By Harry Fawcett Buckley
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Newton ascribed to Galileo not only the first law of mechanics, but also the second, although this was an overstatement: Galileo did not make a clear connection between force and acceleration (when they are different from zero). ” Motion Along an Inclined Plane Galileo considered his most fundamental conclusion to be that during consecutive equal time intervals, a falling body travels distances that are proportional to consecutive odd numbers. He wanted to verify this, but how? He could not continue to throw balls from the Tower of Pisa, since he was already living in Padua.
The division process can be continued endlessly, and we can choose any number of intervals, each requiring more than 12 sec, without reaching O. This means that a body leaving O cannot arrive at A! We assumed that A is at a distance of 1 m from O. But it can be shown analogously that a body leaving O can reach no point whatsoever. This remarkable argument was the beginning of classical mechanics! However, Galileo himself published an unconvincing argument. He tried to reach a contradiction by saying that since velocity is proportional to distance, all intervals beginning at the origin must be traversed in the same time, which is impossible.
We have already said that the measurement of time did not yet play a significant role in people’s lives and that precise clocks were not available. We do not always take into account how gradually the sensation of constantly passing time took root in human psychology. —Transl. Two Tales of Galileo 35 great flexibility in reorienting himself comparatively quickly from distance to time. ). We must not overemphasize the final form of Galileo’s ideas of velocity and acceleration. The idea of an instantaneous, continuously changing velocity is not easy to sense, and it gained acceptance slowly.