Definition:Neusis Construction

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A neusis construction is a technique of drawing geometric figures using only a neusis ruler and a compass.

Also known as

The word neusis can also be seen as neuseis.

Also see

Historical Note

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.

Linguistic Note

The word neusis is the Greek νεῦσις, which comes from the word νεύειν (neuein) meaning incline towards.

Its plural is νεύσεις (neuseis).