Euclid, Elements, BOOK IX., PROPOSITIONS, PROPOSITION 29.

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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 29.

If an odd number by multiplying an odd number make some number, the product will be odd.

For let the odd number A by multiplying the odd number B make C; I say that C is odd.

For, since A by multiplying B has made C, therefore C is made up of as many numbers equal to B as there are units in A. [VII. Def. 15]

And each of the numbers A, B is odd; therefore C is made up of odd numbers the multitude of which is odd.

Thus C is odd. [IX. 23] 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 29.

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

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Table of Contents:

PROPOSITION 29.

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