cone, which cone is made tangible and measurable by the shadows
cast by the non-luminous bodies; since, continuing, he clearly
states in proposition nine, that "when the sun is totally
eclipsed, an observer on the earth's surface is at an apex of a
cone comprising the moon and the sun." Various propositions deal
with other relations of the shadows which need not detain us
since they are not fundamentally important, and we may pass to
the final conclusions of Aristarchus, as reached in his
propositions ten to nineteen.

Now, since (proposition ten) "the diameter of the sun is more
than eighteen times and less than twenty times greater than that
of the moon," it follows (proposition eleven) "that the bulk of
the sun is to that of the moon in ratio, greater than 5832 to 1,
and less than 8000 to 1."

"Proposition sixteen. The diameter of the sun is to the diameter
of the earth in greater proportion than nineteen to three, and
less than forty-three to six.

"Proposition seventeen. The bulk of the sun is to that of the
earth in greater proportion than 6859 to 27, and less than 79,507
to 216.

"Proposition eighteen. The diameter of the earth is to the
diameter of the moon in greater proportion than 108 to 43 and
less than 60 to 19.

"Proposition nineteen. The bulk of the earth is to that of the
moon in greater proportion than 1,259,712 to 79,507 and less than
20,000 to 6859."

Such then are the more important conclusions of this very
remarkable paper--a paper which seems to have interest to the
successors of Aristarchus generation after generation, since this
alone of all the writings of the great astronomer has been
preserved. How widely the exact results of the measurements of
Aristarchus, differ from the truth, we have pointed out as we
progressed. But let it be repeated that this detracts little from
the credit of the astronomer who had such clear and correct
conceptions of the relations of the heavenly bodies and who
invented such correct methods of measurement. Let it be
particularly observed, however, that all the conclusions of
Aristarchus are stated in relative terms. He nowhere attempts to
estimate the precise size of the earth, of the moon, or of the
sun, or the actual distance of one of these bodies from another.
The obvious reason for this is that no data were at hand from
which to make such precise measurements. Had Aristarchus known
the size of any one of the bodies in question, he might readily,
of course, have determined the size of the others by the mere
application of his relative scale; but he had no means of
determining the size of the earth, and to this extent his system
of measurements remained imperfect. Where Aristarchus halted,
however, another worker of the same period took the task in hand
and by an altogether wonderful measurement determined the size of
the earth, and thus brought the scientific theories of cosmology
to their climax. This worthy supplementor of the work of
Aristarchus was Eratosthenes of Alexandria.


ERATOSTHENES, "THE SURVEYOR OF THE WORLD"

An altogether remarkable man was this native of Cyrene, who came
to Alexandria from Athens to be the chief librarian of Ptolemy
Euergetes. He was not merely an astronomer and a geographer, but
a poet and grammarian as well. His contemporaries jestingly
called him Beta the Second, because he was said through the
universality of his attainments to be "a second Plato" in
philosophy, "a second Thales" in astronomy, and so on throughout
the list. He was also called the "surveyor of the world," in
recognition of his services to geography. Hipparchus said of him,
perhaps half jestingly, that he had studied astronomy as a
geographer and geography as an astronomer. It is not quite clear
whether the epigram was meant as compliment or as criticism.
Similar phrases have been turned against men of versatile talent
in every age. Be that as it may, Eratosthenes passed into history
as the father of scientific geography and of scientific
chronology; as the astronomer who first measured the obliquity of
the ecliptic; and as the inventive genius who performed the
astounding feat of measuring the size of the globe on which we
live at a time when only a relatively small portion of that
globe's surface was known to civilized man. It is no discredit to
approach astronomy as a geographer and geography as an
astronomer if the results are such as these. What
Eratosthenes really did was to approach both astronomy and
geography from two seemingly divergent points of attack--namely,
from the stand-point of the geometer and also from that of the
poet. Perhaps no man in any age has brought a better combination
of observing and imaginative faculties to the aid of science.

Nearly all the discoveries of Eratosthenes are associated with
observations of the shadows cast by the sun. We have seen that,
in the study of the heavenly bodies, much depends on the
measurement of angles. Now the easiest way in which angles can be
measured, when solar angles are in question, is to pay attention,
not to the sun itself, but to the shadow that it casts. We saw
that Thales made some remarkable measurements with the aid of
shadows, and we have more than once referred to the gnomon, which
is the most primitive, but which long remained the most
important, of astronomical instruments. It is believed that


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