Can someone help me here? the language is archaic. This is (translation of) Galileo
If two particles carried at a uniform rate, the ratio of their speeds will be the product of the ratio of the distances traversed The inveerse ratio of the time-intervals required
I think this is just $d = vt$ phrased in an elaborate way. Here is another one from the same section:
In the case of unequal speeds, the time-intervals required to traverse a given space are to each other inversely as the speeds.
and in the proof he draw a diagram
A |----------| C |-----------------|E|-------------| D B |--------|
How did these diagrams help Gaileo reason about uniform motion? Some of these propositions follow readily from his definition of uniform motion:
By steady or uniform motion I mean one in which the distances traveersed by the moving particle during any equal intervals of time, are themselves equal.
This is a bit of an idealization, no? Even a car starts and stops and exhibits small amounts of acceleration driving up a hill or down a road. Perhaps on a very smooth highway and for short periods of time. One could argue hardly anything moves in the way he is decribing.