Verse 25 · The Rules for resolving the questions on Time, the position of places, and directions. · Surya Siddhanta · siva.sh

siva.sh/surya-siddhanta/3/25

माध्याह्निको भुजो नित्यम् छाया माध्याह्निकी स्मृता । लम्बाक्षजीवे विषुवच्छायाद्वादशसङ्गुणे ॥

sanskrit

Multiply the cosine of the latitude by the Equinoctial shadow or the sine of the latitude by 12; the product (which is the same in both cases) divided by the sine of the Sun's declination gives the hypothenuse of the gnomonic shadow at the time when the Sun reaches the prime vertical.[1] [1. This is shown thus, Let l = latitude of the place; e = the equinoctial shadow; d = the sine of the Sun's declination; p = altitude; x = the hypothenuse of the shadow; Then, sin l : d = R : p; and R : p = x : 12; ∴ x = 12 sin ⁡ l d = e cos ⁡ l d {\displaystyle \therefore x={\frac {12\sin {l}}{d}}={\frac {e\cos {l}}{d}}} (because cos l : sin l = 12 : l and e. cos ^ d d 12 sin I).]

english translation

mAdhyAhniko bhujo nityam chAyA mAdhyAhnikI smRtA । lambAkSajIve viSuvacchAyAdvAdazasaGguNe ॥

hk transliteration by Sanscript

siva.sh/surya-siddhanta/3/25

माध्याह्निको भुजो नित्यम् छाया माध्याह्निकी स्मृता । लम्बाक्षजीवे विषुवच्छायाद्वादशसङ्गुणे ॥

sanskrit

Multiply the cosine of the latitude by the Equinoctial shadow or the sine of the latitude by 12; the product (which is the same in both cases) divided by the sine of the Sun's declination gives the hypothenuse of the gnomonic shadow at the time when the Sun reaches the prime vertical.[1] [1. This is shown thus, Let l = latitude of the place; e = the equinoctial shadow; d = the sine of the Sun's declination; p = altitude; x = the hypothenuse of the shadow; Then, sin l : d = R : p; and R : p = x : 12; ∴ x = 12 sin ⁡ l d = e cos ⁡ l d {\displaystyle \therefore x={\frac {12\sin {l}}{d}}={\frac {e\cos {l}}{d}}} (because cos l : sin l = 12 : l and e. cos ^ d d 12 sin I).]

english translation

mAdhyAhniko bhujo nityam chAyA mAdhyAhnikI smRtA । lambAkSajIve viSuvacchAyAdvAdazasaGguNe ॥

hk transliteration by Sanscript