  Ratios and coefficients are used to simplify calculations. For geometric
usage these values also called function values. Like in Egypt also in Babylon
such a value system can be shown. The reconstructed calculation sequence, of
the Plimpton 322 cuneiform tablet, presented and described here, shows in its
completeness that, around 3800 years ago there already was a systematically
applied exact measuring system, with the usage of trigonometric function
values. With this approach one can plausibly explain that, as we still it
practice today, a geometry of the circle has been used for this calculation. It
is based on, but not only, of the usage of the regularities, which 1200 years
later, were named after Pythagoras. During a second calculation step, for an
intended scaled documentation, presentation or transfer to other locations, the
dimensionless calculated function value, was extended, with a fractional part,
or more exact spelled a common factor. This transformation creates a real
measurable length from the ratios, always related to the smallest unit. The
systematic usage by means of inclining triangles already in old Babylonian
times, goes far beyond the previously known level of this age. The accuracy of
the individual calculation is just as verifiable and on exactly the same level
as the trigonometric functions used today. However, at least at this point in
time, the Babylonians were content with dividing a quarter circle into at least
150 inclining triangles. This old Babylonian trigonometric function value
system, together with the here described "Babylonian diagonal calculation", is
thus the forerunner of the Greek chord calculation and the Indo-Arabic
trigonometric functions of the early Middle Ages, which we still use today. In
addition, the new approach to Plimpton 322 plausible explains why and how such
values could have been used.
