In 1902, the merger that formed the International Harvester Co. included Milwaukee Harvester, Piano Mfg. Co.; Warder, Bushnell & Glessner (which built the Champion line of harvesting machines), Deering Harvester and
McCormick Harvesting Machine Co. IHC continued to make and sell all five lines into the 1920s, when the McCormick-Deering line was introduced and the others were phased out. Milwaukee Harvester Co. used the distinctive logo you found on your mower. It actually represents four triangular mower sections arranged to form a cross with their points together and overlaid with the words "The Milwaukee Leads." Sometime after the IHC merger, a Milwaukee gear-driven mower was introduced, although it appears that the chain-drive model was retained as well, so your machine could be either chain or gear driven.
You're lucky you found such an unusual mower in good condition.