“In the Middle Ages, a quire (also called a ‘gathering’) was most often formed of 4 folded sheets of vellum or parchment, i.e. 8 leaves, 16 sides. The term ‘quaternion’ (or sometimes quaternum) designates such a quire. A quire made of a single folded sheet (i.e. 2 leaves, 4 sides) is a ‘bifolium’ (plural ‘bifolia’); a ‘binion’ is a quire of two sheets (i.e. 4 leaves, 8 sides); and a ‘quinion’ is five sheets (10 leaves, 20 sides). This last meaning is preserved in the modern Italian meaning of quire, quinterno di carta.
“The current word ‘quire’ derives from OE ‘quair’ or ‘guaer’, from OF ‘quayer’, ‘cayer’, (cf. modern Fr. cahier), from L. quaternum, ‘by fours’, ‘fourfold’….
“It also became the name for any booklet small enough to be made from a single quire of paper. Simon Winchester, in The Surgeon of Crowthorne, cites a specific number, defining quire as ‘a booklet eight pages thick.’ Several European words for quire keep the meaning of ‘book of paper.’”