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I was wondering who used the term 'mass' in physics and in what context? The Online Etymology Dictionary says it is in use since 1704. According to the Wiki article the year is contemporary to the work of Newton on Principia Mathematica.

Had Newton anything to do regarding the first use of 'mass' as a quantitative term for expressing aspects of nature?

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Yes, Newton was definitely using the term "mass". His Principia were written in Latin but the English translation of his Latin definition of gravity said:

Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.

The Latin original of the Principia may be interesting to study. I am no Latin expert but my understanding is that Newton used the word "gravitas" both for the force or mechanism he proposed as well as for the mass as a quantity – in this sense, "gravitas" translates as "heaviness".

The concept of mass or weight of an object was known long before Newton and the same word – although in different languages than the modern languages – was used for that concept for many and many millenniums. The history of weighing scales goes back to balances used between 2400 and 1800 BC in what we call Pakistan today. In Egypt, scales existed around 1878 BC or earlier. It's clear that they had to use some word for the "amount" of food etc. that was measured by these balances/scales and whatever the words were should be translated as mass. But this is a claim about a sensible habit in linguistics, not a claim about physics.

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