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Definitions 6 through 8

Def. 6. The inclination of a plane to a plane is the acute angle contained by the straight lines drawn at right angles to the intersection at the same point, one in each of the planes.

Def. 7. A plane is said to be similarly inclined to a plane as another is to another when the said angles of the inclinations equal one another.

Def. 8. Parallel planes are those which do not meet.

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As the previous definitions require certain assumptions, so does definition 6. It assumes that any two such acute angles are equal, something Euclid does not prove but could have in the course of Book XI.

Definition 8 is analogous to definition I.23 for parallel lines in a plane.

Book XI Introduction - Definitions 3 through 5 - Definitions 9 and 10.

© 1997
D.E.Joyce
Clark University