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have told you of the virtue of the firmament, as briefly
as we could, we will now describe below, briefly enough,
how the world was measured, in height and
depth, in length and width, by those who knew
the seven arts, geometry being one of them. [Geometry] is
the one by which the sun, the moon, the earth, and the
firmament are measured, internally and externally,
to determine their size. [It also calculates] how far it
is from the earth to the firmament and the size of the stars.
For this is proven by careful examination. And those
who have discovered this art perceived that they could
never properly know astronomy nor the nature of
the stars without knowing anything about their measurements,
and for that reason they wanted to measure them and prove
their size. [rubric:] Why and how one measures the world. [/rubric]
First of all, the ancient philosophers wanted to measure the
size of the world all around the earth, before any other task,
by which they could prove the height of the stars and the
size of the firmament all around. They did not find
anything larger to measure. And then