Note the angle stroke.
An advertisement from the November 26, 1910 issue of The Saturday Evening Post (Palm Coast, Florida, USA), showing the “Gillette Slide”.
The Gillette Slide is/was a technique for shaving, claiming to cut closer and with less irritation. The basic idea is to slide sideways at the same time as you slide down. This supposedly creates a shearing motion – in other words the same idea that various vibrating razors through the ages have tried to capitalise on.
It seems like the Gillette Slide – along with techniques like the J-hook – fell out of general usage by the time thinner, sharper blades came along. To me this implies that the “need” for a shearing stroke was due to the blade not being up to job of cleanly slicing through the hairs.