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Proposition 24

The rectangle contained by medial straight lines commensurable in length is medial.
Let the rectangle AC be contained by the medial straight lines AB and BC which are commensurable in length. I say that AC is medial.
| Describe the square AD on AB. Then AD is medial.
And, since AB is commensurable in length with BC, while AB equals BD, therefore DB is commensurable in length with BC, so that DA is commensurable with AC. | VI.1 X.11
But DA is medial, therefore AC is also medial. | X.23,Cor.
Therefore, the rectangle contained by medial straight lines commensurable in length is medial.
Q.E.D.

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(Forthcoming)

Book X Introduction - Proposition X.23 - Proposition X.25.

© 1996
D.E.Joyce
Clark University