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I have a question from the first two paragraphs of this answer:

Newton's idea of absolute space simply appeared as an answer to the following question: What is an inertial system? Saying that an inertial system is one with constant velocity relative to another inertial system of course does not answer the question. To avoid such logical weakness in Newton's first law one has, at some point, to assume that there is a frame of reference, called absolute space, that - by definition - is inertial.

On the other hand Galilean relativity consists on transformations among inertial frames of reference and such relations do not forbid an absolute space. In fact, the idea is that we can use Galilean relativity transformations to relate any inertial frame to the absolute space.

Reading between the lines, I understand that Newton first defined absolute space, and then defined every other inertial system in reference to it. This makes sense to me and is quite intuitive.

However, what was then the analogue for inertial frame for Galileo?

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    $\begingroup$ Galileo did not deal with high-minded abstractions like inertial frames, transformations and "Galilean relativity", that came later. Practical considerations sufficed for him. The Earth was inertial enough in practice, as in his observations of motion on a moving ship (with constant velocity relative to the Earth). He even believed that bodies would maintain circular motion around the center of the Earth inertially, "a ship, for instance, having once received some impetus through the tranquil sea, would move continually around our globe without ever stopping." $\endgroup$
    – Conifold
    Commented Apr 29, 2023 at 6:15

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