# Condition for Existence of Fourth Number Proportional to Three Numbers

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## Theorem

In the words of Euclid:

*Given three numbers, to investigate whether it is possible to find a fourth proportional to them.*

(*The Elements*: Book $\text{IX}$: Proposition $19$)

## Proof

## Historical Note

This theorem is Proposition $19$ of Book $\text{IX}$ of Euclid's *The Elements*.

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 2*(2nd ed.) ... (previous) ... (next): Book $\text{IX}$. Propositions