# Euclid:Proposition/X/1

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## Proposition

In the words of Euclid:

*Two unequal magnitudes being set out, if, from the greater there be subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this process be repeated continually, there will be left some magnitude which will be less than the lesser magnitude set out.*

(*The Elements*: Book $\text{X}$: Proposition $1$)

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 3*(2nd ed.) ... (previous) ... (next): Book $\text{X}$. Propositions