History of Hindu Mathematics: A Source Book v2.c17.s8.40

v2.c17.s8.40

There is a certain astronomical problem which involves the quadratic equation² $(72+a²)x² 24apx = 144((R²)/2 - p²),$ where a = agra (the sine of the amplitude of the sun), b = palabha (the equinoctial shadow of a gnomon 12 *aṅguli* long), R = radius, and x = koṇaśaṅku (the sine of the altitude of the sun when his altitude is 45°). Dividing out by (72+a²), we have $x² 2mx = n,$ where $m = 12ap/(72+a²), n = (144(R²/2 - p²))/(72+a²).$