vocabulary
The first and most important rule of legitimate or popular government, that is to say, of government whose object is the good of the people, is therefore, as I have observed, to follow in everything the general will
Would you tell me what the following mean?
The good of the people
follow in everything the general will
In addition, what does will mean here?
Can you please give the source?
Your sentence is
You will find no other motive than that of assuring the property, life and liberty of each member by the protection of all.
"that" here stands for "motive". So rewriting the sentence with he replacement of "that" we find
You will find no other motive than the motive of assuring the property, life and liberty of each member by the protection of all.
Here are a few more example sentences which have similar kind of construction -
The language used was simpler and chattier than that of Pravda or even of Trud , the main labor organ.
In Zambia, although it has a population at least ten times smaller than that of Nigeria, localism has also been the prime concern of domestic politics.
Is it fine now?
I think you may safely ignore what this author says. There is no substantive difference between an assumption and a supposition.
It is true that assumption is far more common than supposition; but this Google NGram suggests that that is merely historical fashion:
Scholars today are more likely to use assumption than presupposition; a hundred and fifty years ago the opposite was true.
It is also true that you are likely to hear people scorn a proposition as "merely an assumption". But it is equally true that you may to this day hear such propositions scorned as "the merest supposition". Either may be an "unfounded belief"; equally, either may be taken as the starting point of an argument intended to prove that it is false.
And the etymology is wholly irrelevant—to argue otherwise is the etymological fallacy. Etymology tells you where a meaning started, not what it has come to mean today.
These two words are essentially synonymous. They are both significantly different from hypothesis in one critical respect. An assumption or supposition is usually (but not always) taken as a true proposition on which one will base an argument, even if that argument leads in the end to proving the proposition false. But a hypothesis is always advanced as a proposition whose truth is, from the outset, in question. The purpose of the following discourse is to establish whether it is or is not true.
Best Answer
"For the good of the people" means "in the best interests of the citizens". It's an important distinction that the line does not mean that the government should always make the most popular decision. It's saying that the government should always consider what will most benefit the people that they represent or rule.
The second line (follow in everything the general will) does suggest that the government should make the popular choice.
As a whole and without further context, the author is suggesting (wrongly, in my opinion) that the best interests of the people are served by always making the most popular choice.
"Will" in this context means that which the people want and desire. So the government should do what the people want.
It is every parent's "will" that their child be healthy. As children, it is our "will" that our parents always treat us fairly.
EDIT: I addressed the quotes you listed, please do not assume that the answers address the essay in its entirety.