A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: John D. Howard
Date: 2017 Nov 21, 17:35 -0800
Think logarithmns and negative numbers.
Not so long ago if you wanted to multiply or divide you used log tables ( or slide rules - same thing ) but there are no logs for negative numbers.
The work-around was to work in positive numbers and then have rules like " If same name, subtract; if contary name, add". By using mederian angle, T, and not GHA you could limit angles to 0 to 90 d. Another work-around was the weird trig functons like haversine where there are no negative numbers. We, today, think nothing of South dec being negative or West long being negative but still, I for one, must rember to ADD when subtracting a negitive number.
The " ~ " was used with some rule - usually when to add or subtract. Like many have pointed out, the formulas are the same.