In this picture it's easier to see the 45 degree cut and how the two ends of the packing will join together. The shaft nut will actually compress these two ends together and create a better butt joint than if they were cut vertically for a circumference (think hose clamp) type compression. I told you this was a little confusing.
Once the ring is cut be very, very careful to minimize fraying before installing it. If you're using the "imitation" PTFE or traditional "wax" flax fraying is not an issue but with Gore GFO it is.
NOTE: When you cut rings this way they will usually not wind up the correct length. Shave one end down until you get the right fit.