Surveying
According to Napier's Rules of circular parts for a right angled triangle, sine of middle part equals the product of

Tangents of two adjacent parts
Cosines of two adjacent parts
Both (A) and (B) above
Sines of two adjacent parts

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Surveying
For mapping any country

Geodetic triangulation of greatest possible sides and accuracy is carried out
Secondary triangles are further broken into third and fourth order triangles, the points of which are used for detail surveys
All listed here
Primary triangles are broken down into secondary triangles of somewhat lesser accuracy

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Surveying
The rise and fall method

provides a check on the reduction of intermediate point levels
quicker and less tedious for large number of intermediate sights
is not suitable for levelling with tilting levels
is less accurate than height of instrument method

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