1. To show or demonstrate clearly
2. To overcome, subdue, or prevail over
From Latin evincere, 'to vanquish', which comes from e-, 'out', and vincere, 'to conquer'
From the United States' Declaration of Independence: "But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security."
So which definition of evince is used in the above quotation? I leave it to you to figure out from the context. =D