1. According to Newton mass is a ‘quantity of matter’.
Yes, with the emphasis on quantity. Newton’s definition is a quantitative definition.
Meaning of quantitative (Merriam-Webster):
1. : of, relating to, or expressible in terms of quantity
2. : of, relating to, or involving the measurement of quantity or amount
2. Wikipedia: ‘A common way of defining matter is as anything that has mass and occupies volume’
3. A quantity of matter without accompanying gravity is a contradiction.
Gravity is a property of mass. Matter has mass and exhibit gravity.
4. A quantity of matter without inertia against a force is a contradiction.
Mass of a body is a measure of its inertia.
5. Gravitation without matter is a contradiction.
6. Inertia without matter is a contradiction.
These are just the reverse consequences of 3 and 4.
7. Then according to one of your own sources:
<Newton> defined <mass> as the amount of matter. The generally accepted definition of matter does not exist even today.
From the wiki on matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume. However, different fields use the term in different and sometimes incompatible ways; there is no single agreed scientific meaning of the word “matter”.
However, in Newtonian physics, matter can be considered as “anything that has mass and occupies volume”. Newton did not define matter.
8. Same source:
Though the definition of mass (“Definition I: The quantity of matter is the measure of the same, arising from its density and bulk conjointly”) given by Newton in his “Principia” was so unclear that scholars are discussing its logical consistency even today, the equations of Newtonian mechanics are absolutely self-consistent.
OTOH, from another source HERE
So, contrary to nearly everything that has ever been written on Newton’s definitio 1, this definition is not one of “mass”, nor is it circular, as some have opined; rather it is a formula for the quantitative determination of an even experimentally measurable quantity of a body’s material contents.
9. Determining the gravity constant G is also known under the phrase ‘weighing the earth’. It is the only way to determine the ‘quantity of matter’ of the earth.
From this article HERE
Quantum Measurement of Gravitational Constant
The new method involves using an atom interferometer to split a beam of cesium atoms into two, which are then sent along different paths to produce interference fringes (yes, even though they’re atoms - don’t forget about wave-particle duality). By placing a massive object - a 540 kilogram lead weight in this case - near the beams, the path, and therefore the final interference pattern, is affected.
The paper on the new method is HERE