# Definition:Neusis

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## Definition

### Neusis Ruler

A neusis ruler is a straightedge on which two points have been marked with a specific fixed length between them.

## Definition

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.

## 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).

## Linguistic Note

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

Its plural is νεύσεις (neuseis).