previous next

PROPOSITION 5.

If a cube number by multiplying any number make a cube number, the multiplied number will also be cube.

For let the cube number A by multiplying any number B make the cube number C; I say that B is cube.

For let A by multiplying itself make D; therefore D is cube. [IX. 3]

Now, since A by multiplying itself has made D, and by multiplying B has made C, therefore, as A is to B, so is D to C. [VII. 17]

And since D, C are cube, they are similar solid numbers.

Therefore two mean proportional numbers fall between D, C. [VIII. 19]

And, as D is to C, so is A to B; therefore two mean proportional numbers fall between A, B also. [VIII. 8]

And A is cube; therefore B is also cube. [VIII. 23]

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: