Zatana, Let's see....you have three clauses in this sentence. You have an independent clause -We are SO familiar with the fact that man ages, which introduces a dependent clause -THAT people have for years assumed which introduces an independent clause -THAT the process of losing vigour with time, ......PROCESS is the subject of this clause which is redefined in an appositive phrase ,of becoming more likely to die the older we get, = process of becoming more likely to die...etc. was something self-evident, .........WAS is the verb of this clause.....SOMETHING (self-evident) is a predicate nominative followed by a prepositional phrase describing SOMETHING LIKE the cooling of a hot kettle or the wearing-out of a pair of shoes.