Condition for Existence of Fourth Number Proportional to Three Numbers
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This theorem requires a proof.
This result is hopelessly confused. I'm going to leave it until I've been able to make some sense of it.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
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
This result is hopelessly confused. I'm going to leave it until I've been able to make some sense of it.
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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