"It is the design of this, and of the two succeeding chapters, to describe the prosperous condition of their empire; and afterwards, from the death of Marcus Antoninus, to deduce the most important circumstances of its decline and fall; a revolution which will ever be remembered, and is still felt by the nations of the earth." This is the sentence that speaks about the purpose of the text.
It is the design means " to have as a purpose", so this phrase introduces the purposes which are: first, to describe the conditions of the Roman Empire and, second , to deduce the important factors that led to the decline and fall of Marcus Antoninus. The excerpt adds information about the fall of Marcus Antoninus; this was a revolution which is stil peresent today in any nation's memory.