Euclid's Elements: Proposition 7

[AntiMe]

Alright so, I decided to read some Euclid's Elements for my own personal gain (became interested while reading Stewart's Precal, and I think it might help with Calculus) and I'm stuck on proposition 7, mainly because I really want to understand the reasoning behind it and I just can't seem to make a connection.I pretty much understand the basis of what proposition 7 is trying to prove or demonstrate, but I just can't get around the fact that in the statement that "the angle ADC is greater than the angle DCB; therefore the angle CDB is much greater than the angle DCB" doesn't make sense to me. ADC is not equal to CDB.

Maybe I'm just too stupid to understand, but where is the assumption that angle CDB must be greater than DCB made plausible?

Here is the link to the proposition

 

[mathwonk]

CDB is greater than CDA, which equals DCA, which is greater than DCB. Thus CDB is "much" greater than DCB.