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

20 PAÑCASIDDHĀNTIKĀ I.20 [मासाधिपः] त्रिंशद्भक्ते मासाः प्रपन्नसहिता द्विसंगुणा [व्येकाः] | सप्तोद्धृतावशेषे मासाधिपतिस्तथैवार्कात् || १९ || Lord of the Month 19. Take the remainder set apart (as mentioned in verses 17-18), divide by 30 and take the quotient. Add 1, multiply by 2 and deduct 1. The remainder, after dividing out by 7, is the Lord of the month, counted from the Sun. The rule is (Q + 1)2 − 1, where Q is the quotient taken. Here in the place of the reading 'kāryāḥ' accepted both by TS and NP, we have adopted the read- ing vyekāḥ, given by Bhaṭṭotpala in his Br. Sam. commentary, as being the correct one and as neces- sary here. Also in the place of prapanna Bhaṭṭotpala reads pratipada. Whatever be the reading here, we want the meaning '1'. The rule is derived thus: As mentioned before for the Lord of the year, to get the Lord of the month the days are divided into sāvana month of 30 days duration and the Lord of the first day of the month is the Lord of the Month. Thus the Lord of the very first day, viz. the Sun is the Lord of the first month. As the days in the month, 30, divided out by 7 leaves the remainder 2, the Lords of the successive months are those of 2, 4, 6 etc. days after that of the first month, i.e. the Lord of the nth month is given by (n − 1)2 + 1 = n × 2 − 1. As n is the current month, it is equal to (Q + 1). Therefore n × 2 − 1 = (Q + 1)2 − 1, which is divided out by 7 gives the Lord of the month. Here too the derivation of M.M. Sudhakara Dwivedi is wrong (vide his commentary on the verse. p. 6). The translation of both TS and NP are incorrect for having taken the reading kāryāḥ for vyekāḥ ('deduct 1'), not realising which NP complain: “The text’s (I.19) ‘increase the (resulting) months by the current one’ should be replaced by ‘discard the fractional part of the current (month)’ (Pt. II, p. 13, footnote). On verses 17-19, K.S. Shukla has a detailed note in his paper, ‘The PS of VM (2)’ Gaṇita, 28 (1977) 99ff.” Example 6. For the same day as given in Ex. 5 give the Lord of the month. The remainder set apart (in the Ex. 5) is 666. Dividing by 30, the Quotient, Q, obtained is 22. (22

• 1)2 − 1 = 45. Dividing out by 7, the remainder is 3. Hence, the third from the Sun, viz. Bhauma is the Lord of the month. [होराधिपः] सप्तोद्धृते दिनेशः त्रिगुणेऽ(ध्येके) [युते च] होराभिः | (पञ्चघ्ने) सप्तहते विज्ञेयः कालहोरेशः || २० ||

19. Quoted by Utpala on BS 2. p.31. 19a. B1.2. प्रभवसहिताः; U. प्रतिपत्सहिताः b. A1.2. B1.2. C.D. कार्याः for व्येकाः c. B1.2. सप्तोधृता U. शेषे d. B1. वार्ध्यात्