A theodolite is an optical instrument that can measure angles between any predetermined points along a horizontal and vertical plane. It has been traditionally used for land surveying, but it has also been used for the construction of buildings and infrastructure as well as for other more specialized applications (such as meteorology and rocket launching).
It has a mounted telescope that can be rotated both horizontally and vertically, and it has angular readouts that indicate the orientation of the telescope. They can also be used to relate the first sighted point through the telescope to the detection of other points from the same position.
These angles can be measured with an incredible degree of accuracy (down to microradians or seconds of arc). And from these readings, a plan can be drawn or objects can be placed in accordance with an existing design.
Learn more about theodolites in the following infographic, courtesy of EngineerSupply.
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