Erasmus was founded by Dutch settlers in 1786, and the original Academy building is still standing in the courtyard (you can just catch a glimpse of it through the gated entryway) of the grand, Gothic-style campus that was built after Erasmus was donated to the public school system. The building pictured here was the first part of that campus to be constructed, and it was opened in 1906.
If this photo looks familiar to you, it's because both schools were designed by Charles B.J. Snyder during his prolific tenure as NYC's Superintendent of School Buildings from 1891 to 1923. His lofty ideals for municipal architecture revolutionized the school system and "symbolized the commitment of the city to care for and even uplift its citizens", according to the NY Times.
(As you may recall, I passed by the backside of Erasmus on Bedford Avenue last month.)