Yes, this method is quite elegant. You are doing 2 times 2 the same procedure. Although it may be a lengthy procedure, it's routine procedure all around. No need for choosing a particular bearing-line to do further geometrical constructions that looks more usefull than others.
First starting with a near and far assumption on position on the first bearing. Then choose a point on the second bearing to assume a target course (for that particular case). Then these are projected forward to the 3rd bearing time and target course corrected (for that particular case) to find the point on the 3rd bearing (using the parallel of the 1st bearing) that satisfies the constant target speed across the 3 bearings at that distance. From those 2 near and far lines you predict the point of the locusline for the time of the 4th bearing. The target has to be somewhere on that line at the 4th bearing time depending on the initial unknown distance. Then the position of the target at the time of the 4th bearing is fixed by the actual 4th bearing intersecting the locusline.
To find the position of the target at the time of the 1st bearing Efshapo does the same thing in reverse, starting from the 4th back to the first. Then he fixes the line through the 2 points which is the target course. And the overall distance between them, or the intermediate bearing intersections, indicate the target speed.
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