The constant is omitted in your notes, though it shouldn't be. Affine transformations of the parameter do not alter geodesy.
Let be a regular surface, and a geodesic, where is an open interval in . We have that , a constant , i.e.
where s is the arc length parameter , . I understand what is happening up to here but then my notes claim that . However do we not get that upon rearranging (1)
where A is some constant? Why is A zero? Any help would be appreciated