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“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. ”