User blog comment:Reximus55/Government Series - Introduction/@comment-29118948-20131024053317/@comment-1375165-20131025030002

If I may be pedantic:

(1) Democracies are a type of republic. Namely, a democracy is a republic where the electors have equal representation (or equal voting power).

(2) "Squares and rectangles" is actually a great analogy for "Democracies and republics". Squares are a type of rectangle while democracies are a type of republic.

(3) "It is impossible for something to be a type of something without being the same thing." is false. A subset of a set is not the same as the set (it is the same type of thing but not the same thing). It would be like saying that a dog is the same as an animal (or being a dog is the same as being an animal). LG, I assume you didn't mean to say that it's impossible for something to be a type of something without literally being the same thing, but it sounds like it :P