When Euclid turned to solid geometry in Book IX, he began with three theorems to show successively that a straight line cannot lie partly in a plane and partly not, that if two straight lines cut one another they lie in a plane and every triangle lies in a plane, and that if two planes meet then they do so in a line.
Since the door cannot open partly and let "half a person" through, the flow rate depends only on how frequently the door is opened to let whole people through.
It's the sort of book you cannot put down, partly because it is so addictive and partly because if you do put it down, you know you will spend the next few hours startling at every creaking door.
The Somalis cannot do that, partly because their clusters are too dispersed, and partly because so many of their specific needs (long-distance call centres, mosques, halal butchers) are readily met by others.As a result, Somalis find themselves in a kind of ethnic limbo, suffering all the disadvantages of isolation and none of the advantages.
Diplomats in the region say the issues cannot be resolved, partly because they are not just political – they are personal, too.
That may be why Mr Abbas adds that the army hopes to forge yet another pact with Mr Mehsud.For now, it cannot fight him, partly because it has its hands full elsewhere.
Fear, for example, cannot be even partly constituted by the belief that the feared object is dangerous, such that fear is correct whenever that proposition is true.
The knock-on effect of local success stories and homegrown companies attracting substantial investor support cannot be underestimated, partly because many entrepreneurs would prefer to remain in their native countries, he notes.
However, we concluded that a risk difference at baseline cannot be excluded, partly because an intention-to-treat ('fixed') analysis also showed a lower risk of cancer in users of insulin glargine.
