Confused about Eagle libraries (can't add parts I see in control panel to schematic)

Question

I want to add a diode with an SOD80 package to a schematic. In the Eagle control panel under diodes.lbr, I see a part named SOD80C:

Question 1: I'm confused at this point. Am I looking at a device or a package?

I right clicked on the library, clicked on "Use," went back to my schematic, clicked to add a new part, and there's no part named SOD80C in the diode's library:

Question 2: Why isn't the part showing up in the ADD dialog, when it does show in the control panel?

Answer 1

1) You are looking at a package in that view.

To use that library in your schematic, click the "use" button in the schematic editor or find out how the use command works.

2) The parts are showing up fine -- you can not add a package to a schematic, only a part or symbol.

A part consists of symbol(s) hooked up to an optional package.