Frequencies measurements and DF or direction finder azimuths. He enjoys abstract mathematics and can plot artillery azimuths and triangulations in his head. The spherical azimuths are relabeled as formula 34 (from formula 33). Simultaneous independent observations at various discrete azimuths are possible. Mercator also gives a refined method which is useful for small azimuths. However, rotation subjects heads to mechanical stresses and inevitably changes their absolute azimuths. His only known surviving work on astronomy was on the calculation of azimuths. They all have the property that directions (the azimuths) from a central point are preserved. This means the observations must have different azimuths.