A few comments on CL (now, if I could write in sub- and super-scripts, wouldn't that be wonderful ..) ...
CL, and a bunch of other terms (eg Re, M, etc.) are derived from a math technique called "dimensional analysis" - a typical story is given
here but, unless you fancy brain strain, I wouldn't worry too much about the detail.
This technique arose as a result of the empiricism of the Industrial Age when some bright folk figured that there had to be an easier, more compact way of presenting data for engineering use.
Looking at forces generated in fluid flow, one considers all the parameters which might reasonably be involved ..
(a) mass (density is more appropriate for fluids)
(b) some sort of size measure (a big sheet of ply is harder to hold in a breeze than a little sheet)
(c) airflow speed
(d) viscosity (sticky-ness of the fluid eg compare honey with water)
(e) compressibility
.. viscosity and compressibility reflect the fact that we want to deal with real fluids in the real world.
The technique uses an exponential form of expression and, for force, gives a result that force is proportional to
dynamic pressure * Re * M * a representative area
If we hide Re (relevant to low speed) and M (relevant to high speed) within a constant of proportionality (this doesn't mean they go away .. have a look at any of the text books which will show the effect on CL slope at higher M values .. just that it would be a routine and not very useful complication to have them in the expression for normal use) we might write
force = constant * dynamic pressure * area
or, in the more usually seen form
L = CL * (1/2*rho*V2) * S
and, similarly, we can run up an expression for drag forces.
The area, S, need not be wing area, but that is probably the most important shape (area) consideration so it is conventional so to choose.
The advantage of DA to we boring old engineering folk is that we can put a huge amount of data into a very simple form rather than having reams of empirical data looking at the relationship between one variable and another ..
It is held, generally, that all the meaningful dimensionless values have been discovered .. find yourself a new one and you, too, could get your name in text book lights ...
As an aside, be aware that this use of the term "dimensional analysis" tends to be the engineers' view of life .. other meanings may be seen, including the simple dimensional checks of equations to make sure that the dimensions all balance out ...
I've never seen the book referred to in this thread so I can have no view on its usefulness etc.