In Hobbes' Leviathan, specifically section The Fundamental Law Of Nature contained in Chapter XIV, Hobbes says:
"And consequently it is a precept, or generall rule of Reason, “That every man, ought to endeavour Peace, as farre as he has hope of obtaining it; and when he cannot obtain it, that he may seek, and use, all helps, and advantages of Warre.” The first branch, of which Rule, containeth the first, and Fundamentall Law of Nature; which is, “To seek Peace, and follow it.” The Second, the summe of the Right of Nature; which is, “By all means we can, to defend our selves.”"
From my interpretation of this passage, Hobbes is describing a "precept, or generall rule of Reason" that incorporates both the First & Fundamentall Law of Nature and the Right of Nature (which he previously defined), Hobbes directly saying that it "containeth the first, and Fundamentall Law of Nature" and contains "the summe of the Right of Nature" -- 'summe' I take to mean 'summary' or 'gist' from the corresponding Wiktionary article.
And commentators on Hobbes, such as David Gauthier -- in their article "Hobbes: the laws of nature" -- have seemed to confirm my interpretation, referring to it as:
"Hobbes’s first law of nature, “to seek peace, and follow it”, or “that every man ought to endeavour peace, as far as has hope of obtaining it” is easily inferred as “a precept, or general rule of reason”.
Which is the "Seek Peace" precept (Fundamental Law of Nature) isolated from the Right of Nature "If Necessary, Defend yourself by any means"
However other sources, such as the Internet Encylopedia of Philosophy, specifically their article "Thomas Hobbes: Methodology", define the First/Fundamental Law of Nature as:
"The first law of nature is that every person should seek peace with others, unless others are not willing to cooperate, in which case one may use the “helps of war.” This law of nature has two parts to it."
These two parts being the "Seek Peace" precept --i.e., what was originally the First/Fundamental Law of Nature -- and the Right of Nature.
So with this information, It seems that IEP (Stephen Finn) is suggesting that the First/Fundamental Law of Nature actually refers to the incorporation of the "Seek Peace" precept and the Right of Nature, where Gautheir and myself see it as referring to the "Seak Peace" precept by itself.
Now previously Hobbes defined a Law of Nature as:
a Precept, or generall Rule, found out by Reason, by which a man is forbidden to do, that, which is destructive of his life, or taketh away the means of preserving the same; and to omit, that, by which he thinketh it may be best preserved
This 'precept' then, incorporating the "Seak Peace" precept and Right of Nature by my own interpretation, seems to refer to a different Law of Nature (A '0th Law of Nature' perhaps) as opposed to the First/Fundamental Law of Nature.
Is my thinking correct?