Archimedes' Problema Bovinum

Number the sun god's cattle, my friend, with perfect precision.
Reckon them up with great care, if any wisdom you'd claim:
How many cattle were there that once did graze in the meadows
On the Sicilian isle, sorted by herds into four,
Each of these four herds differently colored: the first herd was milk-white,
Whereas the second gleamed in a deep ebony black.
Brown was the third group, the fourth was spotted; in every division
Bulls of respective hues greatly outnumbered the cows.
Now, these were the proportions among the cattle:  the white ones
Equaled the number of brown, adding to that the third part
Plus one half of the ebony cattle all taken together.
Further, the group of the black equaled one fourth of the flecked
Plus one fifth of them, taken along with the total of brown ones.
Finally, you must assume, friend, that the total with spots
Equaled a sixth plus a seventh part of the herd of white cattle,
Adding to that the entire herd of brown-colored kine.

Yet quite different proportions held for the female contingent:
Cows with white-colored hair equaled in number one third
Plus one fourth of the black-hued cattle, the males and the females.
Further, the cows colored black totaled in number one fourth
Plus one fifth of the whole spotted herd, in this computation
Counting in each spotted cow, each spotted bull in the group.
Likewise, the spotted cows comprised the fifth and sixth part
Out of the total of brown cattle that went out to graze.
Lastly, the cows colored brown made up a sixth and a seventh
out of the white-colored herd, female and male alike.
If, my friend, you can tell me exactly what was the number
gathered together there then, also the accurate count
Color by color of every well-nourished male and each female
Then with right you'll be called skillful in keeping accounts.

But you will not be reckoned a wise man yet; if you would be,
Come and answer me this, using new data I give:
When the entire aggregation of white bulls and that of the black bulls
joined together, they all made a formation that was