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

192 PAÑCASIDDHĀNTIKĀ VIII.17 It is a matter of experience that an object looks bigger, the nearer it is, smaller the farther away it is, i.e. the angle formed by the object at the eye is inversely proportionate to the distance. We have already mentioned that approximately the daily true motion of the Sun and the Moon is inversely proportionate to the distance. Therefore, the angle at the eye is proportionate to the daily true motion, approximately. Hence, from the proportion, Mean motion: True motion:: Mean angular diameter; True angular diameter, we have, True angular diameter = Mean angular diameter × true motion ÷ mean motion, which is the rule given. [ग्रहणकालः] अवनतिवर्गं जह्याद् रवीन्दुपरिमाणयोगदलवर्गात् । तन्मूलात्तु द्विगुणात् तिथिभुक्तवदादिशेत् कालम् ॥ १६ ॥ Moment of the eclipse 16. Subtract the square of the parallax-corrected latitude from the square of the sum of the semi-diameters. The square root of the remainder, multi- plied by two, is the number of minutes of arc giving the duration. These minutes, multiplied by 60 and divided by the minutes of relative true daily motion gives the time of duration in nāḍikās. The following is to be done: (i) Minutes of arc of duration = 2 √(sum of the semi-diameters)² - (parallax corrected·latitude)². (ii) Time duration in nāḍīs = minutes of arc of duration × 60 ÷ daily relative true motion in minutes of arc. (Half this, subtracted from, and added to the time of new moon corrected for parallax gives the first and last contacts respectively). The rationale of the work has been shown in connection with the Paulīśa (chap. VII). We must add the following: If the latitude as corrected for parallax is found separately, each for the time of first contact and the time of last contact, and used in the work, then each will be more correct. Thus, the corrected latitude and the time are interdependent, each requiring the other for its computa- tion, and therefore the method of successive approximation is indicated here. This is not mentioned by the work, as being easily understood, or the author does not give it because it is not found in the original. [ग्रहणपरिलेखाः] रविशशिमानयुतिदलादवन [ति] हीनाद्वदन्ति या लिप्ताः । तान्यङ्गुलानि विद्याद् भानोश्छन्नानि चन्द्रमसा ॥ १७ ॥ 16. Quoted by Utpala on BS 5.18 b. A. रविन्दु. B. ०द्दलवग्रति 16a. A1.B1.2. वर्गे; A2. वग्र c. A. ०मलात्तु. B. द्विगुणा