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

112 PAÑCASIDDHĀNTIKĀ IV. 37 Now we shall show that sin prime vertical alt = sin dec × radius ÷ sin lat. In Fig. 12, SZD₂ is the prime vertical, and the part D₂S is the altitude of the Sun S, and the sine of the altitude is to be found. But, sin D₂S = Cos SZ, since D₂Z = 90°, and SZ = 90° – D₂S. Observe the triangle S Z NP, right angled at Z. Here, Z NP is the co-latitude. S NP = 90° – SS₂, (∵ NP S₂ = 90°). Now, from fundamental formula i, cos SZ = cos S NP × radius ÷ cos Z NP. ∴ sin Pv alt = cos (90° – dec) × radius ÷ cos co-lat = sin dec × radius ÷ sin (90° – colat) = sin dec × radius ÷ sin lat. As stated earlier, the Sun crossing the prime vertical can occur, if at all, only when it is in the northern hemisphere, (of course for north-latitudes) and this is mentioned in the verse by uttara- gole. It should be noted that it is this sin pv. alt that is asked to be derived in IV. 32 by the statement: iṣṭottaragolāpakramāṃśakajyāṃ khabhāskarābhystāṃ hṛtvākṣajīvayā, which can be seen by comparing the work. Only, the name Sama-śaṅku (i.e. sin pv.alt.) is not mentioned there. So, the arrangement would have been better if the author had first given the formula for sin pv.alt, and then given the time of crossing the prime vertical by either IV. 34 or IV. 32-33, and, last of all, the shadow of the Sun on prime vertical. But the great transcend all restriction! Or, there is plenty of all sorts of errors committed by scribes in this part of the text, as we have reason to think. [गणकस्य योग्यता] सममण्डलले(खा)संप्रवेशवेलाः करोति योऽर्कस्य । तत्प्रत्ययं च जनयति जानाति स भास्करं सम्यक् ॥ ३६ ॥ वर्षेण भगणमर्को यदि भुङ्क्ते किं त(तो) यथेष्टदिनैः । अज्ञोऽप्येवं गणयति किं न रविं लोष्टरेखाभिः ॥ ३७ ॥ Astronomer's qualifications 36. Only he is fit to be called an expert astronomer knowing the problems dealing with the Sun, who can compute the time of the Sun crossing the prime vertical, and prove his method mathematically and graphically. 37. Even a person with very little knowledge can, by using pieces of pot- sherds, and strokes tackle (by means of computation) problems like finding the Sun's motion in a desired number of days, given the motion is twelve rāśis per year. The idea is that anybody can tackle problems depending on mere proportion. Only an expert can understand how to solve difficult problems like computing the time of the Sun's crossing the prime vertical, and prove the soundness of his method by means of graphical representations. 36. Quoted by Utpala on BS 2, p.42 b. A. वेला; P. U. वेलां. A. करोतियोर्कस्य a. A. लेषा सं० 37b. A. तयो