Definition:Neusis Construction
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.
See the linguistic note.
Also see
- Results about neusis constructions can be found here.
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).
Sources
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: Problems for the Greeks