One more that need explaining

This problem was proposed by Archimedes about 2200 years ago.

Compute, O friend the host of oxen of the sun, giving thy mind thereto, if thou hast a share of wisdom. Compute the number that once grazed upon the plains of the Sicilian isle Trinacria (Sicily itself) and that were divided according to color into four herds, one milk-white, one black, one yellow and one dappled. The number of bulls formed the majority in each herd and the relations between them were:
1. White bulls = yellow bulls + (1/2 + 1/3) black bulls
2. Black bulls = yellow bulls + (1/4 + 1/5) dappled bulls
3. Dappled bulls = yellow bulls + (1/6 + 1/7) white bulls
4. White cows = (1/3 + 1/4) black herd
5. Black cows = (1/4 + 1/5) dappled herd
6. Dappled cows = (1/5 + 1/6) yellow herd
7. Yellow cows = (1/6 + 1/7) white herd

If thou canst give O friend the number of bulls and cows in each herd, thou art not all knowing nor unskilled in number, but not yet to be counted among the wise. Consider however the additional relations between the bulls of the sun:
8. White bulls + Black bulls = triangular number
9. Dappled bulls + yellow bulls = square number

When thou hast then computed the totals of the herd, O friend go forth as the conqueror, and rest assured that thou art proved most skilled in the science of numbers.

Whim