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 7. 
 
 
If a composite number by multiplying any number make some number, the product will be solid. 
 
 
For let the composite number A by multiplying any number B make C;  I say that C is solid. 
   
   
For, since A is composite, it will be measured by some number. [VII. Def. 13]  Let it be measured by D;  and, as many times as D measures A, so many units let there be in E.  Since then D measures A according to the units in E,  therefore E by multiplying D has made A. [VII. Def. 15]  And, since A by multiplying B has made C, and A is the product of D, E,  therefore the product of D, E by multiplying B has made C.  Therefore C is solid, and D, E, B are its sides.  Q. E. D. 
                 
                 
 
Permanent link
Go to Wiki Documentation
Enhet: Det humanistiske fakultet   Utviklet av: IT-seksjonen ved HF
Login