When dealing with a laser printer, or, for that matter, an IBM Selectric Composer, a point is exactly what it tends to be thought of as being nominally: 1/72nd of an inch, or 0.01388888...89 inches.
However, with printer's type, a point is slightly different: 0.013837 inches (or 0.03514598 centimeters). And Linotype machines work to a point which is 0.014 inches (or 0.03556 centimeters) in size. (This point is descended from the 0.0137 inch point of Fournier and the 0.0138 inch point of Nelson C. Hawks.)
In Continental Europe, a different type of point, the Didot point or Didone is used. Fourteen Didot points are very close to 15 points in height; a more precise figure is about 14.975 points. Another value for the ratio between the old French measure and English measure is 1142 to 1071, referenced to a history by Poggendorff by this web site.
Originally, the Didone was 1/72nd of the pre-Revolutionary inch, which in turn was 1/12 of the pied du Roi. As the French foot was originally 12.7892 inches in length, this works out to about 0.0148023 inches or 0.0375979 centimeters.
In 1879, Firmin Berthold revised the Didot point system to connect it with the metric system: a Didot point became 1/2660th of a metre, which is about 0.014800781 inches or 0.037593985 centimeters.
A metric Didot point of exactly 0.0375 centimeters has been proposed, and may in fact be in use, and the French Imprimerie Nationale is said to use a point of 0.04 centimeters. Also, it has been proposed to measure printing type directly in millimeters.
The first laser printers tended to print at a resolution of 300 dpi. This already was high enough for the dots of which text was composed to be invisible. And 300 is a multiple of 60; since typewriters in the English-speaking world tended to type either at 10 characters per inch, or 12 characters per inch, Pica or Elite, dividing the inch into 60 parts was to achieve the largest unit that could produce both character widths. Proportionally-spaced fonts for electronic daisywheel typewriters, therefore, were based on 1/60th of an inch as the unit.
Some laser printers adopted the resolution of 360 dpi, so that in addition to being able to reproduce 1/60th of an inch with an exact number of dots, one could do the same for 1/72nd of an inch. In this way, lines with different point sizes could fit together in the expected way without having, occasionally, to make a line of type one pixel taller or shorter at times.
Today, of course, laser printers may print at 600 dpi or higher resolutions. It seems to me that it might be beneficial if fonts could be reproduced on a laser printer with an exact unit system, so that the way characters fit together would not change as characters are scaled up for different font sizes.
At 360 dpi, this would mean that fonts could be designed around a system of 5 units to the em, and be reproducible at any integer point size. Such a unit system, however, is too crude for quality typography, although it was used to good effect on some early proportionally-spacing typewriters.
The Monotype type-casting machine used a system of 18 units to the em. This could be achieved with a laser printer resolution of 72 * 18 or 1296 dpi. This would not seem too unreasonable. But it isn't a multiple of 60! Would we have to multiply the resolution by another factor of five?
The fact that a printer's point is 0.013837 inches, not exactly 1/72 of an inch, comes to our rescue. If we raise the resolution to 1320 dpi, which is 22 times 60, then we could reproduce typography by using a point of 0.13636... inches.
But that is a bit small. Also, what about our European friends, who use the Didot point?
Perhaps, instead of using the Monotype standard of an 18-unit system, we could compromise, and use a 14-unit system. Then, for a point of 1/72 inch, we would need a laser printer resolution of 1008 dpi. To achieve a multiple of 60, we could adjust this to 1020 dpi, giving a point size of about 0.0137255 inches. This is still a bigger difference from 1/72 inches than a real printer's point provides, though.
Why a 14-unit system? Then, we could also devise a separate version of each font, designed around a 15-unit system! And *that* version of each font would be the one used when setting things to Didot points; one Didot point would be divided into 15 dots at that resolution, two Didot points into 30, and so on, just as one English/American point would be 14 dots, two points 28 dots, and so on.
But while the two kinds of points would be nearly in the correct ratio, they would both be too small. Thus, to satisfy all the conditions more closely, perhaps the way to go would be to use a resolution of 360 * 3 dpi, or 1080 dpi, and a 15-unit system for fonts based on the 1/72 inch point. The Didot point would just be more crudely approximated by using a 16-unit system. 16 dots at 1080 dpi would be 0.37629629... millimeters, though; this is too large instead of too small, and is actually closer to the traditional Didot point of 0.37593985 millimeters than the metric Didot point of 0.375 millimeters is. Thus, it seems as if this should yield an acceptable result.
Given this discussion, it seems opportune to mention here the old names for type sizes:
Canon 48 48 1 1/2 Two-line Great Primer 36 36 2 Two-line Columbian 32 32 2 1/4 Two-line English 28 28 4/5 2 1/2 Double Pica 24 24 3 Two-line Pica 22 21 3/5 3 1/3 Paragon 20 19 1/5 3 3/4 Great Primer 18 18 4 Columbian 16 16 4 1/2 English 14 14 2/5 5 Pica (Cicero) 12 12 6 Small Pica 11 10 4/5 6 2/3 Long Primer 10 9 3/5 7 1/2 Bourgeois 9 9 8 Brevier (Petit) 8 8 9 Minion (Colonel) 7 7 1/5 10 Emerald (Mignonette) 6 1/2 6 2/5 11 1/4 Nonpareil 6 6 12 Agate (Ruby) 5 1/2 5 1/3 13 1/2 Pearl 5 4 4/5 15 Diamond 4 1/2 4 1/2 16 Brilliant (Gem) 4 4 18 Ruby 3 1/2 3 3/5 20 Excelsior 3 3 24
The first two columns give the old typeface names as used in English-speaking countries followed by the size, in points, of type usually thought of as corresponding to those sizes today.
However, before the point system was adopted, the different sizes of type were not actually all multiples of a single small unit. Thus, as noted on this site, before the point system came into general adoption, one George Bruce proposed a system in which successive sizes of type would be in the ratio of the sixth root of two.
It is my suspicion that the previous tendency had been to divide the column inch into a fixed number of parts. Dividing it into 72 points would, naturally, have allowed many such divisions, such as those into 6, 8, 9, and 12 parts, to remain exact. Thus, I add a third column in which I express what sizes in points I think the named sizes really may have corresponded to, and a fourth which gives that size in terms of lines per inch. Note that these sizes do have a common unit, corresponding to 1/15th of a point; being based on 2, 3, and 5, they are reminiscent of the frequencies of musical notes in just intonation as well.
It may also be noted that not all the authorities I have encountered have agreed on the ordering of the names for the four smallest type sizes.
As for old books, it may also be of interest to note the terms for page sizes:
Traditional American Demy Metric
Sheet size: 18" x 24" 17" x 22" A0: 841mm x 1189mm
Quarto 4to 9" x 12" 8 1/2" x 11" A2: 420.5mm x 594.5mm
Sextodecimo 16mo 4 1/2" x 6" 4 1/4" x 5 1/2" A4: 210.25mm x 297.25mm
Folio 12" x 18" 11" x 17" A1: 594.5mm x 841mm
Octavo 8vo 6" x 9" 5 1/2" x 8 1/2" A3: 297.25mm x 420.5mm
Tricesimo-secundo 32do 3" x 4 1/2" 2 3/4" x 4 1/4" A5: 158.625mm x 210.25mm
Duodecimo 12mo 6" x 6"
Vicesimo-quarto 24to 4" x 4 1/2"
Many different paper sizes exist, a different series of sizes being used in the United States and in Britain. Some of the most common British paper sizes are:
Imperial 29 1/2" x 21 1/2" Royal 23 1/2" x 19 Demy 19 1/2" x 15 1/4" Foolscap 16 1/2" x 13 1/4"
American Foolscap was 14" x 17", thus giving rise to the traditional legal size page of 8 1/2" x 14", just as American Demy gave the standard 8 1/2" x 11" sheet of typewriter paper, which is approximated by the metric A4 size.