To put this thread in context, note that Hewitt's discussion of the
Earth and Moon shadows is intended to explain Aristarchus' estimation
of the ratio of the size of the Earth to that of the Moon. Knowing
that the Earth's shadow tapers by (approximately) one Moon diameter
on the way to the Moon and that the remaining shadow is still 2.5
times the diameter of the Moon, it is trivial (if also clever) to
deduce that the Earth's diameter is about 3.5 times that of the Moon.
I think Hewitt may be fairly criticized for tossing off the remark
that the Earth's shadow tapers by the same amount as the Moon's both
because it isn't obvious and because it isn't even (quite) true.
Nevertheless, showing that the Earth's shadow tapers at *nearly* the
same rate as the Moon's is a pretty simple exercise in geometry. The
result is that the Earth's shadow tapers about 99.4% of the amount
that the Moon's shadow does.