The Radius multiplied by the desired shadow and divided by its hypotenuse is the Sine of altitude; from its square subtracted from the square of the Radius, the square root is the gnomon.
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.36
The Radius multiplied by the desired shadow and divided by its hypotenuse is the Sine of altitude; from its square subtracted from the square of the Radius, the square root is the gnomon.
The length of the day is 30 Ghatis increased or
decreased by twice the Cara, depending on the Sun's Ayana (hemisphere).
Calculate the length of the day (Dinamana).
[Ch. III, v.36]
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.36
Sanskrit (Devanagari):
अभीष्टच्छाययाभ्यस्ता त्रिज्या तत्कर्णभाजिता। दृग्ज्या तद्र्गसंशुदधात् त्रिज्यावर्गाच्च यत् पदम्।।
Translation (Burgess):
The Radius multiplied by the desired shadow and divided by its hypotenuse is the Sine of altitude; from its square subtracted from the square of the Radius, the square root is the gnomon.
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.36
Sanskrit (Devanagari):
अभीष्टच्छाययाभ्यस्ता त्रिज्या तत्कर्णभाजिता। दृग्ज्या तद्र्गसंशुदधात् त्रिज्यावर्गाच्च यत् पदम्।।
Translation (Burgess):
The Radius multiplied by the desired shadow and divided by its hypotenuse is the Sine of altitude; from its square subtracted from the square of the Radius, the square root is the gnomon.