Inlaid work or intarsia quilts.
Left: From the collection of Colonial Williamsburg. Right: Dated 1718 from the British Quilt Museum and Gallery in York
The earliest patchwork quilts seem to be done in a technique that is neither piecing nor applique, but a kind of inlaid work called intarsia. Intarsia was more commonly done in woodwork and stone work, for example this marble intarsia from the Taj Mahal.
Craftsmen in several European cultures created intarsia patchwork hangings, as in the four pictured below, which are featured in a current exhibit in Vienna. Inlaid-Patchwork in Europe from 1500 to the Present will be up until March 14th at the Austrian Folk Art Museum.
Christianity is a common theme, but notice the geometric blocks that resemble piecework in the one above and those below. Many of these are probably pieced over paper.
Welsh Tailor's Quilt, about 1842, from the National Museum of Wales
Click here for more about this quilt:
The Masonic symbol of the all-seeing eye is in the center of this one.
When Nancy Hornback and I went to Germany a few years ago looking for sources of applique design we saw several of these, called tailor's quilts, very complex patchwork of wool made by tailor's apprentices as a rite of passage or a project to develop sewing skills (or patience).
A related style: uniform quilts, military quilts or soldier's quilts. The wools in these tend to be very tightly woven fabric known as serge or baize that has the bright color and the texture of felted wool. (Baize is the wool that covers pool tables today.) Uniforms were made of this dense fabric and soldiers in hospitals and on dull duty occasionally passed the time by making complex quilts of uniform pieces.
Soldier's Bed Cover, made by Jewett W. Curtis (1847-1927), Alaska, dated 1889-1893. 99" square. Collection of the Smithsonian Institution.
View a British example in the Victoria and Albert Museum by clicking here:
And see more photos of some amazing quilts in Inlaid-Patchwork in Europe from 1500 to the Present by clicking here to see an online exhibit in their press release.http://www.volkskundemuseum.at/?id=225