You are here: BP HOME > BPG > Euclid: Elementa > fulltext
Euclid: Elementa

Choose languages

Choose images, etc.

Choose languages
Choose display
  • Enable images
  • Enable footnotes
    • Show all footnotes
    • Minimize footnotes
Search-help
Choose specific texts..
Euclid: Elementa
    Click to Expand/Collapse Option Complete text
Click to Expand/Collapse OptionTitle
Click to Expand/Collapse OptionPreface
Click to Expand/Collapse OptionBook I
Click to Expand/Collapse OptionBook ΙI
Click to Expand/Collapse OptionBook IΙΙ
Click to Expand/Collapse OptionBook IV
Click to Expand/Collapse OptionBook V
Click to Expand/Collapse OptionBook VI
Click to Expand/Collapse OptionBook VII
Click to Expand/Collapse OptionBook VIII
Click to Expand/Collapse OptionBook ΙΧ
Click to Expand/Collapse OptionBook Χ
Click to Expand/Collapse OptionBook ΧI
Click to Expand/Collapse OptionBook ΧIΙ
Click to Expand/Collapse OptionBook ΧIΙΙ
Back to library
PROPOSITION 6. 
THEOR. 5. PROPOS. 6. 
第六題 
If two circles touch one another, they will not have the same centre. 
SI duo circuli sese mutuò interius tangant; eorum non erit idem centrum. 
兩圜內相切。必不同心。 
For let the two circles ABC, CDE touch one another at the point C;  I say that they will not have the same centre. 
   
   
For, if possible, let it be F; let FC be joined, and let FEB be drawn through at random. 
 
 
Then, since the point F is the centre of the circle ABC, FC is equal to FB.  Again, since the point F is the centre of the circle CDE, FC is equal to FE.  But FC was proved equal to FB;  therefore FE is also equal to FB, the less to the greater: which is impossible.  Therefore F is not the centre of the circles ABC, CDE. 
         
         
Therefore etc.  Q. E. D. 
   
   
 
Permanent link
Go to Wiki Documentation
Enhet: Det humanistiske fakultet   Utviklet av: IT-seksjonen ved HF
Login