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Gaṇitānanda pp 357-369 | Cite as

Solution of the Astronomical Triangle as Found in the Tantrasaṅgraha (AD 1500)

  • K. RamasubramanianEmail author
Chapter

Abstract

The spherical triangle formed on the celestial sphere by the positions of the Sun, north pole and the zenith on it is called an astronomical triangle.

Symbols and Select Glossary

A

Azimuth measured from the north.

B

Bhā-bhuja (‘Shadow-arm’) which is the distance of the Sun’s projection on the plane of the celestial horizon from the east--west line.

C

Cosine of the local hour angle; \( \sqrt {R^{2} - J^{2} } \).

D

Certain divisor ( s).

‘Day-sine’

Radius of the Sun’s diurnal circle; \( R\cos \delta \).

‘Gnomon’

Sine of the altitude of the Sun.

H

Hour angle measured eastward.

J

Svanata-jyā, the Sine of the local hour angle defined by \( J = \frac{(R\sin H).(R\cos \phi )}{R} \).

K

Bhā-koṭi (‘Shadow-upright’) which is the distance of the Sun’s projection on the plane of the celestial horizon from the north--south line.

R

Radius, norm, trijyā or sinus totus.

‘Shadow’

Cosine of the altitude of the Sun.

\( \alpha \)

Altitude of the Sun or its co-zenith distance.

\( \gamma \)

Digagrā (directional amplitude), the (Indian) azimuth measured from the east--west line; so that we have \( A = 90^{ \circ } \pm \gamma \).

\( \delta \)

Declination of the Sun.

\( \varphi \)

Terrestrial latitude.

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Cell for Indian Science and Technology in Sanskrit, Department of Humanities and Social SciencesIndian Institute of Technology BombayMumbaiIndia

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