Therefore the triangle ABC is equiangular with the triangle DGF. Therefore, proportionally, as BA is to AC, so is GD to DF. [VI. 4] But, by hypothesis, as BA is to AC, so also is ED to DF; therefore also, as ED is to DF, so is GD to DF. [V. 11] Therefore ED is equal to DG; [V. 9] and DF is common;
Therefore the triangle ABC is equiangular with the triangle DGF. Therefore, proportionally, as BA is to AC, so is GD to DF. [VI. 4] But, by hypothesis, as BA is to AC, so also is ED to DF; therefore also, as ED is to DF, so is GD to DF. [V. 11] Therefore ED is equal to DG; [V. 9] and DF is common;
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
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.