In the original algorithm of 1846 Jacobi would search the whole upper triangle of matrix A' and set the largest element to zero. But computers are incapable of finding the largest element simply by glancing at the whole matrix, the way we do. They can only do things like that by looking at each element in separation from others.
Computers are woefully shortsighted.
In our case we'll annihilate elements in a strict order by proceeding down the rows: P12, P13, P14 and so on, then P23, P24, etc. One such set of n(n-1)/2 Jacobi rotations is called a sweep.