Euclid, Elements, BOOK IX., PROPOSITIONS, PROPOSITION 21.

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PROPOSITIONS

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PROPOSITION 1. PROPOSITION 2. PROPOSITION 3. PROPOSITION 4. PROPOSITION 5. PROPOSITION 6. PROPOSITION 7. PROPOSITION 8. PROPOSITION 9. PROPOSITION 10. PROPOSITION II. PROPOSITION 12. PROPOSITION 13. PROPOSITION 14. PROPOSITION 15. PROPOSITION 16. PROPOSITION 17. PROPOSITION 18. PROPOSITION 19. PROPOSITION 20. PROPOSITION 21. PROPOSITION 22. PROPOSITION 23. PROPOSITION 24. PROPOSITION 25. PROPOSITION 26. PROPOSITION 27. PROPOSITION 28. PROPOSITION 29. PROPOSITION 30. PROPOSITION 31. PROPOSITION 32. PROPOSITION 33. PROPOSITION 34. PROPOSITION 35. PROPOSITION 36.

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PROPOSITION 21.

If as many even numbers as we please be added together, the whole is even.

For let as many even numbers as we please, AB, BC, CD, DE, be added together; I say that the whole AE is even.

For, since each of the numbers AB, BC, CD, DE is even, it has a half part; [VII. Def. 6] so that the whole AE also has a half part.

But an even number is that which is divisible into two equal parts; [id.] therefore AE is even. Q. E. D.

Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.

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Euclid, Elements
Thomas L. Heath, Sir Thomas Little Heath, Ed.

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Table of Contents:

PROPOSITION 21.

Euclid, Elements Thomas L. Heath, Sir Thomas Little Heath, Ed.

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Table of Contents:

PROPOSITION 21.

Euclid, Elements
Thomas L. Heath, Sir Thomas Little Heath, Ed.