The corpus, every claim citable.

Surya-Siddhanta IV.12-13 (~5th c. CE) gives a computational procedure for the half-duration of a lunar eclipse: the moon's latitude offsets the lunar centre from Earth's shadow; first/last contact occurs when this offset equals (shadow±moon) radii; a right-triangle Pythagorean step plus a relative-motion divide gives the time. NASA's modern eclipse-timing code uses the same triangle structure.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860