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Early Trigonometry for River Crossings – 1858
The GLO surveyors (even in Nebraska) had to occasionally use trigonometry when faced with obstacles they could not measure directly across. If a right angle triangle could not be performed, the oblique triangle could easily be solved by carrying a book of logarithms. All the deputy surveyor had to know was simple addition and subtraction. This simple math was something most of the illiterate crew could not even do, so the availability of a book of logarithms was important to have.
Below is a document I put together showing how they accomplished it.
http://www.penryfamily.com/surveying/images/earlytrigonometry.pdf
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