The name occurs also as Margaliot, Margolis, Margulies.
Polish family of Talmudic scholars that traces its descent from Rashi, on the one side, and from the families of Shor and Samuel Edels on the other. The first Margolioth known was Samuel, dayyan at Posen about 1550; one of his sons, Moses Mordecai, was rabbi at Krakau. www.jewishencyclopedia.com
(See this site for more information on the Margolioth Famlies, from 1550 - 1850.)
Our Margulies line descends from Menachim Menish Margolioth. Although only two children are shown
on the above tree, Menachim had five sons. Our particular Margulies Family is descended from
Elyakim Getzel Margolioth (1765), a brother of the famous Ephraim Zalman Margolioth (1760-1828).
Jacob Margoles was the direct ancestor of the great Talmud Scholar Salman Margulies, a historical adornment of Brody. His grandson, Moritz Margulies [my Greatgrandfather] a profound Talmud adept, was one of the early "Maskilim", ... 
I don't know which came first here, but I suspect that Meir Faerber got his information from the
same source as the person who created our hand-drawn family tree.
New data shows that the Elyakim Getzel Margulies (b.1827) from whom we descend is not the son of Ephraim Zalman M. (b.1760), but the grandson of another Elyakim Getzel M. (b.1765) who was Ephraim Salman's brother.
So our branch of the hand-drawn tree should look like this: