शङ्कुच्छायाहते त्रिज्ये विषुवत्कर्णभाजिते । लम्बाक्षज्ये तयोश्चापे लम्बाक्षौ दक्षिणौ सदा ॥
Translation (Burgess):
The sine of the latitude (Akshajya) is found from the equinoctial shadow... the arcs are the latitude and co-latitude.
Modern Technical Commentary:
The fundamental formula for Geodesy: sin(latitude) = (Equinoctial Shadow * R) / Hypotenuse. It converts the observed physical shadow at noon on the equinox into the observer's angular latitude (Aksha).
शङ्कुच्छायाहते त्रिज्ये विषुवत्कर्णभाजिते । लम्बाक्षज्ये तयोश्चापे लम्बाक्षौ दक्षिणौ सदा ॥
Translation (Burgess):
The sine of the latitude (Akshajya) is found from the equinoctial shadow... the arcs are the latitude and co-latitude.
Modern Technical Commentary:
The fundamental formula for Geodesy: sin(latitude) = (Equinoctial Shadow * R) / Hypotenuse. It converts the observed physical shadow at noon on the equinox into the observer's angular latitude (Aksha).
The shadow of a 12-digit gnomon on the day of the
equinox, representing the tangent of the location's latitude.
Calculate the equinoctial shadow (Vishuvachaya) from latitude.
[Ch. III, v.13]
Siddhantic Proof: Tri-Prasna (Shadows & Direction) v.13
Sanskrit (Devanagari):
शङ्कुच्छायाहते त्रिज्ये विषुवत्कर्णभाजिते । लम्बाक्षज्ये तयोश्चापे लम्बाक्षौ दक्षिणौ सदा ॥
Translation (Burgess):
The sine of the latitude (Akshajya) is found from the equinoctial shadow... the arcs are the latitude and co-latitude.
Modern Technical Commentary:
The fundamental formula for Geodesy:
sin(latitude) = (Equinoctial Shadow * R) / Hypotenuse. It converts the observed physical shadow at noon on the equinox into the observer's angular latitude (Aksha).Siddhantic Proof: Tri-Prasna (Shadows & Direction) v.13
Sanskrit (Devanagari):
शङ्कुच्छायाहते त्रिज्ये विषुवत्कर्णभाजिते । लम्बाक्षज्ये तयोश्चापे लम्बाक्षौ दक्षिणौ सदा ॥
Translation (Burgess):
The sine of the latitude (Akshajya) is found from the equinoctial shadow... the arcs are the latitude and co-latitude.
Modern Technical Commentary:
The fundamental formula for Geodesy:
sin(latitude) = (Equinoctial Shadow * R) / Hypotenuse. It converts the observed physical shadow at noon on the equinox into the observer's angular latitude (Aksha).