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 Equally broad and deep; the far-flung Silician meadows Now were thoroughly filled, covered by great crowds of bulls. But when the brown and the spotted bulls were assembled together, Then was a triangle formed; one bull stood at the tip; None of the brown-colored bulls was missing, none of the spotted, Nor was there one to be found different in color from these. If this, too, you discover and grasp it well in your thinking, If, my friend, you supply every herd's make-up and count, Then with justice proclaim yourself victor and march about proudly, For your fame will glow bright all through the world of the wise.