Mathematical Corre^ondtnce^ 139 



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ir. a a'. 



lA 2i'. 4-^'. <i*. » C.^*. 4is. 





&c. 



The variations which a change of figns in the original equation will produce are too ob- 

 vious to need defcription. 



Hence we get the following rules for the arithmetical folution of the three forms of qua- 

 dratics, which maybe reduced to two cafes. 



C A S E I. K- ±ax = b. 

 RULE. — Place the numerical values of a and b ns divtfor and dividend, as in commtn divi/lon, 

 — Having found the firjl figure cf the quotient, add it in its proper place (which is the fame as 

 that of fuch figure of the dividend b as finnds over the units place ofthefirfl produEl of the increafed 

 divifar into juch quotient figure, -when placed for fubtrailion ) to the original divifor a ; multiply 

 the fum by fuch added figure, and fultracl the produil from the dividend, ns in common diniifion. 

 Then, if the next fipire of the quotient to be found will fall under any of the figures of the firfl 

 increafed divifor, [o as not to increafe the number of its digits when added to it, bring down the 

 next figure of the dividend, as in common divifiofi ; bift, if fuch next figure of the quotient will, 

 •when added in its proper place, increafe the number of figures in the divijor, bring down the two 

 next figures, as in the extraflion of the fqunre root. — Vind fuch next figure of tlie quotient, and add 

 both the figures of the quotient to the firfi increnfid dii-ifor for a new divifor (as in extraBing the 

 fquare root J ,• multiply fuch lafi increajed divifor by the lafi found figure ; fubtraB the produS} ; 

 bring down another figure or figures of the dividend, and proceed as before: always adding to the lafi 

 divifor the two lafi figures of the quotient, iwluding the quotient-figtirt obtaied by each divi/ion, 

 for a new divifor, as in extraBing the fquare reel .• andfo on till the operation be finifhed. 



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