The difference of the epicycles of the odd and even quadrants, multiplied by the sine of the anomaly and divided by the radius, is additive to or subtractive from the even epicycle.
Modern Technical Commentary:
Implements 'Epicyclic Contraction'. The Siddhanta recognizes that the solar and lunar epicycles are not fixed circles but vary slightly in size depending on the planet's position. This specific formula calculates the 'Corrected Circumference' used for the Equation of the Center.
The difference of the epicycles of the odd and even quadrants, multiplied by the sine of the anomaly and divided by the radius, is additive to or subtractive from the even epicycle.
Modern Technical Commentary:
Implements 'Epicyclic Contraction'. The Siddhanta recognizes that the solar and lunar epicycles are not fixed circles but vary slightly in size depending on the planet's position. This specific formula calculates the 'Corrected Circumference' used for the Equation of the Center.
Implements the universal Siddhantic rule for epicyclic
contraction, which applies to both Manda and Sighra cycles.
Calculate the dynamically corrected epicycle circumference based on anomaly.
[Ch. II, v.38]
Siddhantic Proof: Spashta (True Longitudes) v.38
Sanskrit (Devanagari):
ओजयुग्मान्तरगुणा भुजज्या त्रिज्ययोद्धृता। युग्मवृत्ते धनर्णं स्यादोजादूनेऽधिके स्फुटम्॥
Translation (Burgess):
The difference of the epicycles of the odd and even quadrants, multiplied by the sine of the anomaly and divided by the radius, is additive to or subtractive from the even epicycle.
Modern Technical Commentary:
Implements 'Epicyclic Contraction'. The Siddhanta recognizes that the solar and lunar epicycles are not fixed circles but vary slightly in size depending on the planet's position. This specific formula calculates the 'Corrected Circumference' used for the Equation of the Center.
Siddhantic Proof: Spashta (True Longitudes) v.38
Sanskrit (Devanagari):
ओजयुग्मान्तरगुणा भुजज्या त्रिज्ययोद्धृता। युग्मवृत्ते धनर्णं स्यादोजादूनेऽधिके स्फुटम्॥
Translation (Burgess):
The difference of the epicycles of the odd and even quadrants, multiplied by the sine of the anomaly and divided by the radius, is additive to or subtractive from the even epicycle.
Modern Technical Commentary:
Implements 'Epicyclic Contraction'. The Siddhanta recognizes that the solar and lunar epicycles are not fixed circles but vary slightly in size depending on the planet's position. This specific formula calculates the 'Corrected Circumference' used for the Equation of the Center.