100 AN ESSAY ON THE ROOTS OF INTEGERS, 



zf. Multiply this found 4 into this 246,536,144, and write the pro- 

 duct 986,144,576 in the Rank of the Biquadrate, opposite to 758,593, the 

 third period, and immediately above 4,197,615, the upper number by Art. y' 

 in the Rank of the Biquadrate. 



-4/'. Add the figures in this situation, 986,144,576 



41,976,15 



And it becomes . . 42,962,294,576. Write this sum 

 opposite to and immediately above 986,144,576, and this 42,962,294,576 is 

 now the upper number in the Rank of the Biquadrate. 



a/. Multiply this found 4 into this 42,962,294,576, and write the pro- 

 duct 171,849,178,304 in the Rank of the Quadratus Cubi, opposite to 

 758,593, the third period, and immediately above 38,618,058, the upper 

 number by Art. u' in that Rank. 



I'. Add the figures in this situation, 171,849,178,304 



3,861,805,8 



And it becomes . . 4,033,654,978,304. Write this sum 

 opposite to 758,593, the third period, and immediately above 171,849,178,304, 

 and this 4,033,654,978,304 is now the upper number in the Rank of the 

 Quadratus Cubi. 



«-»'• Multiply this found 4 into this 4,033,654,978,304, and the pro- 

 duct is 16, 1 34,619,913,216, which is less than 18,535,911,753,593, the second 

 Resolvend by Art.j'. 



And 4 is the highest number which will answer these conditions. 



For let 5 be substituted in these operations, and they will be- 

 come — 



