The second, which has been a cliche for the past seven years since Sept. 11 but came forth clear and new from a president who launched his political career in opposing the Iraq War, was that "Our nation is at war, against a far-reaching network of violence and hatred."
Despite its truth, this statement was hardly expected. It could have been said by President George W. Bush or Vice President Dick Cheney. Yet it runs against the current mood of the Democratic Party, which prefers to believe the term "war on terrorism" is a profound misstatement and that terrorism is better seen as a crime, as a pathology and as a diplomatic challenge.
So by declaring in the opening moments of his office that America is at war, Obama has changed the terms of the domestic policy debate over Afghanistan and Iraq. There is no doubt that he will deploy every available weapon -- diplomatic, humanitarian and the tools of social development -- in its pursuit. But war is inherently a military matter, and in hailing the American military he reminded many of his own voters how their freedoms had been won and defended.
"We remember with humble gratitude those brave Americans who, at this very hour, patrol far-off deserts and distant mountains. They have something to tell us today, just as the fallen heroes who lie in Arlington whisper through the ages," he said.
The phrases that will be pored over in embassies and presidential palaces around the world, as friends and foes seek clues to the core policies and the guiding principles of the new American president, were plain, simple and not very compromising.
"To the Muslim world, we seek a new way forward, based on mutual interest and mutual respect," he said, which suggests a great deal but promises nothing.
"To those leaders around the globe who seek to sow conflict, or blame their society's ills on the West -- know that your people will judge you on what you can build, not what you destroy," he said, a subtle rebuke to the more apologetic of his own supporters but also a quiet appeal over the heads of unfriendly foreign leaders to their own public opinion, however silenced or repressed.
"To those who cling to power through corruption and deceit and the silencing of dissent, know that you are on the wrong side of history; but that we will extend a hand if you are willing to unclench your fist," he went on, in as plain a statement of realism in foreign policy as any president has made.
We may not like or respect you, Obama suggested, but we are prepared to do business on formal terms and to deal with you without illusions. This was the pragmatic approach to dealings with the Soviet Union that lasted throughout the Cold War, and it will be interesting how far this cool but fastidious acceptance of reality will govern his dealings with China, Russia, Iran and North Korea.
Nor was there any whiff of appeasement in his remarks to a watching world, words that had his predecessor George Bush rising to his feet, and Dick Cheney rising painfully from his wheelchair, to join the applause.
"We will not apologize for our way of life, nor will we waver in its defense," he said. "And for those who seek to advance their aims by inducing terror and slaughtering innocents, we say to you now that our spirit is stronger and cannot be broken; you cannot outlast us, and we will defeat you."
It was a stinging rebuke to those who had assumed that America had gone soft in voting for Obama, or that its painful years in Iraq and Afghanistan had sapped the nation's will and its readiness to fight for its principles.
For all the differences over strategy between the new president and the old -- and Obama made it clear that he did not support any weakening of constitutional rights or any trade-off between America's safety and its ideals -- the strategy of resolute war against terrorists is common to them both. This perhaps explains the otherwise unlikely accord that has developed between Bush and Obama, the apparently genuine affection in their farewells after Obama made the rare gesture of personally escorting the outgoing president to his helicopter.
But there were other parts of the speech that resonated beyond the usual bond that links all men together who have held that lonely and awesome office, links that went back to Franklin Roosevelt's first inaugural speech in 1933, when he declared: "The money changers have fled from their high seats in the temple of our civilization. We may now restore that temple to the ancient truths ... honesty, on honor, on the sacredness of obligations, on faithful protection, on unselfish performance."
Obama too spoke to the ancient truths in the closing section of his own inaugural address, harking back to George Washington's embattled army in the worst winter of the War of Independence and his appeal to virtue and hope.
"Those values upon which our success depends -- hard work and honesty, courage and fair play, tolerance and curiosity, loyalty and patriotism -- these things are old. These things are true. They have been the quiet force of progress throughout our history. What is demanded then is a return to these truths. What is required of us now is a new era of responsibility," Obama said.
In his own way, Obama also echoed that famous phrase of FDR that "we have nothing to fear but fear itself."
Obama acknowledged that there was a mood of fear in the country. He called it "a sapping of confidence across our land -- a nagging fear that America's decline is inevitable, and that the next generation must lower its sights."
He did not deny it or seek to minimize it. Indeed, he accepted that this mood was a fact and had to be confronted with the quiet but stunningly effective determination that has been his hallmark throughout his presidential campaign, throughout the transition and now in the first glare of his presidency.
"Today I say to you that the challenges we face are real. They are serious and they are many. They will not be met easily or in a short span of time. But know this, America -- they will be met."