Archimedes' cattle problem has two versions, based on alternate readings of its second paragraph; what are...

Problem

Archimedes' cattle problem has two versions, based on alternate readings
of its second paragraph; what are these two readings?

    If thou art diligent and wise, O stranger, compute the number of
    cattle of the Sun, who once upon a time grazed on the fields of the
    Thrinacian isle of Sicily, divided into four herds of different
    colours, one milk white, another a glossy black, a third yellow and
    the last dappled.  In each herd were bulls, mighty in number
    according to these proportions: Understand, stranger, that the white
    bulls were equal to a half and a third of the black together with the
    whole of the yellow, while the black were equal to the fourth part of
    the dappled and a fifth, together with, once more, the whole of the
    yellow.  Observe further that the remaining bulls, the dappled, were
    equal to a sixth part of the white and a seventh, together with all
    of the yellow.  These were the proportions of the cows: The white
    were precisely equal to the third part and a fourth of the whole herd
    of the black; while the black were equal to the fourth part once more
    of the dappled and with it a fifth part, when all, including the
    bulls, went to pasture together.  Now the dappled in four parts were
    equal in number to a fifth part and a sixth of the yellow herd.
    Finally the yellow were in number equal to a sixth part and a seventh
    of the white herd.  If thou canst accurately tell, O stranger, the
    number of cattle of the Sun, giving separately the number of well-fed
    bulls and again the number of females according to each colour, thou
    wouldst not be called unskilled or ignorant of numbers, but not yet
    shalt thou be numbered among the wise.

    But come, understand also all these conditions regarding the cattle
    of the Sun.  When the white [Editor: "while" in the original] bulls
    mingled their number with the black, they stood firm, equal in depth
    and breadth, and the plains of Trinacia, stretching far in all ways,
    were filled with their multitude.  Again, when the yellow and the
    dappled bulls were gathered into one herd they stood in such a manner
    that their number, beginning from one, grew slowly greater till it
    completed a triangular figure, there being no bulls of other colours
    in their midst nor none of them lacking.  If thou art able, O
    stranger, to find out all these things and gather them together in
    your mind, giving all the relations, thou shalt depart crowned with
    glory and knowing that thou hast been adjudged perfect in this
    species of wisdom.

Complaints as to the wording of this puzzle may be directed variously to
the English translator (Ivor Thomas in 1939), its editor (G. E. Lessing
in 1773) or the famous mathematician with whom this epigrammatic puzzle
is primarily associated.

The straightforward representation of this puzzle unfortunately produces
what has been described as an intolerably difficult solution.  This has
led to two versions of the problem, based on alternate readings of the
second paragraph.  What are these two readings?

-- Peter Suzman <suzman@netcom.com>