Why 'dedicate' used passive voice in this sentence of the Gettysburg Address?
Here is the full, final paragraph of the Gettysburg Address:
But, in a larger sense, we can not dedicate, we can not consecrate, we can not hallow this ground. The brave men, living and dead, who struggled here, have consecrated it far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us that from these honored dead we take increased devotion to that cause for which they here gave the last full measure of devotion - that we here highly resolve that these dead shall not have died in vain that this nation, under God, shall have a new birth of freedom, and that government of the people, by the people, for the people, shall not perish from the earth.
This paragraph immediately follows Lincoln's description of the formal occasion that has brought him and his audience to Gettysburg:
We have come to dedicate a portion of that field, as a final resting-place for those who here gave their lives, that that nation might live. It is altogether fitting and proper that we should do this.
So Lincoln's speech offers this progression: We are here to dedicate a portion of the Gettysburg battlefield as a national memorial; doing this is fitting and proper; and yet we are clearly not in a position to dedicate this field. It is in the context of this surprising assertion that the poster's sentence appears. And in this context, the wording "It is for us the living, rather, to be dedicated here..." appears as a logical next step beyond Lincoln's assertion that "we can not dedicate ... this ground [the Gettysburg battlefield]."
In effect (as Global Charm's answer suggests), Lincoln is arguing not merely that "we" (the living) are in no position to dedicate anything in memory of the sacrifice of the Union forces at Gettysburg, but that "we" are the thing to be dedicated—to the unfinished work at hand, which is victory in the Civil War. In fact, Lincoln says this twice, in consecutive sentences, both times in passive voice: "It is for us the living, rather, to be dedicated here..." and "It is rather for us to be here dedicated to the great task remaining before us..."
Who or what is dedicating "us" in this way and to this purpose? Lincoln doesn't say. It might be God, history, duty, loyalty, moral obligation, love of the Union, the Weltgeist, the sacrifice that others have made. Lincoln simply doesn't say. But it is quite clear that he does not want to say, in active form, "It is now most fitting and necessary for us the living to dedicate ourselves here to the unfinished work..." Whatever purpose has moved the unnamed mover to dedicate "us" to the unfinished work at hand, Lincoln is not merely urging his hearers to dedicate themselves more unstintingly to the great cause; rather, he is asking them to accept their being dedicated to that cause—as if they were themselves an offering made by some other force to the world yet to come.