Ethos

Yes, there is a little bit of pathos and logos sprinkled in here and there. But let's be honest, Ike's farewell is rooted almost entirely in ethos. It rings with the authority of the President of the United States, the five-star general, the Supreme Commander of NATO and the Allies in Europe, and Lord of the Putting Green. It sings of the moral idealism that was the foundation of the American identity.

Even in the places where Ike is trying to use pathos (VII.5, for instance) or logos, it's much less about emotion or logic and much more about the truth as told by a man who knows what's what. Honestly, Ike probably wasn't consciously thinking about using ethos while he was writing the speech. But he just couldn't help it. The man was ethos personified.

Take, for example, this nugget about America's mission in life:

Throughout America's adventure in free government, our basic purposes have been to keep the peace; to foster progress in human achievement, and to enhance liberty, dignity and integrity among people and among nations. To strive for less would be unworthy of a free and religious people. Any failure traceable to arrogance, or our lack of comprehension or readiness to sacrifice would inflict upon us grievous hurt both at home and abroad. (III. 1-3)

Now, Ike doesn't argue in favor of this version of the American purpose, nor does he wax poetic about how great liberty and dignity are. He just straight up tells us that's how it is. It carries the implicit authority of a man who has held the highest offices possible for a couple decades. And it emphasizes the implicit American tradition, which holds such things as liberty, dignity, and cheeseburgers to be essentially American values.

Maybe it was all those years being a military man that made his writing style so declamatory, and which made even the more colorful passages so… ethosy.