1. You inquire into the numbers according to music as follows:
setting down the extremes, as for example, VI and XII, you see by how
many units VI is surpassed by XII, and it is by VI units; you square
it; six times six make XXXVI. You add those first-mentioned extremes,
VI and XII; together they make XVIII; you divide XXXVI by XVIII;
two is the result. This you add to the smaller amount, VI namely;
the result will be VIII and it will be the mean between VI and XII.
Because VIII surpasses VI by two units, that is by a third of six,
and VIII is surpassed by XII by four units, a third part [of twelve].
By what part, then, the mean surpasses, by the same is it surpassed.
2. Just as this proportion exists in the universe, being constituted
by the revolving circles, so also in the microcosm—not to speak of
the voice—it has such great power that man does not exist without
harmony.[263]
[263] The general sense of the passage: “ut sine ipsius
perfectione etiam homo symphoniis carens non consistat.” 3, 23,
2. See p. 65.
ON ASTRONOMY
INTRODUCTION
The science of astronomy, in its history from the great period
of Greece down to the dark ages, furnishes almost as complete a
spectacle of decay as does geometry. It is quite certain “that
Aristarchus taught the annual motion of the earth around the sun, and
both he and Seleukus taught the diurnal rotation of the earth,”[264]
but the general scientific development of the age was not sufficient
to assimilate this advanced theory, and astronomers went back to a
geocentric universe. Strange to say, the later rise of practical
astronomy at Alexandria, and the development of pure mathematics,
did not secure a return to the more advanced theory, the efforts of
the later astronomers being devoted, not to a reconsideration of the
fundamental theses of the subject, but to putting the geocentric
theory on a secure mathematical basis. The greatest of these
astronomers, Ptolemy (second century A.D.), left in his _Syntaxis_ a
comprehensive summing up of mathematical astronomy.
[264] J. L. E. Dreyer, _History of the Planetary Systems from
Thales to Kepler_ (Cambridge, 1906), p. 141.
Among the Romans no scientists arose to assimilate the results of the
work of the Greeks, and sound ideas as to the form of the universe
were rare even in the most intelligent circles. Since systematic
observation was not practiced, and a knowledge of the higher
mathematics did not exist among the Romans, their astronomy was a
matter of tradition and authority. Therefore upon the acceptance of
Christianity and the realization that there was a conflict between
the Greek and the Hebrew cosmologies, it was a comparatively easy
matter to accept the Scriptures instead of the secular writers as the
source of authority.
In Isidore’s ideas on cosmology a curious inconsistency appears. On
the one hand, he shows that he regards the words of the Scripture as
the final authority, and he frequently gives expression to primitive
notions in accord with the Hebrew cosmology. On the other hand, he
displays a greater liberality than is shown by his predecessor,
Cassiodorus, or by any other Christian writer in the Latin language
up to his time, in borrowing from the pagan writers on astronomy.
The explanation of this may be that it was a natural reaction
from dogmatic narrowness, made possible for him by the favorable
conditions offered by contemporary Spain; but the more probable
supposition is that his natural vagueness of mind and lack of
critical power enabled him to be much more liberal in effect than he
in reality would have wished to be.[265]
[265] See Introduction, p. 51.
Another feature of Isidore’s _De Astronomia_ that deserves notice
is his attitude toward the forbidden science of astrology.[266] He
denies a fundamental assumption of the science, namely, that Mercury
and Venus, for example, have as planets an influence analogous to
their characters in mythology, and he asserts that the names of the
planets and fixed stars, as used in astrology, have no validity. This
was vigorous reasoning for the dark ages, and to all appearance it
completely cut away the foundation of astrology.[267] Nevertheless
Isidore believed that astrology had some truth—the magi who announced
the birth of Christ were, he believed, astrologers—but this truth
arose “out of a deadly alliance of men and bad angels.” His
attitude, then, seems to be that astrologers may forecast the future,
but that their ability to do so depends on the assistance of demons,
and that the drawing up of nativities is merely a pretence to cloak
this partnership.
[266] Tannery in his _Recherches sur l’histoire de l’astronomie
ancienne_ (Paris, 1893), has an interesting discussion of the
successive names of the science of the heavenly bodies. He
attributes the revival of the older term astronomy about the
end of the third century A.D., to the association of the term
astrology with divination. In Varro the name used was astrology.
[267] 3, 71, 21–40. See pp. 152–4.
Little is known of astronomy as a subject in the Roman schools. It
no doubt formed part of the curriculum, but apparently no text-book
was produced between the time of Varro and that of Martianus Capella.
The three school treatises of late Roman and early medieval times,
written by Capella, Cassiodorus, and Isidore, were all the work
of educational encyclopedists from whom nothing of a scientific
character could be expected.
EXTRACTS
Book III, Chapter 24. On the name of astronomy.
1. Astronomy is the law of the stars, and it traces with inquiring
reason the courses of the heavenly bodies, and their figures, and the
regular movements of the stars with reference to one another and to
the earth.