Bush also spoke of fear, and of the fight against those who killed thousands in last week's attacks. He said America would not cease until every terrorist group across the globe had been defeated.
"Freedom and fear are at war," he said.
During the Great Depression, Roosevelt, too, spoke of freedom and fear. Roosevelt, one of America's greatest leaders - a four-term president who led the country through hardship and war - pledged a war on the Depression with the ringing phrase "we have nothing to fear but fear itself".
Perhaps Bush's words carried the faintest echo of one of the memorable phrases of last century, coined when Roosevelt described December 7, 1941 - the day of the Pearl Harbor attack - as a "date which will live in infamy".
Said Bush: "Each of us will remember what happened that day and to whom it happened. We will remember the moment the news came, where we were and what we were doing."
Bush has repeatedly said the war on terrorism is the first war of the 21st century. Yesterday, he warned his people: "Americans should not expect one battle, but a lengthy campaign unlike any other we have ever seen."
More than 80 years earlier, President Woodrow Wilson stood in the same place and committed American troops to war in Europe in 1917, saying: "There are, it may be, many months of fiery trial and sacrifice ahead of us."
During his address yesterday, Bush vowed to preserve liberty.
"As long as the United States of America is determined and strong, this will not be an age of terror; this will be an age of liberty, here and across the word."
Liberty has long echoed through presidential speeches.
At his inauguration in 1961, John F. Kennedy pledged his country to its ideal: "Let every nation know, whether it wishes us well or ill, that we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe to assure the survival and the success of liberty."
But the most famous call came from Patrick Henry, an orator whose speeches fuelled the American Revolution. On March 23, 1775, he proclaimed: "I know not what course others may take, but as for me, give me liberty or give me death."
Bush also spoke yesterday of America's recovery from the terror attacks.
"I know there are struggles ahead, and dangers to face," he said. "But this country will define our times, not be defined by them."
It could have been his father 11 years ago. Speaking before the Gulf War, President George Bush sen said: "Out of these troubled times, our fifth objective - a new world order - can emerge; a new era, freer from the threat of terror, stronger in the pursuit of justice, and more secure in the quest for peace."
Another echo from this 1990 speech was heard in George W. Bush's declaration that the US was not against Muslims or Afghanistan.
Said Bush sen: "Let me also make clear that the United States has no quarrel with the Iraqi people. Our quarrel is with Iraq's dictator and with his aggression."
One of the greatest presidents, Abraham Lincoln, spoke of the healing of the nation in his Gettysburg Address, delivered in 1863, during the American Civil War.
"These dead shall not have died in vain, that this nation, under God, shall have a new birth of freedom."
Said Bush: "We are a country awakened to danger and called to defend freedom. Our grief has turned to anger and anger to resolution."
Map: Opposing forces in the war against terror
Afghanistan facts and links
For coverage of the attacks on the United States, see:
Full coverage: Terror in America
