Have you looked up Galileo's experiment?
In those days people worked in terms of proportion, not equations as we know know them.
A piece of wooden moulding or scantling, about 12 cubits long, half a cubit wide, and three
fingerbreadths thick, was taken; on its edge was cut a channel a little more than one finger
in breadth; having made this groove very straight, smooth, and polished, and having lined it
with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth,
and very round bronze ball. Having placed this board in a sloping position, by lifting one
end some one or two cubits above the other, we rolled the ball, as I was just saying, along
the channel, noting, in a manner presently to be described, the time required to make the
descent. We . . . now rolled the ball only onequarter the length of the channel; and having
measured the time of its descent, we found it precisely onehalf of the former. Next we tried
other distances, comparing the time for the whole length with that for the half, or with that
for twothirds, or threefourths, or indeed for any fraction; in such experiments, repeated a
full hundred times, we always found that the spaces traversed were to each other as the
squares of the times, and this was true for all inclinations of the plane, i.e., of the channel,
along which we rolled the ball.3

This lead to some complicated reasoning.
Galileo did deduce a constant of proportionality.
Can you say how this compares to a modern version?