The golden canon, and the arithmetic under it
Medieval scribes placed a text block by drawing nine lines and reading the answer off the diagonals. No measuring, no arithmetic, no taste required — and the proportions that fall out are still the best default anybody has for a page of running text.
Nobody in a scriptorium measured a margin. They drew diagonals across the spread, marked where the lines crossed, and put the text block's corners on those marks. Van de Graaf reconstructed the method in the 1940s from books nobody had thought to measure, and what he found was that a construction with no numbers in it produces the same proportions over and over.
The result is a text block whose width is exactly two thirds of the page width, sitting on margins in the ratio 2 : 3 : 4 : 6 — inner, top, outer, bottom.
Why the inner margin is the small one
Because two facing pages are read as one surface. The inner margins of a spread sit against each other, so half of each adds up to a gutter the same weight as a single outer margin. Set them equal and the spread looks like two pages that happen to be near one another.
The bottom margin is the largest, and it is the one people cut first when a page is tight. It is also the one holding the block up: an evenly-margined block appears to sink, because the eye puts the optical centre of a rectangle above its geometric centre.
The arithmetic, once
For a page of width and height , the canon gives a text block of
with the inner margin at and the top at . Every other measurement follows, which is the whole appeal: one division, and the page is set.
For an arbitrary page ratio the outer margin comes out as
so the outer is twice the inner and the bottom is twice the top. That is the 2 : 3 : 4 : 6 written another way.
The same division, on the shelves
Run the ninths over the trim sizes a designer actually meets and the canon stops being a diagram and becomes a set of margins you could hand a printer today:
| Page | Trim | Inner | Top | Outer | Bottom |
|---|---|---|---|---|---|
| A5 | 148 × 210 mm | 16 mm | 23 mm | 33 mm | 47 mm |
| Trade paperback | 5.5 × 8.5 in | 16 mm | 24 mm | 31 mm | 48 mm |
| Royal octavo | 6 × 9 in | 17 mm | 25 mm | 34 mm | 51 mm |
| A4 report | 210 × 297 mm | 23 mm | 33 mm | 47 mm | 66 mm |
Two things fall out of the table. The first is how large the canon's margins are — nearly half of an A4 sheet is margin, which is why it reads as luxurious and why nobody selling paper by the page will default to it. The second is that the proportions barely move across formats: the canon does not know what a millimetre is, so it cannot be thrown off by one.
Note
The canon assumes a spread. On a screen there is no facing page and no gutter, so the inner and outer margins have no reason to differ — take the ratio for the vertical and let the horizontal be symmetrical.
What it is actually for
Not for copying. For having somewhere to start that is not the default margin of whatever tool you opened. Move away from the canon deliberately and the page usually survives; arrive somewhere by accident and it usually does not.