From Daniel Tammet’s book Thinking by Numbers, the chapter on Shapes of Speech:
“In the mid-nineteenth century, more than two millennia after Euclid, a copy of his Elements traveled in the carpetbag of a circuit lawyer from Illinois…
“The pages and their propositions made a deep impression on Lincoln’s mind, following him into his subsequent career in politics. In a speech given to an Ohio crowd in 1859 in opposition to a pro-slavery rival…
“‘Now if Judge [Stephen] Douglas will demonstrate somehow that this is popular sovereignty – the right to make a slave out of another, without any right of that other, or anyone else to object; demonstrate it as Euclid demonstrated propositions – there is no objection. But when he comes forward, seeking to carry a principle by bringing it to the authority of men who themselves utterly repudiate that principle, I ask that he shall not be permitted to do it.’
“Definitions and axioms would shape President Lincoln’s most famous addresses. His powers of rhetoric, persuasion, deduction and logic were all subjected to the severest tests.”
His defense of the Union, and the requirement to keep it together, was that based on universal law and the Constitution. The “Union of the States” is perpetual because no proper government ever had a provision for its own termination.