Gaṇitānanda pp 357-369 | Cite as

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

## 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.