Are Potato Eyes Poisonous?

As I was peeling potatoes today, and digging out the eyes, I remember something my Mother?, my Grandmother?, some bit of arcane knowledge picked up who knows where?, that you should cut the eyes out of potatoes because they're poisonous.  So after peeling my potatoes I went to the Net and researched this to see if it's really true or just some old wive's tale.
Well, the answer is yes and no.  The eye itself is not toxic, but the sprouts (you know, those ugly white things)  that grows from them are.  They  contain glycoalkaloids that can cause nausea, cramping, vomiting, stomach upset, and diarrhea.  So that's the part that should be removed, you don't have to dig the eyes out, but I will, I know me.
The article I read went on to say that potatoes exposed to light will have higher concentrations of glycoalkaloids and cooking only makes that stronger.  Potatoes exposed to light will also develop green areas, this is chlorophyll, which is not toxic, be is an indicator that there is a high concentration of  glycoakaloid and the green area should be cut out.
Should also mention that potatoes, but not sweet potatoes, tomatoes, sweet and hot peppers and egg plant are members of the nightshade family.  The potato itself is the only part of the plant that isn't poisonous.  Just a little something to think about as you fix dinner.
I've always removed the eyes (dig those puppies out) and the sprouts, but I didn't know about removing the green area from a potato, one more thing to look for while peeling potatoes instead of day dreaming.