The original and most credited authors of the three laws

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Lets ask the Authors. Rudolf Julius Emanuel Clausius for First and Second,
Walther Hermann Nernst for the Third.

Commentary

Finally! First Law "a" captures the fact that heat and work are transformed to each other in equal amounts.

First Law "b" restates this in terms of the system (usually being a heat engine). It loses clarity on the idea that heat is converted to work. It also fails to assert that no more work will be made than heat in the system.

Second Law "b" is claimed a restatement of "a", but isn't. The key things that are different are simultaneous occurrence, and that "result" implies the sum of all actions, not every action necessary to accomplish this. So if we had a process that moves heat and heat derived from work from a to b, then converts the same amount of work back to heat, Clausius's actual version "a" allows for that possibility, while "b" does not.

Third... Whew. This third law just comes right out and says you can't reach absolute zero in your lifetime. Its a lot easier to tell that's what it is supposed to mean than the last page's. (Still not getting crystal)

So, pretty much, the actual AUTHORS said it pretty clearly, and did not need clever anonymous people to correct them.

Clausius on First and Second Laws of Thermo

The first explicit statement of the first law of thermodynamics, by Rudolf Clausius in 1850.
Take your pick.
First law of thermodynamics:

  1. "In all cases in which work is produced by the agency of heat, a quantity of heat is consumed which is proportional to the work done; and conversely, by the expenditure of an equal quantity of work an equal quantity of heat is produced."
    This is stated as a property of Energy
  2. "In a thermodynamic process of a closed system, the increment in the internal energy is equal to the difference between the increment of heat accumulated by the system and the increment of work done by it."
    This is stated as a property of closed systems.

Second law of thermodynamics:

  1. Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.
  2. (Restated by unknown) No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

Walther Hermann Nernst

Around year 1912.

Third law of thermodynamics:

  1. It is impossible for any procedure to lead to the isotherm T = 0 in a finite number of steps.