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 supplemento