previous next

PROPOSITION 17.

If a cube number do not measure a cube number, neither will the side measure the side; and, if the side do not measure the side, neither will the cube measure the cube.

For let the cube number A not measure the cube number B, and let C be the side of A, and D of B; I say that C will not measure D.

For if C measures D, A will also measure B. [VIII. 15]

But A does not measure B; therefore neither does C measure D.

Again, let C not measure D; I say that neither will A measure B.

For, if A measures B, C will also measure D. [VIII. 15]

But C does not measure D; therefore neither will A measure B. Q. E. D.

Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.

The National Science Foundation provided support for entering this text.

Purchase a copy of this text (not necessarily the same edition) from Amazon.com

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 United States License.

An XML version of this text is available for download, with the additional restriction that you offer Perseus any modifications you make. Perseus provides credit for all accepted changes, storing new additions in a versioning system.

load focus Greek (J. L. Heiberg, 1883)
hide Display Preferences
Greek Display:
Arabic Display:
View by Default:
Browse Bar: