It was the weekend and my optometrist's office was closed. I am a pastor and had to lead the worship service on Sunday without my glasses. There is a lot of reading involved. I got by with a pair of reading glasses, but everything more than fifteen feet away was a big blur.
I searched the Internet for eyeglass repair. There was nothing about replacing a broken monofilament lens retainer.
Step 1: Anatomy of an eyeglass frame
The left portion of the drawing shows the end of the frame if the glasses are upside down on a countertop as in my first photo and you are viewing the frame from the side where the bows attach. There are two small holes near the end of the frame. The monofilament line loops through these holes. The 90 degree bends the line must make keep the line from slipping when the lenses are in place. The graphic in the next step will give you a clearer picture of how that works.
The right portion of the drawing shows a cross section of the metal in the frame and the channel on the inside of the frame where it contacts the lens and supports it. The gray circle is a cross section of some monofilament line permanently embedded in the frame. There is a corresponding groove around the circumference of the lens and that groove fits over the embedded monofilament line to keep your lens in place where the frame goes around the lens.