Chapter VI: Cosmogony, Cosmology, and Cosmography

Footnote 565:

On this rational spirit, see C. B. Jourdain, _Dissertation_, 1838, pp.
20ff.

Footnote 566:

Poole, _Illustrations_, 1920, p. 148.

Footnote 567:

“... secundum physicam et ad litteram” (_De sex d. op._, p. 52).

Footnote 568:

“Causas ex quibus habeat mundus existere et temporum ordinem in quibus
idem mundus conditus et ornatus est rationabiliter ostendit”
(_ibid._). See C. B. Jourdain, _loc. cit._ On Adelard’s rationalism,
see the same, pp. 1O4ff.

Footnote 569:

Hauréau, _Thierry de Chartres_, 1890, p. 51.

Footnote 570:

Haskins, _Studies_, 1924, pp. 40–41.

Footnote 571:

_Quaest. nat._, ch. 6 in printed edit.; fol. 25v. in Bibliothèque
Nationale MSS., fonds lat., no. 6415 (as cited by Haskins, _loc.
cit._).

Footnote 572:

_ibid._, ch. 1 in printed edit.; fol. 24 in MS.

Footnote 573:

_ibid._, ch. 4 in printed edit.; fol. 25 in MS.

Footnote 574:

_De phil. mundi_, II, 3.

Footnote 575:

“... principium a magistro, sed perfectio debet esse ab ingenio”
(_ibid._, I, 21; quoted by Duhem, _Système_, vol. iii, 1915, p. 99).

Footnote 576:

_Entheticus_, 601–624, in: Migne, _Pat. lat._, vol. cxcix, col. 978.
See Ganzenmüller, _Naturgefühl_, 1914, p. 227.

Footnote 577:

Translation from Moffat, _Complaint of Nature_, 1908 (in the
Bibliography under Alan of Lille), p. 27. See also Ganzenmüller, _loc.
cit._

Footnote 578:

See above, p. 223.

Footnote 579:

_Historia Norwegiae_, Storm’s edit., p. 95.

Footnote 580:

_ibid._, p. 96.

Footnote 581:

Duhem, _Système_, vol. iii, 1915, p. 69.

Footnote 582:

_Symb. elect._, II, 1.

Footnote 583:

_Topog. Hiber._, I, 13.

Footnote 584:

_De laud. div. sap._, III, 97–98, 123–124. This point of view was also
that of William the Breton, who, in more than one place in his
_Philippis_, writes that it is enough for us to know the facts of such
natural phenomena as tides, miraculous springs, and the like, but that
the causes of them will forever remain hidden from men (_Philippis_,
VI, 550–551; VIII, 82–90; see above, pp. 193–194).

Footnote 585:

Haskins, _Michael Scot_, 1921–1922, pp. 271–272; idem, _Studies_,
1924, p. 295.

Footnote 586:

_Otia imper._, vol. i, pp. 885–890.

Footnote 587:

See K. Werner, _Wilhelms von Auvergne Verhältniss zu den Platonikern
des XII. Jahrhunderts_, in: Kaiserliche Akademie der Wissenschaften in
Wien, Sitzungsberichte, Philosophisch-historische Classe, vol. lxxiv,
Vienna, 1873, pp. 119–172.

Footnote 588:

_De mundi univ._, I, _passim_.

Footnote 589:

_De sex d. op._, pp. 52–54.

Footnote 590:

_ibid._, p. 60.

Footnote 591:

_Sententiae_, II, 12, 1.

Footnote 592:

Zöckler, _Geschichte_, vol. i, 1877, pp. 415–421.

Footnote 593:

_Hist. schol._, Gen. 1.

Footnote 594:

Though Comestor here denies the teachings of Plato in regard to the
existence of matter prior to the “Creation,” he adopted a traditional
medieval view based on the _Timaeus_ of Plato and given expression by
Augustine: that God created time and the universe simultaneously (see
above, p. 52). How these two conceptions were reconciled is shown by
Daniel of Morley where he writes: “Primus mundus est in eternitate
figuratus, secundus cum tempore creatus, tercius in tempore formatus”
(_De philosophia_, Sudhoff’s edit., p. 8). (For Daniel of Morley’s
views on hyle see Singer, _Daniel of Morley_, 1920, p. 267.)
Essentially the same Platonic doctrine was shared by Hugh of Amiens,
archbishop of Rouen, who wrote in his _Tractatio in hexaemeron_ that
God precedes the world by eternity, not by time (Migne, _Pat. lat._,
vol. cxcii, col. 1249). The _De imagine mundi_ (II, 1) applied the
term _aevum_ to God alone; _tempora aeterna_, beginning before the
world and continuing with and after it, to the _architypus mundus_ and
to the angels; and _tempus_ to the world (Robbins, _Hexaemeral Lit._,
1912, p. 7, note 1).

Footnote 595:

_De phil. mundi_, I, 21.

Footnote 596:

Bede and Hugh of St. Victor also held that the elements were thus
segregated at the moment they were called into existence by God
(Zöckler, _op. cit._, vol. i, 1877, pp. 248, 401).

William of Conches argues specifically against the Aristotelian
doctrine of a fifth element of which the heavenly bodies are composed
(_Dragmaticon philosophiae_, III, 80–83, cited by Schneider,
_Abendländische Spekulation_, 1915, p. 40, note 1). Duhem (_Système_,
vol. iii, 1915, pp. 105, 194) saw in William’s _De philosophia mundi_
what seemed to be a remarkable analogy between the ideas there
expressed and those expressed by Aristotle in the fourth book of his
_Physics_. Schneider (_op. cit._, pp. 40–42) points out that Duhem,
through failure to take into account the passage in the _Dragmaticon_
to which we have just referred, was led to think that William was
actually a believer in the main theories set forth in the _Physics_.
On the contrary, in referring to the elements in the _Dragmaticon_
William merely adopted the traditional Platonic doctrine, and he went
on to explain Aristotle’s theory of the fifth element and vigorously
to denounce it. Though this shows that William may not have agreed
with Aristotle in essentials, it would seem to be, nevertheless, an
argument in favor of the existence of an Aristotelian trend of thought
in William’s time. See above, p. 401, note 58.

Footnote 597:

Though William denied the possibility of chaos preëxisting the
“Creation,” he was none the less accused of heresy by Walter, prior of
St. Victor in Paris during the last part of twelfth century, because
of his failure to make it clear that God created everything out of
nothing. William’s atomic theories suggest the possibility of belief
in his mind that matter in the form of atoms had coexisted with God
and that at the so-called “Creation” God had merely organized and
arranged these atoms. See Hauréau, _Singularités_, 1861, p. 258;
Poole, _Illustrations_, 1920, pp. 300–301.

Footnote 598:

_De sex d. op._, p. 62.

Footnote 599:

See above, pp. 15–16. Belief in the World Soul (_anima mundi_) was a
doctrine of Platonism. Theodoric of Chartres (_De sex d. op._, pp.
60–62), Bernard Sylvester (_De mundi univ._, _passim_), and William of
Conches (see Poole, _op. cit._, p. 151) shared it with Peter Abelard
(Hauréau, _op. cit._, p. 253). The two latter, like Theodoric,
identified this mysterious unifying conscious spirit of all things
with the Holy Ghost and maintained that belief in the World Soul was
not inconsistent with the Christian teaching that each individual has
a personal soul of his own. The personal soul in some way was thought
to be merged with and to form a portion of the World Soul. The theory
of the World Soul, however, could not be purged of an heretical taint.
At the very beginning of our period Manegold argued as vigorously
against it (_Contra Wolfelmum Coloniensem opusculum_, 1–3) as he
argued against the possibility of antipodeans (see above, p. 161). It
was also severely condemned by other defenders of more old-fashioned
and orthodox beliefs. Peter Comestor says, for example: “Hunc locum
male intellexit Plato, dictum hoc putans de anima mundi” (_Hist.
schol._, Gen. 1, 2), and Peter Lombard’s whole treatment of the
question of the Trinity in the _Sententiae_ (II, 17) precludes the
possibility of a World Soul. Peter Lombard specifically states that
the soul of man is not of the same substance as the soul of God.

Footnote 600:

Theodoric adduced various reasons for the rotary motion of the heavens
and gave explanations of this phenomenon which so closely resembled
the arguments given by Aristotle in his _De caelo_ (I, 8; II, 3),
_Physics_ (IV, 4), and _De motu animalium_ (II, 698b) (see above, p.
370, note 42) that Duhem was led by them to the opinion that the
Chartres scholar must have had direct access to Arabic translations of
versions of Aristotle. See above, p. 154, and p. 401, notes 57, 58.

Footnote 601:

_De sex d. op._, p. 54.

Footnote 602:

_ibid._, p. 55.

Footnote 603:

_ibid._, p. 57.

Footnote 604:

See above, p. 141.

Footnote 605:

_De phil. mundi_, I, 23; Werner, _Kosm. Wilhelm von Conches_, 1873, p.
320.

Footnote 606:

This curious opinion is expressed in _De phil. mundi_, I, 23. William
retracted it in the preface to the sixth book of his _Dragmaticon
philosophiae_ on the ground that it contradicts the Scriptural account
according to which Eve was made from Adam’s rib. See above, p. 398,
note 28.

Footnote 607:

_De civitate Dei_, XI, 33, in: _Corpus script. eccl. lat._, vol. xl,
pt. 1, pp. 562–564. See also Zöckler, _Geschichte_, vol. i, 1877, p.
238.

Footnote 608:

_Hexaemeron_, I, in: Migne, _Pat. lat._, vol. xci, cols. 17–18. See
also Zöckler, _op. cit._, pp. 247–248.

Footnote 609:

_De sacramentis_, bk. I, pt. 1, ch. 11, in: Migne, _Pat. lat._, vol.
clxxvi, col. 195. See also Zöckler, _op. cit._, vol. i, p. 401.

Footnote 610:

_Hist. schol._, Gen. 1, 3. See also Zöckler, _op. cit._, vol. i, p.
417.

Footnote 611:

So Rupert of Deutz, Arnold of Chartres, Hugh of Rouen (_ibid._, pp.
395, 405, 406).

Footnote 612:

_Sententiae_, II, 13, 2–6. See also Zöckler, _op. cit._, pp. 413–414.

Footnote 613:

See Bauer, _Philos. Werke des Grosseteste_, 1912 (under Grosseteste in
the Bibliography), p. 76*.

Footnote 614:

_De luce seu de inchoatione formarum_, Baur’s edit., pp. 51–59.

Footnote 615:

See Duhem, _Système_, vol. iii, 1915, pp. 284–287, and vol. v, 1917,
pp. 356–358.

Footnote 616:

_De sex d. op._, pp. 53–54.

Footnote 617:

_Adnotat. elucidat. in Pentateuchon_, Gen. 6, in: Migne, _Pat. lat._,
vol. clxxv, cols. 34–37; _De sacramentis_, I, pt. 1, 1–16, in: Migne,
_op. cit._, vol. clxxvi, cols. 187–199. See also Zöckler, _op. cit._,
vol. i, p. 401.

Footnote 618:

_De Genesi ad litteram_, V, 5, in Migne, _Pat. lat._, vol. xxxiv,
cols. 325–327. See also other passages in Augustine’s works cited in
Zöckler, _op. cit._, pp. 236–237.

Footnote 619:

Zöckler, _op. cit._, p. 406.

Footnote 620:

See above, p. 366, note 7.

Footnote 621:

See above, p. 9.

Footnote 622:

See above, p. 401, note 60.

Footnote 623:

See above, p. 99.

Footnote 624:

See above, p. 82.

Footnote 625:

See above, p. 82.

Footnote 626:

_De phil. mundi_, III, 19.

Footnote 627:

Zöckler, _Geschichte_, vol. i, 1877, pp. 429–430. Averroës discussed
the origin of matter in his commentary on Aristotle’s _Metaphysics_,
XII (Renan, _Averroès_, 1866, pp. 108–115). On medieval opposition to
the Averroïstic doctrine of the eternity of the world, see the same,
pp. 258, 274. On Michael Scot’s denial of this doctrine see Haskins,
_Michael Scot_, 1921–1922, pp. 260–261; the same, _Studies_, 1924, p.
285.

Footnote 628:

Duhem, _Système_, vol. v, 1917, p. 277.

Footnote 629:

Notably in the _De finitate motus et temporis_ and in the unpublished
_Hexaemeron_; see Baur, _Philos. Werke des Grosseteste_, 1912 (under
Grosseteste (under Grosseteste in the Bibliography), pp.
19*-24*—especially p. 23*—93*-95*, 101–106). Robert Grosseteste’s
pupil, Roger Bacon, “believed that he was in a position to demonstrate
by philosophical proofs that the world had a beginning; and besides he
maintained that Aristotle never maintained a contrary doctrine”
(Duhem, _op. cit._, vol. v, p. 402). Albertus Magnus, on the other
hand, did not categorically deny the truth of the Aristotelian
teaching, “but rather treated it as a theory that must be accepted
from the philosophical point of view but rejected from the
theological” (Zöckler, _op. cit._, vol. i, p. 439). Bacon discussed
this matter in an unpublished work now preserved in the Bibliothèque
Municipale at Amiens, MS. no. 406, fol. 69, col. a; see Duhem, _op.
cit._, vol. iii, 1915, pp. 260–277. Albertus Magnus discussed the same
subject in _Summa theologiae_, pt. II, tract. 11, and in _De quattuor
coaevis_, both cited by Zöckler, _op. cit._, vol. i, p. 436.

Footnote 630:

See the summary of the _De mundi univ._ in: _Histoire littéraire de la
France_, vol. xii, Paris, 1763, pp. 267–269.

Footnote 631:

See Anderson, _Younger Edda_, 1880 (under Snorri Sturluson, II, in the
Bibliography).

Footnote 632:

Ginungagap may be related to the great “northerly gulf” referred to
above, p. 349.

Footnote 633:

Quotation is here from Anderson’s paraphrase of the leading ideas of
the _Edda_ of Snorri Sturluson (Anderson, _op. cit._, Preface, p. 5).

Footnote 634:

_Quod homo sit minor mundus_, Baur’s edit., p. 59. See also Thorndike,
_Magic_, 1923, vol. ii, p. 446.

Footnote 635:

See above, pp. 213–214.

Footnote 636:

Cumont, _After Life_, 1922, p. 12.

Footnote 637:

See above, p. 185, and also below, p. 436, note 17.

Footnote 638:

It is to be recalled that the _De mundi universitate_ is divided into
two books, _Megacosmus_ and _Microcosmus_. See above, p. 146.

Footnote 639:

There are marked analogies between the theory of the microcosm as
expounded by Herrad and by Hildegard of Bingen. Singer believes that
“the theory, in the form in which these writers present it, reached
the upper Rhineland somewhere about the middle or latter half of the
twelfth century” (Singer, _Visions of Saint Hildegard_, 1917, p. 20).

Footnote 640:

See Singer, _op. cit._, pp. 30–43, for a discussion of the theory of
the macrocosm and microcosm according to Hildegard and for highly
interesting reproductions of miniatures illustrating this theory.
Singer, believing that the _Causae et curae_ and _Subtilitates_ are
spurious (see above, p. 396, note 8), omits consideration of these
works in this connection.

Footnote 641:

“In creatione hominis de terra alia terra sumpta est, quae homo est,
et omnia elementa ei serviebant, quia eum vivere sentiebant, et obviam
omnibus conversationibus ejus cum illo operabantur et ipse cum illis”
(_Subtilitates_, I, praefatio, in: Migne, _Pat. lat._, vol. cxcvii,
col. 1125).

Footnote 642:

_Causae et curae_, I (Kaiser’s edit., p. 2).

Footnote 643:

Thorndike, _Magic_, vol. ii, 1923, pp. 153–154.

Footnote 644:

_Subtilitates_, praef., in: Migne, _op. cit._, vol. cxcvii, cols.
1125–1128.

Footnote 645:

“Terram centrum idest punctum vocamus eo quod sit media in spera.”
“Terra autem in medio celestris circuli per quem sol currit ut centro
locata est” (Bibliothèque Nationale MSS., fonds latin, no. 8865, fol.
55vo).

Footnote 646:

Grosseteste, _De sphaera_, Baur’s edit., pp. 12–13.

Footnote 647:

_Im. du monde_, I, 13. See above, p. 15.

Footnote 648:

John of Holywood, _De sphaera_, 1.

Footnote 649:

Translation of Al-Farghānī’s _Astronomy_ by John of Seville (or
Johannes Hispanensis, or John of Luna), Nuremberg edit., diff. iv,
fol. 4ro. In the _De sphaera_, _loc. cit._, John of Holywood stated
that Ptolemy and all philosophers had declared that six signs and the
middle of the heaven (_medietas caeli_)—by which he probably meant the
celestial equator—were visible from any place whatsoever to which a
man might go on the surface of the earth. If the earth were not at the
center of the universe it would be impossible, he argued, to see the
_medietas caeli_ from those parts of the earth nearest the firmament:
“aliquis existens in illa parte superficiei terrae quae magis
accederet ad firmamentum non videret caeli medietatem.”

Fig. 10—Diagram to illustrate John of Holywood’s reasoning that the
earth is in the center of the universe.
]

Figure 10 illustrates what appears to have been John’s line of
reasoning as well as the flaws in it. With the earth in position I,
not in the center of the universe, the celestial equator (_E-E′_) is
invisible from all points between _x_ and _y_ through _N_ (the north
pole), _x_ and _y_ being points at which tangents _E-x_ and _E′-y_
touch the earth’s surface. If the earth is in the center of the
universe and the sphere of the universe is incomparably great in
relation to the size of the earth—something which John believed to be
true (see above, p. 155)—the area between _x′_ and _y′_ will be
reduced to a very small area around _N′_. John seems to have assumed
that the universe is large enough to make this area negligible. Such
an area must exist, nevertheless, with all but an infinitely great
celestial sphere. But if the universe were of infinite dimensions,
John’s entire argument based on the invisibility of _E-E′_ from an
earth not in the center would fall to the ground, for all points may
be deemed the center of an infinite universe. See also below, p. 426,
note 118.

Ptolemy’s _Almagest_, I, 4, contains an argument aimed to demonstrate
why the earth must be at the center of the universe. John of
Holywood’s reasoning is a confused attempt to condense the argument of
Ptolemy into a short space.

Footnote 650:

_De imag. mundi_, I, 5.

Footnote 651:

_ibid._, I, 1.

Footnote 652:

_Otia imper._, vol. i, p. 885.

Footnote 653:

_Hist. schol._, Gen. 1, 4.

Footnote 654:

_Im. du monde_, I, 10.

Footnote 655:

_Expos. in hex._, cols. 735–736.

Footnote 656:

_De phil. mundi_, IV, 1.

Footnote 657:

Abelard (_loc. cit._) and William of Conches (_loc. cit._) compare the
shell of the egg to the fire, the skin to the air, the white to the
water, and the yolk to the earth. Daniel of Morley makes the same
comparison, as follows: “Mundus vero ad similitudinem ovi factus est
vel dispositus. Terra est in medio ut vitellum in ovo; circa hanc est
aqua ut circa vitellum album; circa aquam aer ut panniculus continens
album. Extra vero cetera concludens est ignis ad modum teste ovi” (_De
philosophia_, Sudhoff’s edit., p. 20).

Footnote 658:

Haskins, _Michael Scot_, 1921–1922, pp. 271–272; idem, _Studies_,
1924, pp. 295–296.

Footnote 659:

“Et terra modica est et prope fundum firmamenti est, quod si in medio
firmamenti esset, tunc eam oporteret maiorem esse et tunc etiam facile
caderet et dirumperetur, si tantam amplitudinem aeris sub se haberet,
quantam super se habet. Sed et ipsa ad meridiem quasi descensus montis
est, unde etiam ibi maiorem calorem de sole habet, quia sol et
firmamentum ipsi viciniora ibi sunt. Ad aquilonem vero alta est
adversum poenas, et etiam ibi maius frigus est, quia nec firmamentum
nec sol ibi prope terram sunt, sed quaedam maior amplitudo firmamenti”
(_Causae et curae_, II, Kaiser’s edit., p. 49).

Footnote 660:

_Liber div. op._, pars I, visio II, in: Migne, _Pat. lat._, vol.
cxcvii, cols. 751–755, 759–760. In a previous vision referred to in
the passage just cited and described in _Scivias_, I, visio III
(Migne, _op. cit._, col. 405), Hildegard saw the universe as an egg,
in which the earth appeared as follows: “Et in medio istorum
elementorum quidam arenosus globus plurimae magnitudinis erat; quem
eadem elementa ita circumdederant, quod nec hac nec illac dilabi
poterat. Sed dum interdum eadem elementa cum praedictis flatibus se
invicem concuterent, eumdem globum sua fortitudine aliquantulum
moveri. Et vidi inter aquilonem et orientem velut maximum montem, qui
versus aquilonem multas tenebras et versus orientem multam lucem
continebat; ita tamen quod nec lux illa ad tenebras, nec tenebrae ad
lucem pertingere poterant.”

Singer in his _Visions of Saint Hildegard_, 1917, pp. 22–30, discusses
Hildegard’s theories of the structure of the material universe as
revealed in the records of her visions. Particularly striking are the
colored illustrations taken from miniatures in manuscripts of her
works. Singer asserts (p. 22) that “the concentric structure of the
universe is a commonplace of mediaeval science, and is encountered,
for instance, in the works of Bede, Isidore, Alexander of Neckam,
Roger Bacon, Albertus Magnus, and Dante. To all these writers,
however, the universe is spherical. The egg-shape is peculiar to
Hildegard. Many of the _Mappaemundi_ of the Beatus and other types
exhibit the _surface_ of the habitable earth itself as oval, and it
was from such charts that Hildegard probably gained her conception of
an oval universe. In her method of orientation also she follows these
maps, placing east at the top of the page where we are accustomed to
place the north.” This statement would seem to be misleading if it
means that the comparison of the universe with an egg is peculiar to
Hildegard. As is shown by the texts cited above, p. 151, and below,
note 100, _ad fin._, this comparison was a frequent one throughout our
period. It does not, however, necessarily imply belief that the
universe is shaped like an egg, but merely that its concentric
structure corresponds with that of the egg. Furthermore, in the
opinion of the present writer, the fact that the Beatus and other maps
of the period show the surface of the habitable earth as an oval or
rectangle should not necessarily be taken as meaning that the
draftsmen of the maps believed that the earth was oval or rectangular.
The maps were highly conventionalized, and their shape was often
determined by the shape of the page upon which they were drawn. On the
other hand, Hildegard in her Scivias unquestionably meant to describe
an egg-shaped universe. Otherwise she would not have been so careful
to point out at the opening of the _Liber divinorum operum_ that in
the earlier vision described in _Scivias_ the universe had appeared as
an egg whereas in the vision she was about to describe it appeared as
a wheel.

Footnote 661:

“In medio quoque aeris terra posita est, ita scilicet ut aer aequali
mensura super terram, ac sub terra, et in utraque partes terrae sit”
(_Liber div. op._, pars I, visio IV, cap. 63).

Doubts have been thrown on the authenticity of the _Causae et curae_
as a work of Hildegard (see above, p. 396, note 8). The three passages
quoted in this and the two preceding notes show that in both phrasing
and substance the passage from the _Causae et curae_ bears marked
resemblances to the passages from the two other known works of
Hildegard, even though there is inconsistency in regard to the central
issue relating to the position of the earth. If the _Causae et curae_
were not written by Hildegard, it was assuredly the work of someone
thoroughly familiar with her writings.

Footnote 662:

_De imag. mundi_, I, 5.

Footnote 663:

_De phil. mundi_, IV, 2–3.

Footnote 664:

See above, p. 368, note 33.

Footnote 665:

John of Holywood, _De sphaera_, 1.

Footnote 666:

Similar arguments are set forth in Robert Grosseteste’s _De sphaera_,
Baur’s edit., p. 13.

Footnote 667:

See Alexander Neckam, _De nat. rer._, II, 14, where much the same
argument is given. Neckam adds that the roundness of drops of dew is
proof of the inherent tendency of water to assume a spherical shape.

Footnote 668:

The text upon which this accusation is based is from _Otia imper._,
II, 2, where Gervase says: “Nos tamen assignantes orbis divisionem
distributioni filiorum Noë, a quibus summa totius orbis coepit
partitio, orbem totius terrae Oceani limbo circumseptum et quadratura
statuimus secundum Pauli Orosii sententiam, eiusque tres partes Asiam,
Europam et Africam nominamus.” This was interpreted by Daunou
(_Discours_, 1824, p. 120)—who was followed by Santarem (_Essai_, vol.
i, 1848, p. 107), C. B. Jourdain (_Infl. d’ Arist._, 1861, pp. 19–20),
and others—as implying that Gervase believed the earth to be square.
On the other hand, Lecoy de La Marche rallied to the defense of
Gervase (_Connaiss. géogr._, 1884, p. 208). He argued that the passage
should be rendered thus: “Nous calculons, nous pensons, que le monde
terrestre est entouré et encadré (_quadratum_) par une ceinture de
mers” and that elsewhere Gervase asserts definitely that the earth is
a sphere: “Forma eius (terrae) rotunda est ad modum pilae” (_Otia
imper._, vol. i, p. 885). As a matter of fact Gervase was speaking of
the universe and not of the earth when he made this comparison with a
ball, and Lecoy de La Marche would have been more correct if he had
inserted _mundi_ after _eius_ instead of _terrae_. It seems,
nevertheless, that we are justified in rejecting the text first quoted
as furnishing any sure evidence that Gervase believed the earth to be
square, especially since he also adopted the old comparison of the
universe to an egg (_Otia imper._, _loc. cit._) with which it would
have been difficult, though not impossible, to reconcile a theory of a
square earth. Gervase, however, had an uncritical mind. His work was
in large measure one of compilation from the writings of others, and
it would not be surprising to find contradictory statements in it.
Quite as contradictory passages on the same subject occur in Isidore
and in most medieval writings of a similar encyclopedic character. See
above, p. 54. Lecoy de La Marche, it would seem, tried to do the
impossible when he attempted to show that Gervase had clear and
consistent ideas of a scientific nature.

There is no question, however, but that belief in the sphericity of
the earth was well grounded in the consciousness of many Western
Europeans of the late twelfth century. Other evidence of this beside
that already cited is furnished by the fact that in an ecstasy Alpis
(or Alpäis) of Cudot, of the diocese of Sens, was said to have seen
the entire world in the form of a globe, compact and united. The sun
was larger than the earth; and the latter was suspended in the midst
of the air like an egg surrounded by water on all sides (_Histoire
littéraire de la France_, vol. ix, 1750, p. 155). This vision was much
like those of Hildegard of Bingen; see above, p, 423, note 92.

Footnote 669:

_Causae et curae_, II; Kaiser’s edit., p. 49, quoted above, p. 423,
note 91. The fact that Hildegard here states that if the earth were in
the middle of the firmament it would have to be larger or else it
would fall, would seem to necessitate belief in a flat earth
contiguous with the firmament. The passage from _Causae et curae_, I,
Kaiser’s edit., p. 23, translated above, pp. 183–184, would also seem
to require the same belief.

Footnote 670:

See above, p. 54.

Footnote 671:

See passages quoted above, p. 423, notes 91 and 92.

Footnote 672:

_Scivias_, I, visio III, in: Migne, _Pat. lat._, vol. cxcvii, col.
405; _Liber div. op._, pars I, visio II, in: Migne, _op. cit._, cols.
751–755, 759–760; pars I, visio IV, in: Migne, _op. cit._, col. 869.

Footnote 673:

_De arca Noë myst._, 14. For a similar text see Daniel of Morley’s _De
philosophia_, Sudhoff’s edit., pp. 9–10.

Footnote 674:

See above, p. 369, notes 39 and 40.

Footnote 675:

_De imag. mundi_, I, 5.

Footnote 676:

_De sex d. op._, p. 58.

Footnote 677:

See above, p. 370, note 42; p. 401, note 58; p. 419, note 32.

Footnote 678:

_Quaest. nat._, 48 (49). Adelard’s arguments resemble those of
Aristotle in the _De caelo_. See above, p. 370, note 42; p. 401, note
58.

Footnote 679:

Similar Aristotelian arguments are to be found in Alexander Neckam’s
_De nat. rer._, I, 16. Neckam cites Aristotle as his authority.

Footnote 680:

_De sphaera_, 1.

Footnote 681:

“Haec [i. e. terrae] centrum in medio mundi ut punctus in medio
circuli aequaliter collocatur ...” etc. (_De imag. mundi_, I, 5).
“Tanta est firmamenti quantitas ut ipsi totalis terra collata quasi
punctum esse videatur” (Alexander Neckam, _De nat. rer._, I, 5).
Michael Scot, however, believed that “the distance to the extreme of
the waters beneath the earth equals the distance to the moon”
(Haskins, _Michael Scot_, 1921–1922, p. 272; idem, _Studies_, 1924,
pp. 295–296).

Footnote 682:

“Cum ergo corpus solis et terrae aequalia non sunt, quippe cum sit sol
octies major quam terra, umbram terrae κυλίνδρος esse non potest” (_De
phil. mundi_, II, 32).

Footnote 683:

_Im. du monde_, I, 14. This is based on Neckam, _loc. cit._

Footnote 684:

_Im. du monde_, III, 16. Neckam (_De nat. rer._, I, 8), with whose
text the _Image du monde_ here corresponds, borrowed from Ptolemy
certain details in regard to the relative sizes of sun, earth,
planets, and stars. The sun is by far the largest body in the
universe, 166 and a fraction times larger than the earth. Next after
the sun rank fifteen of the largest fixed stars; Jupiter ranks in the
third place, Saturn in the fourth, the remainder of the fixed stars in
the fifth, Mars in the sixth, the earth in the seventh, Venus in the
eighth, the moon in the ninth, and Mercury in the tenth. See Ptolemy,
_Almagest_, V, 16.

Footnote 685:

_De sphaera_, 1.

Footnote 686:

“Item si intelligatur superficies plana super centrum terrae dividens
eam in duo aequalia, et per consequens ipsum firmamentum, oculus
igitur existens in centro terrae videret medietatem firmamenti;
idemque existens in superficie terrae videret eandem medietatem. Ex
his colligitur quod insensibilis est quantitas terrae quae est a
superficie ad centrum et per consequens quantitas totius terrae
insensibilis est respectu firmamenti” (_loc. cit._).

John of Holywood’s argument is here closely related to that employed
by him to prove that the earth must be in the center of the universe
as set forth above, p. 422, note 81. It would seem probable that by
“an eye stationed in the center of the earth” he means an eye on a
line between the center of the earth and the _medietas firmamenti_,
and by “the same (eye) stationed on the surface of the earth” he means
on the surface at a point where a line at right angles to the line
from the center of the earth to the _medietas firmamenti_ cuts the
surface of the earth. Referring, then, to Figure 10, p. 422, above,
let us assume that line _E-E′_ represents the plane through the
_medietas firmamenti_ and the center of the earth (_C_). When the
earth is at the center of the universe line _C-N′_ will represent the
line drawn at right angles to this plane. With a universe of infinite
dimensions obviously _N′-E_ and _N′-E′_ would be parallel to _E-E′_,
and the _medietas firmamenti_ would be visible from _N′_. John assumes
that the universe is so large in relation to the earth that the area
around _N′_ whence _E-E′_ would be invisible is negligible.

Footnote 687:

_Almagest_, I, 5.

Footnote 688:

_De imag. mundi_, I, 5.

Footnote 689:

_Im. du monde_, III, 15.

Footnote 690:

_Liber floridus_, Bibliothèque Nationale MSS., fonds latin, no. 8865,
fol. 55vo. A note illustrating a diagram on the same page of the same
manuscript gives 240,000 stades for the circumference, one of the two
figures of Posidonius. See above, p. 16.

Footnote 691:

_De sphaera_, 1.

Footnote 692:

See the various works referred to on pp. 95–98, above. Robert
Grosseteste’s _De sphaera_ includes a very clear discussion of the
main elements of geocentric astronomy as taught in the early
thirteenth century.

Footnote 693:

See above, pp. 17–18.

Footnote 694:

_De mundi univ._, p. 17.

Footnote 695:

_De imag. mundi_, I, 6.

Footnote 696:

_Otia imper._, vol. i, p. 892.

Footnote 697:

_Etym._, XIII, 6.

Footnote 698:

_De phil. mundi_, III, 2–3.

Footnote 699:

“Extra tres autem partes orbis, quarta pars trans oceanum interior est
in meridie, quae solis ardore incognita nobis est. In cuius finibus
antipodas fabulosae inhabitare produntur.” Text (not legible on our
Fig. 2, p. 69) from Miller, _Mappaemundi_, vol. i, 1895, p. 58. See
Isidore, _Etym._, XIV, 5, 17. Gervase of Tilbury describes the austral
continent in similar terms: “Porro inter mare rubrum et Oceanum plaga
torrida est, propter calorem nobis incognita, in cuius finibus
antipodes esse dicuntur” (_Otia imper._, vol. ii, p. 760).

Footnote 700:

See above, p. 385, note 58.

Footnote 701:

Miller, _op. cit._, vol. iii, 1895, p. 50.

Footnote 702:

“Hic antipodes nostri habitant, sed noctem diversam diesque contrarios
perferunt ...” (_loc. cit._).

Footnote 703:

See above, p. 185.

Footnote 704:

_Microcosmus_, Bibliothèque Nationale MSS., fonds St. Victor, no. 738,
fol. 18vo.

Footnote 705:

_De sphaera_, Baur’s edit., pp. 24–25. Amphitrite is also discussed in
the _Liber de essentiis_ of Hermann the Dalmatian, dating from 1143,
in a geographical passage published recently by Haskins (_Studies_,
1924, pp. 62–64): “Hinc vero per Amphitritis sinus ab Athlante Libico
Strixisque inflexu per littora Gaditana per confinia Thiles proprie
Temiscirios campos e vicino portibus Caspiis usque ad Caucason et
Ethiopici Gangis effluxus.” In another passage of the same work quoted
by Haskins (_op. cit._, p. 64) Hermann indicates that in the latitude
of Lisbon and Toledo eight equal land stages are the equivalent of 4°
of longitude, that the width of Amphitrite is 44°, or the equivalent
of eighty-eight equal land stages, and that there is an opinion that
paradise lies beyond this ocean. “... spatium ... dierum 44 que
secundum quod ratio tribuit est dimidia latitudo Amphitritis, tota
(totam) videlicet itineris terrestris equabilis dierum fere 88. Tantum
ergo spatii vel etiam aliquanto plus que ratio hucusque transnatari
prohibuit nondum audivimus nisi forte illa quam (que) exposuimus. In
ea tamen parte non modica est opinio eam esse regionem quam paradisum
vocant, cuius indicio sunt signa tam ab oriente quam ab occidente.” In
this same passage Hermann states that Toledo is 62° west of Arin (see
above, p. 86). One would therefore expect the width of Amphitrite to
be 44° in order to bring to 90° the total distance from Arin to the
prime meridian in the midst of Amphitrite (Haskins, _op. cit._, p. 64,
note 202).

Footnote 706:

_Im. du monde_, II, 1.

Footnote 707:

“Quid significat globus aureus, qui regum manibus gestatur?
Aureus ille globus pomum vel palla vocatur,
Unde figuratum mundum gestare putatur,
Quando coronatur, palla ferenda datur.
Significat mundum forma peribente rotundum,
Intus habet plenum terrestri pondere fundum,
Quem tenet archanum palla ferenda manu.
Hec fuit ex terris mundi collecta quaternis;
Ut foret imperii manibus gestenda supernis.
Hac tulit imperium Iulius arte suum.
Taliter hunc mundum gestat manus una rotundum,
Regius includit sic omnia climata pugnus,
Taliter omne quod est regia pompa tenet.”
—_Pantheon_, particula xxvi, 4; in: _Mon. Germ.
hist._, Scriptores, vol. xxii, pp. 274–275; pars
19 in Herold’s edit., 1559, col. 620.

Footnote 708:

Eugen Oberhummer, _Das britische Weltreich und die imperialistischen
Staatenbildung früherer Zeit_, in: Mitteilungen der Geographischen
Gesellschaft in Wien, vol. lxiii, 1920, pp. 108–109. See also Miller,
_Mappaemundi_, vol. iii, 1895, pp. 129–131.

Footnote 709:

“In den bûchen vant er ouch dô,
daz eine werlt wêre sô
gelegen under dirre erde:
swen ez hie naht werde,
daz ez danne dort tac sî.”
Schröder, _Sanct Brandan_, 1871, p. 51.

Footnote 710:

_De nupt. Phil. et Merc._, VI, 602–608.

Footnote 711:

The word _antipodes_ as we employ it at the present time refers rather
to the _antichthones_ of Capella. These terms, however, were not used
with consistency by classical and medieval writers.

Footnote 712:

_In som. Scip. com._, II, 5.

Footnote 713:

_De phil. mundi_, IV, 3. Alexander Neckam also did not deny the
abstract possibility of the existence of antipodeans: “Nonne enim et
antipodes sub pedibus nostris esse dicuntur. Si tamen philosophice
loqui volueris, non magis sunt sub pedibus nostris quam nos sub
pedibus eorum. Sed numquid de primis parentibus descenderunt
antipodes? Secundum Augustinum non sunt antipodes, sed doctrinae causa
aut figmenti ita dici solet” (_De nat. rer._, pp. 159–160).

Footnote 714:

_Otia imper._, vol. i, p. 975.

Footnote 715:

“Mira res a messibus subterraneis veniens hyemalia frigora videt in
nostro haemispherio perseverare, quod utique solis absentiae ac
vicariae praesentiae merito adscribendum duxi” (_loc. cit._).

Footnote 716:

Duhem, _Système_, vol. iii, 1915, pp. 64–65. For data relating to
another attack on Macrobius’ cosmography preserved in a
twelfth-century manuscript in Cambrai see Haskins, _Studies_, 1924,
pp. 98–103.

Footnote 717:

The Latin text of the passage of which this is a free paraphrase, runs
as follows: “Suscepto enim semel, quatuor habitationes hominum esse,
quorum ad se invicem nulla penitus possit esse per naturam commeandi
licentia, dic age, quomodo verum erit, quod Sancta, & Apostolica
rationalibiliter confitetur Ecclesia, Salvatorem videlicet, per primos
Patres ab ipsis, ut ita dicam, huius Mundi cunabulis praesignatum, & a
Patriarchis, & Prophetis consequenter multifarie, & multis evidentibus
modis praefiguratum, tandem in plenitudine temporis, ineffabilibus
humilitatis, & caritatis suae operibus cognitum, ac clarificatum, in
salutem totius humani generis advenisse, si tria hominum genera
excepta sunt, quae praedictus Macrobius praeter hanc habitabilem, quam
incolumus, secundum zonarum Coeli, & terrae temperiem, posse esse
persuadet, ad quae tantae salubritatis notitia pervenire non potuit?
Ubi est, quod ille fidelis, quem invenit Dominus virum secundum cor
suum, in spiritu veritatis clamat: ‘Ante conspectum gentium revelavit
justitiam suam Deus.’ Et ibidem: ‘Videbunt omnes fines terrae salutare
Dei nostri,’ si aliqui fines terrae sunt ab hominibus inhabitati, ad
quos sonus Prophetarum, & Apostolorum nostrorum prohibente natura per
inaccessibiles aquarum, frigorum, calorumve distantias transire
nequivit?” (Manegold, _Opusculum_, Muratori’s edit., 1713, pp.
175–176.)

Footnote 718:

Bibliothèque Nationale MSS., fonds latin, no. 14704, fol. 114vo. See
also above, p. 96.

Footnote 719:

_Dialogus_, I, in: Migne, _Pat. lat._, vol. clvii, col. 547.
Bibliothèque Nationale MSS., fonds latin, no. 10722, fol. 77ro, gives
a diagram illustrating the eccentricity of the sun’s orbit. In accord
with the Moslem cartographic tradition, south is at the top.

Footnote 720:

Plato of Tivoli’s translation of Al-Bāttanī’s _Astronomy_, Bologna
edit., 1645, p. 26 (from _Opus astron._, 6, Nallino’s edit., pt. i,
1903, p. 14). Essentially the same ideas, though expressed in somewhat
different terms, are to be found in the _Liber de essentiis_ of
Hermann the Dalmatian. See above, p. 400, note 48.

Footnote 721:

_De lineis angulis_, etc., Baur’s edit., p. 64. Roger Bacon’s views on
the influence of pyramidal rays as set forth in _Opus majus_ (Bridges’
edit., vol. i, 1897, pp. 117–143) are discussed in Werner, _Kosm.
Roger Baco_, 1879, pp. 597–600. Bacon’s indebtedness to Grosseteste,
however, does not seem to be sufficiently emphasized by Werner. See
above, pp. 179–180 and p. 408, note 97.

Footnote 722:

_De natura locorum_, Baur’s edit., pp. 66–67.

Footnote 723:

_De sphaera_, Baur’s edit., pp. 20–24.

Footnote 724:

_De natura locorum_, Baur’s edit., p. 69.

Footnote 725:

Emmanuel de Martonne, _Traité de géographie physique_, 3rd edit.,
Paris, 1920, p. 40.

Footnote 726:

_De sphaera_, Baur’s edit., p. 25.

Footnote 727:

_Opus majus_, Bridges’ edit., vol. i, 1897, p. 192. See Duhem,
_Système_, vol. iii, 1915, pp. 416–419.

Footnote 728:

_De natura locorum_, Baur’s edit., pp. 68–69.

Footnote 729:

See above, pp. 179–180, and below, p. 431, note 7.

NOTES