Speed is defined to be distance divided by time; when and who by was this definition first put forward?
The obvious guess would be Galileo in early modern physics; is this right, and can it be pushed further back?
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Aristotle (Physics, Book VII, Chapter 5) made use of the concept of speed in his laws of motion written around 330 BC.
He said that a force which moves a mass a distance D in time T will move half the mass twice the distance in the same time.
While the result of his equation is not correct where the force is gravity (he was concerned with preserving proportionality), it and his other rules of motion indicate that he employed the concept of average speed.
See this summary: http://faculty.poly.edu/~jbain/mms/lectures/15.GalileoMotion.pdf
Yes, your guess looks correct:
The Italian physicist Galileo Galilei is credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time.
The exact notion of speed, and its precise definition are due to Galileo. But long time before him people had a good intuitive concept of speed, and could use it. (The notions of momentary speed and average speed were confused, of course). One example where the notion of speed was used before Galileo is "ded reckoning" in navigation, which is the computation of the place of the ship using time traveled, speed and direction.
Columbus (who lived roughly a century before Galileo) was a great master of this art, one of his extraordinary achievements was steering his fleet in the second transatlantic voyage exactly to the place where he left a party in his first voyage. So he had a very clear concept of speed, though the means of measuring it were very primitive.