If they know the latitude and longitude, how did they do to define the direction of cities and location from a specific place?
I ask here about the math formula linking between latitude and longitude to obtain the azimuth of a place?
Also, can you mention a real case that was done by them to define a place direction using terrestrial marks like what the prophet PBUH did?
You said" By that time the Petra Qibla had been forgotten, and people were looking for reasons why they mosque might have had a different Qibla", i understand from this that Sana'a people knew that mecca is behind Dhain by a straight line; no no no, is this a rational reasoning? It's totally against the science and the history; if that was the case i will be sure that they were very developed than 20th century people, i guess that they had theodolites, sextants, stopwatch: Else; was this done by coincidence?
The weighting is: this description is superhuman and miraculous.
As I mentioned in the first section, I will post an article on the science of qiyās in the download section.