BRAHMAGUPTA A GREAT CRITIC Rsine of the Sun's prime vertical altitude. Bhaskara also gives the rule in his Mahabhaskariya: 324 Multiply the Rsine of the (Sun's) greatest declination by the Rsine of the Sun's true (sayana) longitude; then divide (the product) by the Rsine of the colati- tude, the result is (the Rsi ne of) the agra of the true Sun. When that (agra) is less than the latitude and when the Sun is also in the northern hemisphere, multiply (the Rsine of the Sun's agra) by (the Rsine of) the colatitude; the result is the Rsine of the Sun's prime vertical altitude.² The condition laid down in the rule that the "Sun's agra should be less than the latitude" is incorrect. The error was originally comitted by Aryabhata and Bhaskara followed it. This error was noticed by Brahmagupta³. Bhaskara I, however, corrected the error in the Laghu-Bhaskarya. There he gives the correct conditions. It is not the agra that should be less than the latitude, it is the Sun's declination (or rather the Rsine of the Sun's northern declination as we have in the Laghu- Bhaskariya), which should be less than the latitude (or rather the Rsine of the latitude). This condition is necessary for the existence of the prime vertical shadow of the gnomon. It may be pointed out that the commentators of Aryabhata I have interpreted the rule given by Aryabhata I as conveying the correct meaning: they say that Aryabhata also meant declination when he used the term agra. 1. परमापक्रमजीचामिष्टव्याहतां ततो विभजेत् । ज्यालम्बकेन लब्धार्काग्रा पूर्वापरे क्षितिजे || सा विषुवज्ज्योना चेद् विषुवदुद्ग्लम्वकेन सँगुणिता ! विषुवज्ञ्ज्यया विभक्ता लब्धः पूर्वापरे शंकु || 2. स्फुटरविभुजनिष्ठां यां परां कांतिजीवां । हरतु समवलम्बज्या कलापेन भूयः || स्फुट दिवस कराया सा यदाऽक्षांशहीना | रविरपि वदेगोले चोत्तरे लम्बकृघ्नाम् ॥ अवज्यया हरेद् भूयः शंकुः स्यात् सममण्डले । तद् वर्ग व्यात कृत्योयद् विश्लेषं तत्पदं प्रमा | 3. योऽग्रयां विषुक्यातो यदुक्तमूनायाम् । समगण्डलगस्तद्वत् कान्तिव्यायां यतो भवति 17 - Arya. V. 30-31 -MBh. III. 37-38 -BrSpSi. XI. 22
