It would appear, combining your research and mine, we could indeed come to the following assumptions.

1)The first example of a rotary mower comes from the 1928 Miller patent.
2)The first example of a petrol rotary mower comes from the 1929 Beazley patent.
3)The first example of a vertical shaft petrol rotary comes from the 1931 rotoscythe patent.

Of course, these are just assumptions, and may yet prove false.

Cheers
Ty

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