They employed calculators. No, not the kind with a screen and buttons to push, actual human beings with pencils and paper, whose job it was to take the measurements from surveyors, do the mathematical calculations (trigonometry, etc.) and come up with the result.
Fun fact, the original pencil and paper calculations for the height of Mount Everest were found to only be off by about 2-3 feet, when compared to satellite images used in modern times to get an accurate number.
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