Congress shall have power...to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful BuildingsU.S. Constitution, Art. I, Sec. 8, Cl. 17.
That quote by itself doesnt say what you imply. It discusses the authority over purchased land, not the authority to purchase land.
Maybe you clipped too much?