The answer is, this measure or amount is the versed sine of the angle through which the body moves.
"Scientific American Supplement, Vol. XXI., No. 531, March 6, 1886" by Various
Versed sine of curvature of toes.
"Remarks on some fossil impressions in the sandstone rocks of Connecticut River" by John Collins Warren
He was the first to make use of sines instead of chords, and versed sines.
"Astronomical Curiosities" by J. Ellard Gore
The versed sine, or deflection of the middle of the catenary, was 50 feet.
"The life of Isambard Kingdom Brunel, Civil Engineer" by Isambard Brunel
Furthermore the versed sine of the angle XI in (4.37) and side xi in (4.38) can be expressed in terms of the sine of half the angle or the side using the relation (A.6).
Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry