All three share a family tree, and dispite what you may think, the Left derives from libertarianism, not the other way around. Libertarianism is the modern representative of the liberal or whiggish tradition (and many who call themselves conservatives are in fact more moderate members of the same tradition). The great early philosopher in that tradition was John Locke. The Left comes from the French philosopher Rousseau, who came after Locke and modified some of his ideas, the social contract in particular, into supports for tyranny. About the time Rousseau's ideas were bearing fruit in the French Revolution, the founder of conservatism was active. Burke was a member of Parliament in the Whig party. In other words, he was one of ours! His arguments were different from Locke's, and probably influenced the arguments of libertarians/liberals/whigs like Bastiat and Hayek (and you can see obvious influence from Bastiat on whiggish conservatives like Sowell).
Locke himself took many of his arguments from Hobbes, but changed around the effect in much the same way Rousseau did to him, but had political forerunners in the Levellers. More about them here.
If authoritarian conservatives have any share in the family tree at all, it might be from Whigs like Cromwell. You must be real proud of that.
Not exactly, the trunk of the tree is Classical Liberalism. From that trunk two branches comprising positive and negative liberty grew. Now I know that the term "authoritarian" is sinister sounding and is used to denigrate many conservatives however; the fact remains that in any civilized society there are those that are in positions of authority based on the privilege granted them by the members of the society who wish to maintain the cultural norms that make up that society hence the term "conservative". There are always those minorities living within that culture that are determined to live unconstrained by the norms of that culture and place themselves above the majority wishes of the surrounding community, hence the term "libertarian". Then there are those that also wish to live above the same cultural restraints of the same society just as the "libertarians" do but, at the same time, want that society to pick up the pieces of their lives caused by their own bad judgment hence the term "liberal". I have nothing at all against a libertarian that just wants to be left alone to live his life isolated and within his definition of personal freedom. I do have a problem with a movement that wants to give us a "libertarian" solution but end up with a "liberal" outcome.