No, Non of the USA Libraries would count as the 3rd.
No, Philadelphia has the oldest library. The Library Company of Philadelphia was founded in 1731.
The Franklin Public Library
Scoville Public Library in Salisbury, Connecticut claims to be the oldest public library; they have a plaque.
I believe it is England, with a public library in England established at the London Guildhall in 1425.
The oldest library in Boston is the Boston Public Library, founded in 1848. It is significant in the city's history because it was the first publicly supported municipal library in the United States, providing free access to books and knowledge for all residents.
Many claims have been made by various countries for the title of "first public library" The Romans had collections of Greek and Latin scrolls which were available in the dry sections of Roman bath houses, but you could not check books out. The North African Islamic empire of the 9th century had sort of lending libraries but access was restricted. The earliest public library in England was established at the London Guildhall in 1425. The Italian Malatestiana Library is a public library dating from 1452 in Cesena. Take your pick!
The oldest library, St. Catherine's Monastary, is located in Sinai, Egypt. It was built in the middle of the 6th century and houses the second largest collection of religious material in the world (after the Vatican). However it is not accessible to the public, only by monks and invited scholars. If you meant this oldest RUNNING LIBRARY, this next paragraph is what you'll want to see: The bibliotheque de Paris (Library of Paris) combined with the National Library of France, is the oldest continually running public library service, dating back to 1368 when it was housed at the Louvre. It has moved several times over the past 700 years, into newer and larger accomodation and new premises again are currently in the design phase. === === I hope I could help. All of this info. was quoted from this website:http://ttglibrary.wordpress.com/2009/03/11/ever-wondered-what-the-oldest-library-in-the-world-is/Thanks, Nicky :)
Mexico
The Library Company is America's first successful lending library and oldest cultural institution. It was founded in 1731 by Benjamin Franklin as a subscription library supported by its shareholders, as it is to this day. See: http://www.librarycompany.org/about/index.htm -- Libarian, University of Hawaii at Manoa
Quaid e Azam Library, Lahore is one of the oldest and largest libraries of the country.
the mf book
Wynnton Elementary School is the oldest building in Georgia still serving as a library. It has been in use as continuously since 1843.