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Operation in surveying

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.

Modern triangulation as, e.g., practiced by Snellius, is the same procedure executed by numerical means. Photogrammetric block adjustment of stereo pairs of aerial photographs is a modern, three-dimensional variant.

In the late 1780s, Jesse Ramsden, a Yorkshireman from Halifax, England who had developed the dividing engine for dividing angular scales accurately to within a second of arc (≈ 0.0048 mrad or 4.8 μrad), was commissioned to build a new instrument for the British Ordnance Survey. The Ramsden theodolite was used over the next few years to map the whole of southern Britain by triangulation.

In network measurement, the use of forced centering speeds up operations while maintaining the highest precision. The theodolite or the target can be rapidly removed from, or socketed into, the forced centering plate with sub-millimeter precision. Nowadays GPS antennas used for geodetic positioning use a similar mounting system. The height of the reference point of the theodolite—or the target—above the ground benchmark must be measured precisely.