I knew the Dutch word maatschappij ‘society, company’ from a former life as a member of the editorial staff of an accounting firm, and I would have guessed that the maat part was a cognate of English mate, but the details, as presented by this entry from N. van der Sijs’s Klein uitleenwoordenboek [Little loan-word dictionary], are quite interesting (thanks for the link go to the estimable Conrad); I present Google Translate’s version, with a few obvious problems cleaned up by me, but I do not know Dutch and will welcome any corrections:
maatschappij. The origin of the word maatschappij for ‘association for carrying on trade’ is closely linked to the founding of the Dutch East India Company [Verenigde Oost-Indische Compagnie] in 1602. The VOC was a company whose capital was provided by a group of wealthy merchants. They also spoke of the Oostindische Maatschappij or maetschappy. The word maatschappij is a derivation of maatschap [‘partnership’], formed in the fourteenth century from maat ‘buddy, companion, helper’ and the suffix –schap for collective names; a maatschap is thus a union of two or more persons.
Because the VOC in the seventeenth century was a leading international trading company, the Dutch word maatschappij was adopted by other languages. It was borrowed into Middle Low German in the form matschoppie, in German they spoke of Maskopei – now it is obsolete and replaced by Gesellschaft.
In Danish and Norwegian the word was borrowed as maskepi, and in Swedish as maskopi. In addition, Danish also borrowed unchanged the Dutch maatschappij, at least according to a Danish dictionary of foreign words. The Danish and Norwegian maskepi and Swedish maskopi have had a pretty significant development, namely they mean ‘covert relations, intrigue.’ This may result from the influence of the Norwegian verb maskere (Swedish maskera) ‘to mask,’ but it is more likely that the shift in meaning occurred because the Danes, Norwegians, and Swedes had little confidence in the traders who had united in the Dutch trading company, which after all was stiff competition for their own trading.
In Polish, maatschappij was borrowed as maszoperia ‘trading company.’ One informant stated that this word appears in Kashubia, an area on the Baltic Sea near Gdańsk, where it is used for a cooperative organization of small fishermen.
In Indonesian the Dutch word was borrowed as maskapai ‘trading,’ in Javanese as maskapé, maskepé, and in Sranantongo as maskapei.
From the examples it appears that some languages have borrowed Dutch maatschappij with the second syllable in –o– in place of the Dutch –a-. The Middle Low German form was pronounced [?] matschoppie. This –o– may restore the former Dutch pronunciation: in that period a was regularly pronounced /ao/ or /oa/; for example, think of the current dialect pronunciation /woater/. The German and Swedish words can also be borrowed from Middle Low German.
The OED etymology for mate ‘associate’ (updated March 2001) reads as follows:
< Middle Low German māt comrade (German regional (Low German) Maat), by aphesis < a Middle Low German cognate of Old High German gimazzo messmate (Middle High German gemazze) < the Germanic base of y– prefix + the Germanic base of meat n. Compare early modern Dutch maat (1546), maet (1573) friend, partner (Dutch maat), and also Middle Dutch maet– (in maetscap company, partnership), probably also a borrowing < Middle Low German (compare Middle Low German mātschop).