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The size and proportions of a book depend on the size of the original full sheet. If a sheet 480 by 640 mm (19 by 25 in) is used to print a quarto, the resulting untrimmed pages, will be approximately half as large in each dimension: width 240 mm ( 9 + 1 ⁄ 2 in) and height 320 mm ( 12 + 1 ⁄ 2 in).
Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the area of the preceding paper size and rounding down, so that the long side of A(n + 1) is the same length as the short side of An. Hence, each next size is nearly exactly half the area of the prior size. So, an A1 page can fit two A2 pages inside the same area.
It is based on the German DIN 476 standard for paper sizes. Each ISO paper size is one half of the area of the next larger size in the same series. ISO paper sizes are all based on a single aspect ratio of the square root of 2, or approximately 1:1.41421. There are different series, as well as several extensions.
A size chart illustrating the ANSI sizes. In 1992, the American National Standards Institute adopted ANSI/ASME Y14.1 Decimal Inch Drawing Sheet Size and Format, [1] which defined a regular series of paper sizes based upon the de facto standard 8 + 1 ⁄ 2 in × 11 in "letter" size to which it assigned the designation "ANSI A".
Recto page from a rare Blackletter Bible (1497). The canons of page construction are historical reconstructions, based on careful measurement of extant books and what is known of the mathematics and engineering methods of the time, of manuscript-framework methods that may have been used in Medieval- or Renaissance-era book design to divide a page into pleasing proportions.
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