"चक्रवाल विधि": अवतरणों में अंतर

'''चक्रवाल विधि''' [[अनिर्धार्य समीकरण|अनिर्धार्य]] [[वर्ग समीकरण|वर्ग समीकरणों]] (indeterminate quadratic equations) को हल करने की चक्रीय विधि है। इसके द्वारा [[पेल का समीकरण|पेल के समीकरण]] का भी हल निकल जाता है। इसके आविष्कार का श्रेय प्राय [[भास्कराचार्य|भास्कर द्वितीय]] को दिया जाता है किन्तु कुछ लोग इसका श्रेय [[जयदेव (गणितज्ञ)|जयदेव]] (950 ~ 1000 ई) को भी देते हैं। ६२८ ई में [[ब्रह्मगुप्त]] ने

: ''(Considering the lesser root, greater root and interpolator (क्षेप) as the dividend, addend and divisor respectively of (pulversier) the indeterminate multiplier of it should be so taken as will make the residue of the प्रकृति diminished by the square of that multiplier or the latter minus the प्रकृति (as the case may be) to be the least. That residue divided by the (original) interpolator is the (new) interpolator; it should be reversed in sign in case of the subtraction from the प्रकृति. The quotient corresponding to that value of the multiplier is the (new) lesser root, like wise is obtained the greater root. The same process should be followed putting aside (each time) the previous roots and the interpolator. This processiscalled चक्रवाल (or the cyclic method). By this method, there will appear two integral roots corresponding to an equation with ±1, ±2 or ±4 as interpolator. In order to derive integral roots corresponding to an equation with additive unity from those of the equation with the interpolator ±2 or ±4, भावना (should be applied).