We start with Alioth. Construct a bearing line from AP in Alioth's direction. Advance along the bearing toward Alioth 2 km because our Ho was 1 arcminute greater than the Hc. Construct a line at a right angle to the star's bearing. This is called the Line of Position for Alioth. All points on this line are 2 km closer to Alioth than is AP. If we have done everything right, our unknown position would be somewhere on the Alioth LOP...
If we were charting on a sphere. But we are charting on a cylinder. And that causes an error we will have to deal with later.
The Alioth LOP is the first side of our error triangle.
