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

132 PAÑCASIDDHĀNTIKĀ IV. 56 Radius: 'Bhuja' :: shadow-hypotenuse : shadow-Bhuja, So we have, (Sūryāgrā ± Agrā) × shadow-hypotenuse ÷ 120 = shadow Bhuja. Our author calls this Koṭi or ‘Perpendicular’, as we have already said. But this does not matter, for in a right angled triangle, with the hypotenuse given (as here the shadow), the other two sides are perpendicular to each other, and any one may be taken as the base, and the other as the perpen- dicular. (v) Base: When the ‘Perpendicular’ is got from the well-known formula of the right angled triangle, Base² + Perpendicular ² = hypotenuse², (the shadow being the hypotenuse here,) we have, ‘Base’ = √shadow² − Perpendicular². Since the Perpendicular is north-south, the ‘Base’ is east-west, and is a part of the east-west line, as the foot of the shadow is on the east-west line. Since the east-west line is known, we can lay the ‘Base’ on it, lay the ‘Perpendicular’, at right angle, and draw the shadow. Clearly, if initially we have the shadow marked on the ground, we can get the directions by using this method. The angle between the shadow and the base gives the direction of the shadow. Obviously the direction of the Sun is given by the equal angle vertically opposite. What has been said here for the shadow may be said for the sun without reversing the direction as we have done for the sake of the shadow, and the Sun’s direction can be got. From that the direc- tion of the shadow may be got as being vertically opposite. But it is clear that the author says every- thing here for the shadow, and not for the Sun. [छायातः रव्यानयनम्] छायासमरेखान्तरगुणिता त्रिज्या स्वकर्णभक्ताऽस्याः । एकत्वे (विश्ले) ष्या सूर्याग्रा संयुताऽन्यत्वे ॥ ५५ ॥ लम्ब [क] गुणिता (भा) ज्या काष्ठामौर्व्या (ततो) ऽर्कः स्यात् । सूर्योद्गवेन विधिना ग्रहा (स्त) तोऽन्येऽपि कर्तव्याः ॥ ५६ ॥ Sun from Shadow 55. (Explanatory translation): By a process reverse to the previous one, the longitude of the Sun can be computed from the shadow, thus: Take the dis- tance of the tip of the shadow in aṅgulas, from the east-west line, multiply it by 120′, and divide by the aṅgulas of the shadow hypotenuse (mentioned in the previous work). This is ‘the sine’. (It may be seen that this is the Sūryāgrā ∓ Agrā, of the previous work). If the shadow is north of the east-west line then ‘the sine’ also is north. If the shadow is south, ‘the sine’ is south. Compute the Sūryāgrā as given already in the previous work. This is to be taken as always north (as already mentioned). If ‘the sine’ and Sūryāgrā are of different direc- tions, then ‘the sine’ plus Sūryāgrā is Agrā. (It must be remembered that they will be of different directions only when the Sun is in the northern hemis- phere, i.e. within the six signs from Aries). If they are of the same direction, then the Agrā is one deducted from the other. (If ‘the sine’ is greater, then the Sun is in the southern hemisphere, i.e. within the six signs from Libra. If