CURIOUS NUMERICAL PROPOSITION DEMONSTRATED. 



TABLE XII. 



193 



Years 



Girt, 



Contents. 



Years 



Girt, 



Content 



5. 



Oney< 



Jar's 



Increase 



old. 





























. 

















perann. 





inch. 



ft- 



in. pts. 





inch. 



ft. 



in. 



jts. 



ft. in. 



pu. 





40 



5 



6 



11 4 



41 



5i 



7 



7 



10 



8 



6 



10-2 



44 



6 



10 







45 



«f 



10 



10 



2 



10 



2 



8-47, 



48 



7 



13 



7 4 



49 



7i 



14 



7 



2 



11 



10 



7-2 



52 



8 



17 



9 4 



53 



K 



18 



10 



10 



1 1 



6 



6-3 



56 



.9 



22 



6 



57 



9t 



23 



9 



o 



1 3 



2 



5-6 



GO 



10 



27 



9 4 



61 



m 



29 



2 



2 



1 4 



10 



5-05 



64 



11 



33 



7 4 



65 



Hi 



35 



1 



10 



I 6 



6 



4-58 



68 



12 



40 







69 



121 



41 



8 



2 



I 8 



2 



4-2 



72 



13 



46 



11 4 



73 



13^ 



48 



9 



2 



I 9 



10 



3-87 



76 



14 



54 



5 4 



77 



14i 



56 



4 



10 



1 11 



6 



3-59 



80 



15 



62 



6 



81 



15.!- 



64 



7 



2 



2 1 



2 



3-35 



100 



20 



111 



1 4 



101 



20f 



113 



10 



10 



2 9 



6 



2-51 



120 



25 



173 



7 4 



121 



25i 



177 



1 



2 



3 5 



10 



2-00 



^To be concluded in our next. J 



IV. 



Demonstration of a curious Numerical Proposition, hj Mt. 

 P. BAaLOW, of the Royal Military Academy, Wool- 

 wich. 



Proposition. 



T 



HE equation 



j;" + ?/" =: 2" 



No power but 

 the square di- 

 ■viiible into 



is abvays impossible either m INTEGERS or fractions, /or ^^° °^,'^® . 



^ , ^ '' same denonji,"- 



every value of n greater than 1. nation: 



This theorem is one of the most interesting in the theory 

 of numbers, both on account of its simphcity and gene- 

 rality, and the celebrity of those mathematicians, who have 

 attempted its demonstration. The theorem itself is due to a proposition 

 Fermat, who first proposed it as a challenge to all the Eng- of Fermai'*, 



Vof.. XXVII.— Nov. 1810. • O li:=h 



I 



