[FOM] Actual and potential infinite in Euclidean geometry

José Félix Costa fgc at math.ist.utl.pt
Tue Dec 20 03:52:25 EST 2005

Alexander Zenkin asked about Aristotle's potential and actual infinite in
the «concept of line» used by Euclides in the Elements.

The concept of line from «Definition 2» (of the Elements) has been deeply
discussed throughout the History of Mathematics.

[Definition 2 of the Elements]
Grammè dè mêkos aplatés : a line is breathless length (Thomas Heath

In what concerns potential and actual infinite,
Sir Thomas Heath, in his translation of the Elements, presents a detailed
history of interpretation of the concepts involved, e.g., in pages 232-233.
The interpretations of Definition 2, together with the taxonomy of lines,
are discussed from page 158 on.

Euclid, The Thirteen Books of the Elements (3 volumes),
Translated by Sir Thomas L. Heath,
Dover Edition.

I know that research on this subject is being done in History of Science,
namely in Lisbon.

J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc at math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm

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