Well, and what about the sample for imitation? Considering the fact that in this book there is not even one, but whole two definitions of the essence the notion of a number, it is possible on this basis to formulate a brief definition the essence of arithmetic, say so: arithmetic is the science about the origin of numbers and methods of computations. Then from understanding the essence of numbers, one can construct their axiomatics and basic properties, which in turn will lead to BTA and other theorems arising from the needs for computations. In a similar way you can build also other knowledge beginning with basic notions and an essence of the science built on them.
Now for example, we need to use arithmetic as a sample for imitation in order to build, say, physics. To do this, we take as one of the basic definitions to this science as follows: Physics is the science about the essence, properties and interaction of material objects. Hmm … It seems here we stumbled upon an insurmountable wall because the definition the notion of matter does not exist. Philosophers spent a huge lot of paper, but all this without some use. However, as popular wisdom says, there is nothing to blame on others if they themselves have curved mugs. Physicists themselves can solve this problem without any special difficulties because no one else will do it for them.
They simply accept as an axiom that all consisting from matter has such properties as mass and energy and so simple the whole problem will be solved. Well, and what about the definition the essence of these properties themselves? But this is still Sir Isaac Newton has very well worked and even used the style of presentation along with approaches from Euclid himself! And now, standing on their shoulders, it’s not at all difficult for us to reveal the essence of these notions especially after physicists have the problem with the units of measurement solved. Indeed, in arithmetic it is only implied that all calculations must be carried out in the appropriate units of measurement while in other sciences these units must always be concrete.
For example, in informatics Bit is used as the unit of measure, but here scientists also screwed up. Since the times of Claude Shannon, it is considered that the quantity of information is measured by Bits, but given that the notion of information is not defined at all, it turns out that they measure unknown what. However, in fact, it is all very well known to everyone that by Bits is measured the capacity of memory of information carrier. But how to measure the quantity of information itself is a problem, the solution of which will largely determine the possibility of implementing the most powerful technological breakthrough in the entire history of our civilization!!!