"with compasses and theodolites"

Theodolite
Creative Commons Attribution Share AlikeTheodolite - Credit: Rama
A theodolite is an instrument used in surveying and engineering.  It can measure both horizontal and vertical angles.  One of the first examples of a theodolite was built by Joshua Habermel in Germany in 1576.  The theodolite replaced a similar, earlier instrument called a dioptra which dated from the 3rd century BC and was used in astronomy.