पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

128 PAÑCASIDDHĀNTIKĀ IV. 54 Here AB is the ‘Base’ which, extended on both sides, is the prime vertical. AC is the ‘Perpendicular’, extending northwards from AB that lies east-west. Angle CAB = 90°. BC is the shadow, and angle ABC is the angle made by the shadow with the east-west line. The direction of the sun is the line CB extended backwards, making the same angle with AB extended. Example 23. For the same place and the same day, find the Sun’s direction, when the shadow is aṅg. 27-30. (i) Shadow hypotenuse = √(27½² + 144) = aṅg. 30 (ii) Sūryāgrā = 12 × 120 × 60 ÷ (30 × 103′ 55″) = 27′ 42″.8 (iii) Agrā = 39′ 51″.4, found in example 22. (iv) ‘Perpendicular’ = (27′ 42″.8 − 39′ 51″.4) × 30 ÷ 120 = aṅg. − 3-2, i.e. aṅg. 3-2 southward. (Or, which is the same, deducting 27′ 42″.8 from 39′ 51″.4, and doing the work with the remainder 12′ 8″.6, the perpendicular obtained is aṅg. 3-2, negative and ∴ southward). (v) ‘Base’ = √(27½² − 3 1/30²) = aṅg. 27-20. Or, by the simplified formula, ‘Perpendicular’ = (12 × 60′ − 30 × 34′ 30″) ÷ 103′ 55″ = (720′ − 1035′) ÷ 103′ 55″ = −315′ ÷ 103′ 55″ = aṅg. 3-2 southward. From the ‘Perpendicular’ the ‘Base’ is found as already done. The direction of the shadow is found graphically thus:

Base                                        B    To Sun
A +-----------------------------------------------+--------->
| 27-20                                        / Angle Shadow / Angle of Sun
P  |                                            /
e  |                                           /
r  | 3-2                                27-30 /
p. |                                         /
|                                        / Shadow
C +---------------------------------------+

Fig. IV. 16 Here, AB is the ‘Base’, which extended both ways, is the prime vertical. AC is the Perpendicular, directed southwards. BC is the shadow. Angle ABC is the direction of shadow. At an equal angle to the east-west on the opposite side is the Sun. Example 24. Sin lat of place = 72′ , whence sin colat = 96′. The longitude of the Sun = rāśi. 11-0, from which sin longitude of the Sun = 60′, and thence sin decl = 24′ 24″, south, since the Sun is within the six signs from Libra. Find the direction when the shadow is aṅg. 27-30. (i) Shadow-hypotenuse = √(144 + 27½²) = aṅg. 30. (ii) Sūryāgrā = 12 × 120 × 72′ ÷ (96 × 30) = 36′.