This is another example of sloppy English usage.  Somehow, "triangulate" is supposed to sound more sophisticated.

That is itself another sloppy use of a word.  See what the dictionary says about that.  Originally, not a compliment. It comes from the Greek "sophist", which (according to Plato) was a guy who could argue any side of any argument and win, usually by use of verbal trickery.

Your first definition is the correct one:  If I'm in Arizona, for example, and I know the compass direction to Los Angeles, and the direction to San Francisco (points 1 and 2), then I can calculate my location (point 3).

The second quote gets it wrong entirely.  The writer's counting on us not knowing what "triangulation" really means, and grabbing an interpretation out of context.   I think the quote marks mean "I'm using this word in some other sense than its real one".

I'm disappointed with Victor Davis Hanson's use.  I'm sure it was just a momentary lapse.  You don't "triangulate between" two points (or in his case, ideologies).  A better choice would be "interpolate" (given two points on a line, find a third point on that line, between them).

Even the Very Wise fall victim to misunderstood usage.  In 2007, Andrew Sullivan wrote "In one simple image, America's soft power has been ratcheted up not a notch, but a logarithm".

Eugene Volokh was all over that  one:

http://volokh.com/posts/1199559637.shtml

He hits the cliche nail on the proverbial head with "... scientific allusions ... tempt people into error ... they sound cool - and people use them because of that rather than because they're apt". 

I think I understand why people use the word triangulation the way they do (whether or not it's right to do so):

The second sense of triangulation (in the American Heritage Dictionary) is given by: "The location of an unknown point, as in navigation, by the formation of a triangle having the unknown point and two known points as the vertices."

If you wished to position yourself between two points, and yet distance yourself from both, you wouldn't position yourself on the line segment connecting those two points, but you'd position yourself on a point that was not on the segment connecting the first two points, yet  still "in between" them in some sense -- in short you'd end up with an (acute) triangle. Here's an example:

Consider the Cartesian plane, and points A = (0,0) and B = (2, 0) on the x-axis. The point C = (1, 8) is "in between" A and B in the sense that its x-coordinate (1) is halfway between A's x-coordinate (0) and B's x-coordinate (2), but C has the "advantage" of being farther away from A and B than the midpoint of A and B would be. (The midpoint is distance 1 from both A and B, but C is a distance of just over 8 from both A and B.)  And ABC forms a triangle.

(If you're wondering, the coordinate-wise definition of "in between"  used above may seem silly but it is sometimes useful in math and physics.)

You know how politicians are: A politician often wants to show himself as "more moderate" ("in between") and yet "so different" from two dissenting factions. That is, he wants to play point C to the other politicians' points A and B. I find it descriptive -- if not entirely accurate -- to call this posturing triangulation. I hope this is what other people mean when they use triangulation in a political context.

I'm a mathematician-in-training, and I hope this comment doesn't grate too loudly on the ears of the sophisticated English users at N.E.R. (mathematical jargon isn't entirely consistent with good English usage, and I write more proofs that ordinary English).

I stumbled across N.E.R while searching for essays by the admirable T. Dalrymple. I find the writing at N.E.R. entertaining and edifying, though I don't always understand the references to life in England today (I'm a damn Yankee, and my exposure to England is mainly through books by P.G. Wodehouse and others). Keep up the good work!

I'm a mathematician-in-training, and I hope this comment doesn't grate too loudly on the ears of the sophisticated English users at N.E.R. (mathematical jargon isn't entirely consistent with good English usage, and I write more proofs that ordinary English).

You are too modest. Your English is precise, clear and eloquent. Thanks very much for your explanation. I feel, however, that "triangulation" is such a specific term that it is more suited to maths (as we English call math) than to politics. When used in a political context, even by good speakers, it loses precision and becomes jargon.

Your comments are welcome. Keep reading.