Understanding the Dot Product of Derivatives in Astrodynamics

[Nabeshin]

In reading a book on astrodynamics I came across the following statement:
$$\vec{a}\cdot \vec{\dot{a}}=a \dot{a}$$

Where the dotting is the time derivative notation.

I put a picture of the original text up, and it's the statement right in the middle:
http://img.photobucket.com/albums/v715/deagleman9/IMG_1178.jpg
Except they use bold to indicate vectors.

Can anyone explain to me why this should be true? It seems akin to saying the angle between a vector and its time derivative is always 90, which is obviously not true. I've also considered it might be a notational problem with the unbolded quantities. At any rate, does anyone know what's going on here?

 

[Nabeshin]

Never mind, I think I figured this one out. I think the right side is the time derivative of the magnitude of a, rather than the magnitude of the time derivative of a.