This section is from the book "School Needlework. A Course of Study in Sewing designed for use in Schools", by Olive C. Hapgood. Also available from Amazon: School Needlework: A Course Of Study In Sewing Designed For Use In Schools.
A plaided, striped, or figured cloth requires great care in cutting. If the breadths of a skirt made from a checked or evenly plaided material are cut off in the middle of a check, the breadths will readily match. In other plaids or designs, cut the lower edge of each breadth on the same line of the plaid or design. In cutting a garment, similar to a dress-waist, which opens in front, first decide what part of the plaid, stripe, or design will look best for the middle of the front and back. Then lay the pattern for the front on the cloth, so that the outer fold of the hem is one-eighth of an inch (or one-half of the width to be lapped) beyond the middle desired. Cut this side out, and cut the other half of the front, by laying the part already cut on the cloth, with the right sides together, and plaids or designs exactly matching. Lay the pattern for the back on the cloth, so that the back edge of the pattern is one-fourth of an inch beyond the middle desired; this allows for the seam. Cut the other half of the back as in cutting the second half of the front.
In order to cut twilled material on the bias, with the twill perpendicular, the cloth must be folded at right angles to the twill. To do this, lay the cloth lengthwise on the table, with the right side downward, fold over the lower right-hand corner, and cut on the fold. Linings for broad hems or a curved edge (as a hat) should be cut on the bias (see page 11).