Book 6
33
And it has been proved that, if the circumference BL is in excess of the circumference EN, the angle BGL is also in excess of the angle EHN; if equal, equal; and if less, less.
33
Therefore, as the circumference BC is to EF, so is the angle BGC to the angle EHF. [V. Def. 5]
33
But, as the angle BGC is to the angle EHF, so is the angle BAC to the angle EDF; for they are doubles respectively.
33
Therefore also, as the circumference BC is to the circumference EF, so is the angle BGC to the angle EHF, and the angle BAC to the angle EDF.
33
Therefore etc. Q. E. D.
