Tatting by Mlle. Riego, 1850
In this first English book devoted entirely to tatting, the join as we know it has not yet been invented, so Mlle Riego overcomes this difficulty by using a netting needle or sewing needle instead of a shuttle. She made joins by passing the needle through picots. This method was soon supplanted by the regular join, but was a revolutionary step by allowing larger pieces to be made without laboriously tying the picots together with bits of thread.
In this book, the needle is manipulated the same way as a shuttle, so this is not needle tatting in the modern sense.
Mlle. Riego's description of the single stitch may seem baffling when you first read it, but take a shuttle in hand and follow along and it becomes clear. Once made, you can recognize this as our "second half" of the double stitch.
On page 6 she writes:
Compare to Mrs. Gaugain's instructions here. Do you think Riego's is clearer? It is a nice touch that she points out that the core thread should be able to slide. And, like all the others before, she includes the ubiquitous 20 half stitch edging.