Definition of mass in classical mechanics
Classical mechanics is a mathematical model describing the kinematics of observables.
.Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology. It is also known as Newtonian mechanics,
As all mathematical models classical mechanics depends on a series of vocabulary/definitions which describe objects and defines their behavior in space as a function of time. All these are logical extension from everyday observations organized in a logical sequence.
Then come the laws,for classical mechanics Newton's laws of motion. When modeling mathematically the behavior of nature, the axiomatic setup of mathematics needs extra axioms so that a subset of all the possible solutions can be defined that pertain to physical observables. These extra axioms are sometimes called laws, and sometimes called postulates ( in quantum mechanics).
The laws of Newton pick up the subset of solutions of the relevant differential equations that have to do with physical phenomena:
First law: In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
Second law: In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant - see below.)
Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
So mass is postulated to be the proportionality constant between the measured acceleration of an object and the force . The force is defined as dp/dt, the change in momentum of an object). This is the classical definition of mass, assumed constant for each specific object..
I want to know how was mass measured and assigned a numerical value
Forces are used to assign a value to mass. In a fixed location, the gravitational force plays this role, identifying mass with weight.
and what are the criteria for saying that two bodies have the same "mass number",
Two objects have the same mass if they behave the same way in the proportionality measurements with the same force. Simple example the gravitational force.