at the aux -namely when the part of the deferent where it is is placed directly above the thicker part of the lower revolving sphere and directly placed beneath the less thick part of the superior revolving sphere, for then it will be at the greatest distance from the center of the earth; but the star [planet] will be in the opposite of the aux when the part of the deferent sphere - and the part where the planet is fixed - is placed above the thinnest part of the lower revolving sphere and placed beneath the thickest part of the higher revolving sphere, for then it will be at the shortest distance from the center of the earth. An image of this is more clearly evident in the figure below.In this figure (provided by the Vatican editors) the asterisk marks the place of the planet in the deferent sphere; cd is the center of the deferent sphere; cm is the center of the world; the shaded areas are the two heavens, possessed of thicker and thinner walls, within which the deferent sphere carrying the planet revolves. In this figure the planet is at the aux (that is, the point of the sphere furthest from the center of the world). It would be at the opposite of the aux (and so closest to the center of the world) when the sphere has revolved 180°. ³³

cd

C"?l

50. Further: since Mercury has a deferent, whose center moves (and not round the earth like the center of the moon but off to one side) by describing a small circle (as is clear in the Almagest statement 9 ch.6), the result is that the deferent sphere is not concentric with the revolving spheres, namely the highest and lowest; and so one must posit there at least five spheres, four revolving and one deferent.

51. Now in addition to these spheres one must posit epicycles (which are not spheres circling the earth but little spheres placed at a determinate point on the spheres that do circle the earth), and this because the departure of the star is greater at some times than at others, and this departure cannot come from the deferent alone. Procession too and stopping and retrograde motion are more easily saved by epicycles.

52. But however it may be with epicycles, there will be at least twenty five movable spheres circling the earth, namely twenty three for the planets [sc. five for Mercury and eighteen - six planets times three spheres - for the rest], and in addition the eighth and ninth heavens.

II. To the Principal Arguments

53. To the arguments.

To the first [n.26] I say that Scripture takes ‘firmament’ for the whole heaven, between the empyrean and the elements.

54. To the second [n.27] I say that the conformity of motions does not entail continuity.

55. To the third [n.28] I say that the heaven cannot yield to a moved star as water or air can yield to a body in motion placed in them, because a naturally incorruptible body is naturally indivisible, and this if it is incorruptible both in its parts and in the whole, as the heaven is posited to be; and thus there could not be a motion of anything in the heaven, unmoved as it is by any natural agent.

The Fifteenth to Twenty Fifth Distinctions are lacking in the Ordinatio

[Fifteenth Distinction: Whether in a mixed body the elements actually remain in substance

Sixteenth Distinction: Whether the image of the Trinity consists in three really distinct powers of the rational soul

Seventeenth Distinction: About the origin of Adam’s soul and the place where it was produced Eighteenth Distinction: About the production of woman and the seminal reasons

Nineteenth Distinction: Whether we had immortal bodies in the state of innocence

Twentieth Distinction: About the offspring of Adam had any been procreated in the state of innocence

Twenty First Distinction: About the venality or gravity of Adam’s sin

Twenty Second Distinction: Whether Adam’s sin came from ignorance

Twenty Third Distinction: Whether God could make a rational creature’s will impeccable by nature Twenty Fourth Distinction: Whether the superior part [sc. of the intellect] is a distinct power from the inferior part

Twenty Fifth Distinction: Whether anything other than the will causes efficaciously an act of willing in the will]