204 



ACCOUNT OF CRETINISM. 



+ 4.104- 4; and being- a square number, it would be sweb 

 when divided by 4— thai is to say 25 a . 10* + K) 3 -\- IQ* 

 -+- 10 f 1, or its equal (25 rt f- 10) . 1 a -1- 10* -f 10 -J- 1, 

 or (25 a -f 11) . 10* -f 1.0 + 1, would be a square number. 

 Now it is evident, that (25 a + 11) • 10*, whatever value 

 be given to a, would end with two ciphers; and therefore,, 

 that the whole expression would terminate in two ones, 

 which is impossible by cor. to prop. 5. Q. E. D. 

 No square can Cor. Hence no square number can be contained under 



^u. t0feqUa,an y n » mher 9j? c q" al di g its - 



Cube6. Scholium. If this speculation be extended to cube nurrjr 



bers, it will be found, that such numbers may terminate 

 with any of the nine digits, and that it is not therefore so 

 easy to ascertain whether a number be a perfect cube from 

 the nature of its terminating figure. 



piquadrates. With regard to biquadrate:., or fourth powers, we may 



observe, that, as these are square numbers also, whatever 

 has beeu demonstrated above relating to square numbers, 

 excepting prop. 1, holds equally true for biquadrates. We 

 may farther remark ? that biquadrates terminate in 0, 1, 5, 

 or 6; and that, when they terminate in or 5, their roots 

 will terminate with or 5 a^so: moreover, that when the 

 root terminates in 5, the biquadrate will terminate in 625. 



XII. 



Some Account of Cretinism, By Henry Reeve, M. D. of 

 Norwich. Communicated by William Hide Wolla{»- 

 ton, M.D. Sec. U.S.* 



Cretinism, a -lF ELIX PLATER, in one of his observations, gives the 

 (Specie; of men- history of a species of mental imbecility, which he saw in 

 e^<lemi c C1 in ty ' passing through the village of Breniis in the Valais. Cre- 

 goate j ;uis of tinism, a word of uncertain derivation, is the name em- 

 5* u and. ployed by the inhabitants of Switzerland to denote this dis- 

 ease, which is endemial in several districts of that country. 



• Fh'bF. Tran~. for 1808, p. Ill, 



it 



