Reading from your second link, Samuel Johnson's Dictionary of the English Language:

> ORDER. s [ordo, Lat.] 1. Method; regular disposition. 2. Established process. 3. Proper state. 4. Regularity; settled mode. 5. Mandate; precept; command. 6. Rule; regulation. 7. Regular government. [8-12: other senses not obviously relevant here] 13. Measures; care. [14: a sense specific to architecture]

(Italics are my emphasis; I've highlighted every word related to "regulated". "s" after the headword seems to indicate a noun.)

> To ORDER, v. a. [from the noun/] 1. To regulate; to adjust; to manage; to conduct. 2. To manage; to procure. 3. To methodize; to depose fitly. 4. To direct, to command. [5: one other irrelevant sense]

Here we see that "regulate", "adjust", "manage", and "conduct" are all synonymous. We see that the concept of "order" has special senses relating to organization and to command, as is also true in English today. The only mention of the verb "regulate", which I discussed in my first comment, clearly indicates that it is used in the sense of organizing. There is a special application of this or a related concept to government, "regular" government, noted in sense 7.

"To REGULATE" is given two senses:

> To REGULATE. v. a. [regula, Lat.] 1. To adjust by rule or method. 2. To direct.

And REGULATION is:

> REGULATION. s. [from regulate.] 1. The act of regulating. 2. Method; the effect of regulation.

This is interesting in that it indicates that (in sense 2) "regulation" is a state of being, like "order", resulting from being regulated. The modern sense of the word, referring to a formal rule, is not listed in this dictionary. However, that appears to be an oversight by Johnson: here are the relevant senses of REGULAR:

> REGULAR. a. [regularis, Lat.] 1. Agreeable to rule; consistent with the mode prescribed. 2. Governed by strict regulations.

I don't see an interpretation of "regulations" as used here other than "formal rules". This is what was meant by "regular government" or "order" - a government itself subject to strict regulations. Sense 1 is so unclearly worded that I've included it in case it's relevant, but I believe it's just the sense in which "played" is the regular past tense of "play", while "went" is the irregular past tense of "go". This "regular" means "conforming to a rule".

And:

> REGULARITY. s. [regularité, Fr.] 1. Agreeableness to rule. 2. Method; certain order.

What does "rule" mean?

> RULE. s. [regula, Lat.] 1. Government; empire; sway; supreme command. [2. a ruler] 3. Canon; precept by which the thoughts or actions are directed. 4. Regularity; propriety of behaviour.

> To RULE. v. a. [from the noun.] 1. To govern; to controll; to manage with power and authority 2. To manage. 3. To settle as by rule.

One word has come up in almost everything we've looked up:

> METHOD. s. [methode, Fr. μέθοδ@.] The placing of several things, or performing several operations in the most convenient order.

This isn't especially clear, but there are related entries:

> METHODICAL. a. [methodique, Fr. from method.] Ranged or proceeding in due or just order.

> To METHODISE v. a. [from method.] To regulate; to dispose in order.

This states explicitly that to regulate something is to bring order to it. The sense survives in modern English in a related word, regularize; that distinction was not drawn in the eighteenth century.

I'll continue in a reply to my own comment, because I'm about to shift topics.