The Sines of one, two, and three signs, respectively, are to be multiplied by the Radius and by the Sine of co-declination (dyujya) and divided by the Radius. The arcs of the results are the rising times.
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.41
The Sines of one, two, and three signs, respectively, are to be multiplied by the Radius and by the Sine of co-declination (dyujya) and divided by the Radius. The arcs of the results are the rising times.
In modern trigonometry, this internalizes the
classical 'Udaya-prana' and 'Cara' corrections. It solves for
the intersection of the local horizon and the ecliptic.
Calculate the ecliptic longitude of the ascendant (Lagna).
[Ch. III, v.41-42]
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.41
Sanskrit (Devanagari):
त्रिभयुकर्णा्द गुणाः स्वाहोरात्रार्दभाजिताः। क्रमादेकद्वित्रिभज्यास्तच्चापानि पृथक् पृथक्।।
Translation (Burgess):
The Sines of one, two, and three signs, respectively, are to be multiplied by the Radius and by the Sine of co-declination (dyujya) and divided by the Radius. The arcs of the results are the rising times.
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.41
Sanskrit (Devanagari):
त्रिभयुकर्णा्द गुणाः स्वाहोरात्रार्दभाजिताः। क्रमादेकद्वित्रिभज्यास्तच्चापानि पृथक् पृथक्।।
Translation (Burgess):
The Sines of one, two, and three signs, respectively, are to be multiplied by the Radius and by the Sine of co-declination (dyujya) and divided by the Radius. The arcs of the results are the rising times.