The fourth section Hipparchus certainly manages
better, though he still maintains the same censorious tone,
and obstinacy in sticking to his first hypotheses, or others
similar. He properly objects to Eratosthenes giving as the
length of this section a line drawn from Thapsacus to Egypt,
as being similar to the case of a man who should tell us that
the diagonal of a parallelogram was its length. For Thapsacus and the coasts of Egypt are by no means under the
same parallel of latitude, but under parallels considerably
distant from each other,The difference of latitude between Thapsacus and Pelusium is about 4° 27′. and a line drawn from Thapsacus to
Egypt would lie in a kind of diagonal or oblique direction
between them. But he is wrong when he expresses his surprise that Eratosthenes should dare to state the distance between Pelusium and Thapsacus at 6000 stadia, when he says
there are above 8000. In proof of this he advances that the
parallel of Pelusium is south of that of Babylon by more than
2500 stadia, and that according to Eratosthenes (as he supposes)
the latitude of Thapsacus is above 4800 stadia north of that
of Babylon; from which Hipparchus tells us it results that
[between Thapsacus and Pelusium] there are more than
8000 stadia. But I would inquire how he can prove that
Eratosthenes supposed so great a distance between the parallels of Babylon and Thapsacus? He says, indeed, that such
is the distance from Thapsacus to Babylon, but not that there
is this distance between their parallels, nor yet that Thapsacus
and Babylon are under the same meridian. So much the
contrary, that Hipparchus has himself pointed out, that, according to Eratosthenes, Babylon ought to be east of Thapsacus
more than 2000 stadia. We have before cited the statement
of Eratosthenes, that Mesopotamia and Babylon are encircled
by the Tigris and Euphrates, and that the greater portion of
the Circle is formed by this latter river, which flowing north
and south takes a turn to the east, and then, returning to a
southerly direction, discharges itself [into the sea]. So long
as it flows from north to south, it may be said to follow a
southerly direction; but the turning towards the east and
Babylon is a decided deviation from the southerly direction,
and it never recovers a straight course, but forms the circuit
we have mentioned above. When he tells us that the journey
from Babylon to Thapsacus is 4800 stadia, he adds, following
the course of the Euphrates, as if on purpose lest any one
should understand such to be the distance in a direct line, or
between the two parallels. If this be not granted, it is altogether a vain attempt to show that if a right-angled triangle
were constructed by lines drawn from Pelusium and Thapsacus to the point where the parallel of Thapsacus intercepts
the meridian of Pelusium, that one of the lines which form the
right angle, and is in the direction of the meridian, would be
longer than that forming the hypotenuse drawn from Thapsacus to Pelusium.The text here is evidently corrupt. Worthless, too, is the argument in connexion with this, being the inference from a proposition not
admitted; for Eratosthenes never asserts that from Babylon to
the meridian of the Caspian Gates is a distance of 4800
stadia. We have shown that Hipparchus deduces this from
data not admitted by Eratosthenes; but desirous to controvert
every thing advanced by that writer, he assumes that from
Babylon to the line drawn from the Caspian Gates to the
mountains of Carmania, according to Eratosthenes' description, there are above 9000 stadia, and from thence draws his
conclusions.