Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/363

Rh For BD is to DC as BA is to AC (VI. 3); and BE is to AC as BA is to AC (VI. A). Therefore BD is to DC as BE is to EC (V. 11). Therefore BD is to BE as DC is to EC (V. 16). Thus of the three straight lines BD,BC, BE, the first is to the third as the excess of the second over the first is to the excess of the third over the second. Therefore BD, BC, BE are in harmonical progression.

This result is sometimes expressed by saying that BE is divided harmonically at D and C.