Definition:Neusis Construction/Historical Note

Historical Note on Neusis Construction

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