Equipollence (geometry)
In Euclidean geometry, equipollence is a binary relation between directed line segments. A line segment AB from point A to point B has the opposite direction to line segment BA. Two directed line segments are equipollent when they have the same length and direction.
The concept of equipollent line segments was advanced by Giusto Bellavitis in 1835. Subsequently the term vector was adopted for a class of equipollent line segments. Bellavitis's use of the idea of a relation to compare different but similar objects has become a common mathematical technique, particularly in the use of equivalence relations. Bellavitis used a special notation for the equipollence of segments AB and CD:
The following passages, translated by Michael J. Crowe, show the anticipation that Bellavitis had of vector concepts:
Thus oppositely directed segments are negatives of each other:
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