In 1927 the Edinburgh Mathematical Society began to publish Series 2 of the Proceedings of the Edinburgh Mathematical Society. The first paper in the new Series was by George Gibson and it was the first part of his two-part paper Sketch of the History of Mathematics in Scotland to the end of the 18th Century. The first part occupied the first 17 pages of Volume I, Part I issued in May 1927. The second part of his paper occupied pages 71 to 93 of Volume I, and was issued as the first paper in Part II. We present a version of the paper below. We have broken the paper into smaller parts for convenience of presenting it in our archive but this is a somewhat arbitrary division and certainly was not intended by Gibson.