But taking this for granted, and proving, as he imagines,
that, according to Eratosthenes, Babylon is east of Thapsacus
rather more than 1000 stadia, he draws from this false hypothesis a new argument, which he uses to the following
purpose; and says, If we suppose a right line drawn from
Thapsacus towards the south, and another from Babylon perpendicular thereto, a right-angled triangle would be the result;
whose sides should be, 1. A line drawn from Thapsacus to
Babylon; 2. A perpendicular drawn from Babylon to the
meridian of Thapsacus; 3. The meridian line of Thapsacus.
The hypotenuse of this triangle would be a right line drawn
from Thapsacus to Babylon, which he estimates at 4800 stadia.
The perpendicular drawn from Babylon to the meridian of
Thapsacus is scarcely more than 1000 stadia; the same
amount by which the line drawn [from the Caspian Gates] to
Thapsacus exceeds that [from the common frontier of Carmania and Persia] to Babylon. The two sides [of the triangle] being given, Hipparchus proceeds to find the third,
which is much greater than the perpendicularOr second side. aforesaid. To
this he adds the line drawn from Thapsacus northwards to
the mountains of Armenia, one part of which, according to
Eratosthenes, was measured, and found to be 1100 stadia; the
other, or part unmeasured by Eratosthenes, Hipparchus estimates to be 1000 stadia at the least: so that the two together
amount to 2100 stadia. Adding this to the [length of the]
side upon which falls the perpendicular drawn from Babylon,
Hipparchus estimated a distance of many thousand stadia
from the mountains of Armenia and the parallel of Athens
to this perpendicular, which falls on the parallel of Babylon.Hipparchus found by this operation that the distance from the parallel of Babylon to that of the mountains of Armenia was 6795 stadia.
From the parallel of AthensSee Humboldt, Cosmos ii. p. 556, note, Bohn's edition. to that of Babylon he shows
that there cannot be a greater distance than 2400 stadia, even
admitting the estimate supplied by Eratosthenes himself of
the number of stadia which the entire meridian contains;Eratosthenes estimated 252,000 stadia for the circumference of the earth.
and that if this be so, the mountains of Armenia and the
Taurus cannot be under the same parallel of latitude as
Athens, (which is the opinion of' Eratosthenes,) but many
thousand stadia to the north, as the data supplied by that
writer himself prove.

But here, for the formation of his right-angled triangle, Hipparchus not only makes use of propositions already overturned,
but assumes what was never granted, namely, that the hypotenuse subtending his right angle, which is the straight line
from Thapsacus to Babylon, is 4800 stadia in length. What
Eratosthenes says is, that this route follows the course of the
Euphrates, and adds, that Mesopotamia and Babylon are encompassed as it were by a great circle formed by the Euphrates and
Tigris, but principally by the former of these rivers. So that
a straight line from Thapsacus to Babylon would neither follow
the course of the Euphrates, nor yet be near so many stadia
in length. Thus the argument [of Hipparchus] is overturned.
We have stated before, that supposing two lines drawn from
the Caspian Gates, one to Thapsacus, and the other to
the mountains of Armenia opposite Thapsacus, and distant
therefrom, according to Hipparchus's own estimate, 2100
stadia at the very least, neither of them would be parallel to
each other, nor yet to that line which, passing through Babylon, is styled by Eratosthenes the southern side [of the third
section]. As he could not inform us of the exact length of
the route by the mountains, Eratosthenes tells us the distance between Thapsacus and the Caspian Gates; in fact, to
speak in a general way, he puts this distance in place of the
other; besides, as he merely wanted to give the length of the
territory between Ariana and the Euphrates, he was not particular to have the exact measure of either route. To pretend
that he considered the lines to be parallel to each other, is
evidently to accuse the man of more than childish ignorance,
and we dismiss the insinuation as nonsense forthwith.