# Definition:Neusis Construction/Historical Note

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## Definition

Many of the constructions performed by Archimedes were **neusis constructions**.

Some sources suggest that Oenopides of Chios (c. $440$ BCE) was the first to rank **compass and straightedge constructions** above **neusis constructions** in importance.

It may have been Hippocrates of Chios (c. $430$ BCE) who publicised the principle to use a **compass and straightedge construction** in preference to a **neusis construction** whenever possible.

Euclid's *The Elements* uses **compass and straightedge constructions** exclusively.

Under Plato, **neusis** was considered a last resort when all other methods of construction had failed.

By the time of Pappus of Alexandria, to use a **neusis construction** when other methods would work was considered a serious error.

## Sources

- 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Problems for the Greeks