Here is a map of Los Angeles, showing rail lines and all its annexed territory as of 1916.
The map was drawn by Homer Hamlin, a city engineer, under the supervision of one J. R. Prince, chief draftsman.
Took me a while to figure this out, but I'm dense: to zoom in on the map you must click on one of the zoom in/zoom out buttons at the bottom, and then click on the map itself. It will get bigger...like magic.
The city's 1850 boundaries are shown in the center, and every annexation of land up through 1916 are noted and dated. Did you know that until 1896, the city limits stopped at Hoover and extended no further west? Or that until the Shoestring Strip was added in 1906, the city's southern boundary was Santa Barbara (MLK) Blvd., or, for a few blocks, Slauson?
The map is part of the American Memory project of the Library of Congress. They have an online exhibit titled "Los Angeles Mapped" which shows all sorts of beautiful, zoomable, old maps.