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 25. 
 
 
If two numbers have to one another the ratio which a cube number has to a cube number, and the first be cube, the second will also be cube. 
 
 
For let the two numbers A, B have to one another the ratio which the cube number C has to the cube number D, and let A be cube;  I say that B is also cube. 
   
   
For, since C, D are cube, C, D are similar solid numbers.  Therefore two mean proportional numbers fall between C, D. [VIII. 19]  And, as many numbers as fall between C, D in continued proportion, so many will also fall between those which have the same ratio with them; [VIII. 8]  so that two mean proportional numbers fall between A, B also.  Let E, F so fall.  Since, then, the four numbers A, E, F, B are in continued proportion, and A is cube, therefore B is also cube. [VIII. 23]  Q. E. D. 
             
             
 
Permanent link
Go to Wiki Documentation
Enhet: Det humanistiske fakultet   Utviklet av: IT-seksjonen ved HF
Login