APPENDIX 449 



" Count 4." Muhamed answers rightly 4. 



The 5 is then displayed on the counting board, written on the 

 blackboard, and named several times. 



" Count 5." Answer 5 



Count 3 ." 3 



" Count 2." 2 



"Count 4." 4 



"Counts." 5 



" Count 3." 3 



Then, as above, the 6 is produced. 



" Count 6." Muhamed answers 6. 



Now begins the first instruction in a sum, accompanied with 

 pointing to the dots on the counting board : 



1 + 3 



" When I add 1+3, how many do I get ? " Answer 4 



55 l ~H 4) 5) 5) )) 5 



" Now I add I + 5, does that make ? " 6 



I + 6, tell me how many does 



that make ? " 7 



After Muhamed has pawed 7 times, the 7 is named. 



" 6 less I is how many ? Here I have 6 (pointing to the counting 

 board, saying I, 2, 3, 4, 5, 6). If I take away I (this is done, the 

 outer point being pushed under the I and then covered) how many 

 remains over ? " Answer 5. 



And so it goes on, by the end of the lesson Muhamed being able 

 to add 2+i-fS and to multiply 2 by 3 and 3 by 3. The 

 marvellous rapidity of this progress is only to be surpassed by 

 the speed with which Muhamed acquired the conception of 

 a square root. This lesson may also, with advantage, be 

 transcribed. 



He is apparently already familiar with the notion of a power. 

 2 2 is written up and he is asked how much does that make ? 



Answer 4 



" Once again ? " 4 



" 2 3 That makes ? " 8 



\/4 = 2 is then written up, and Herr Krall says : "See, that is 

 called a root. ^/ is the sign of a root. *J or ^/ is called 

 the second root or square root. What comes from it, 2, gives, 

 when raised to the second power, the number which is placed 

 under the root sign, so 2 gives 4, as you have already said, and the 

 second root out of 4 gives 2." 



After this luminous explanation ^/i6 is written up. But 

 Muhamed has not yet grasped the matter completely. 



G G 



