PRESENTMENT AND TKOOF IN GEOMKTRV. 



3'3 



Fig. I. 



Next time, after recapitulation, we clenched the matter by the 

 question, "How many points determine a circle?" "Three." 

 " If, then, from any point O I draw three lines to a circle with 

 centre S, and bisect those three lines, and draw a new circle 

 throuo^h those three mid-points, what do \()n know about that 

 circle?" " It will bisect all the other chortl-segments." " And 

 what about the size and jKjsition of it?" " Its radius will be 

 half of that of the original circle, and its centre half-way between 

 O and S." "Very well, then ; now we will do a little Kinder- 

 garten. Draw a large circle and cut it out. Fold over three 

 arcs of it so as to make a contained triangle, irregular and 

 acute. Prick a ])in-hole where two of the folded arcs meet. 

 Fold over the third arc, .and see if it passes through 

 the same point." " It does." " Do you recognise the point?" 

 " It looks like the orthocentre." " Prove that it is so by folding 

 the sides on themselves." This done, " Prove it now geo- 

 metrically l)y considering the angle BOC and the arc opposite 

 A" (Fig. 2.) 11iey succeeded in this. "Now fold over one 

 of the three arcs again, and trace its outline through O. What 

 kind of a figure have you got?''' "A symmetrical figure like a 

 shuttle." 



Fie. 2. 



