dodo - Theodolite

http://en.wikipedia.org/wiki/Theodolite

precision instrument for measuring angles in the horizontal and vertical planes

Prior to the theodolite, instruments such as the geometric square and various graduated circles (see circumferentor) and semicircles (see graphometer) were used to obtain either vertical or horizontal angle measurements.

It was only a matter of time before someone put two measuring devices into a single instrument that could measure both angles simultaneously.
Gregorius Reisch showed such an instrument in the appendix of his book Margarita Philosophica, which he published in Strasburg in 1512. It was described in the appendix by Martin Waldseemüller, a Rhineland topographer and cartographer, who made the device in the same year. Waldseemüller called his instrument the polimetrum.

The first occurrence of the word "theodolite" is found in the surveying textbook A geometric practice named Pantometria (1571) by Leonard Digges, which was published posthumously by his son, Thomas Digges.

The first instrument more like a true theodolite was likely the one built by Joshua Habermel (de:Erasmus Habermehl) in Germany in 1576, complete with compass and tripod.

Triangulation, as invented by Gemma Frisius around 1533, consists of making such direction plots of the surrounding landscape from two separate standpoints. The two graphing papers are superimposed, providing a scale model of the landscape, or rather the targets in it. The true scale can be obtained by measuring one distance both in the real terrain and in the graphical representation.