Commentary on Proposition XI.24

Back to Proposition XI.24.

[Folio 0328 | p. 324]

As Heiberg says, this proposition is carelessly enunciated. Euclid means a solid contained by six planes and not more, the planes are parallel two and two, and the opposite faces are equal in the sense of identically equal, or, as Simson puts it, equal and similar. The similarity is necessary in order to enable the equality of the parallelepipeds in the next proposition to be inferred from the 10th definition of Book XI. Hence a better enunciation would be:

If a solid be contained by six planes parallel two and two, the opposite faces respectively are equal and similar parallelograms.

The proof is simple and requires no elucidation.