I recently answered this question which had been sent to AskNYPL:

"When I visited your main building on 5th Avenue I saw in the entrance a plaque or motto (I think on a pillar) which stated WHY this building was erected. The gist of the thing was that the library was built because a democracy needs an educated and enlightened people. I would love to have the EXACT WORDS of the thing, because the quotation would suite very well into the library discussion we are having here at the library where I work."

After some looking, I found the following inscribed on the west side of Astor Hall, to the left of the top of the central archway:

ON THE DIFFUSION OF EDUCATION
AMONG THE PEOPLE
REST THE PRESERVATION
AND PERPETUATION
OF OUR FREE INSTITUTIONS

Though there's no attribution near this quote (perhaps the stonecutter ran out of room?), these words are Daniel Webster's (1782-1852).  Read more about him in Biography in Context and Wikipedia.

The earliest citation of this quote that I was able to find appeared in the August 1837 edition of the "Common School Assistant: A Monthly Paper, for the improvement of Common School Education" (volume II, number 8) - found in Google Books.

Here's a little more context to the quote that may be of interest:

"DANIEL WEBSTER

From his speech delivered at Madison, Indiana:

'Another of the paramount objects of government... is education. I speak not of college education nor of academic education, though they are of great importance; I speak of free school education—common school education.

'Among the planets in the sky of New England, the burning lights which shed intelligence and happiness on her people, the first and most brilliant is her system of common schools. I congratulate myself that my first speech on entering public life was in their behalf. Education, to accomplish the ends of good government, should be universally diffused. Open the doors of the schoolhouse to all the children in the land. Let no man have the excuse of poverty for not educating his own offspring. Place the means of education within his reach, and if they remain in ignorance, be it his own reproach. If one object of the expenditure of your revenue be protection against crime, you could not devise a better means of obtaining it. Other nations spend their money in providing means for its detection and punishment, but it is for the principles of our government to provide for its never occurring. The one acts by coercion, the other by prevention. On the diffusion of education among the people rests the preservation and perpetuation of our free institutions.

I apprehend no danger to our country from a foreign foe. The prospect of a war with any powerful nation is too remote to be a matter of calculation. Besides, there is no nation on earth powerful enough to accomplish our overthrow. Our destruction, should it come at all, will be from another quarter. From the inattention of the people to the concerns of their government—from their carelessness and negligence. Make them intelligent, and they will be vigilant—give them the means of detecting the wrong, and they will apply the remedy.' ..."

Amazing how that last paragraph seems fresh enough to have been ripped from this morning's op/ed pages!