ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

298 BRAHMAGUPTA'S ASTRONOMY: ITS HIGHLIGHTS 1 as the remainder. we subtract one from it, and get 1,850,569 as the correct ahargaṇa for the day. An Alternative Rule for Ahargaṇa Both Bhāskara I and Brahmagupta give an alternative rule for calculating out ahargaṇa¹ : Multiply the number of (solar months) elapsed since the beginning of kaliyuga by the number of lunar months (in a yuga) and divide by the number of solar months (in a yuga). Reduce the quotient to days (and add the number of lunar days elapsed since the begin- ning of the current lunar month); then multiply by the number of civil days (in a yuga) and divide by the number of lunar days (in a yuga); the quotient denotes the ahargaṇa. Mean Longitude of a Planet (i) The mean longitude of a planet in revolutions is given by the expression : (Brahmagupta² and also Bhāskara³).

1. शशांकमासैरभिताडितान् हरेदतीतमासानथ वार्कसम्भवैः । दिनीकृतान् भूमिदिनैर्हतान् दिनैर्विभज्य लब्धश्शशिजैर्हरर्गणः ॥ MBh. I. 7 युगगतशशिमासवधाद्रविमासाप्तं दिनीकृतं सदिनम् । भूदिनगुणितं शशिदिनहृतमाप्तमहर्गणः सैकः ॥ —BrSpSi. XIII. 18
2. इष्टग्रह भगण गुणादहर्गणात् कल्पसावन द्यु हृतात् । भगणादि फलं मध्यो लंकायां भास्करौदयिकः ॥ BrSpSi. I. 31
3. उद्दारितान् यान् भगणान् क्षमादिनैर्लभामहे कान् कलियातवासरैः । इति प्रलब्धा भगणास्ततः क्रमाद् गृहाशलिप्ता विकलाः सतत्पराः । —MBh. I. 8 पर्यायाहर्गणाभ्यासो ह्रियते भूदिनैस्ततः । लभ्यन्ते पर्यायाः शेषाद्राशि भागकलादयः ॥ भास्करै स्त्रिंशता षष्ट्या सङ् गुणय्य पृथक् पृथक् । तेनैव भागहारेण लभ्यन्तेऽर्कोदयावधेः ॥ —LBh. I. 15-17 (Divide the product of the revolution-number of a planet and the ahargaṇa by the (number of) civil days (in a yuga); thus are obtained the (number of) revolutions (performed by that planet). From the (successive remainders multiplied respectively by 12,30 and 60 and divided by the same divisor (i.e. the number of civil days in yuga) are obtained the signs, degrees and minutes etc. (of the mean longitude of that planet) for (mean) sunrise (at Laṅkā).