Euclid, Elements, BOOK VIII., PROPOSITIONS, PROPOSITION 22.

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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 11. 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.

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PROPOSITION 22.

If three numbers be in continued proportion, and the first be square, the third will also be square.

Let A, B, C be three numbers in continued proportion, and let A the first be square; I say that C the third is also square.

For, since between A, C there is one mean proportional number, B, therefore A, C are similar plane numbers. [VIII. 20]

But A is square; therefore C is also square. 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 22.

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

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Table of Contents:

PROPOSITION 22.

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