Approximation of one of Henri CARTAN's books: first try

The aim of this page is simple: is it possible with the state of the art tools together with (La)TeX to produce such a neat book layout and typography as Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes published in 1964 by Hermann? This little game will be performed with the idea to review the means available to modify different aspects of typography inside LaTeX(2e), especially in the case of a book with a large amount of maths. In fact, as it is shown by the tons of font samples in the pages attached to this one, text font diversity is rather easily achieved. The situation is different when one comes to typesetting mathematics. I only know of 4 font families usable with TeX without spending years to customize them for this task (for this reason I do not count Adobe's Mathematical Pi--this one omitted, there is however not much choice remaining...):

- the "native" fonts of TeX (cmmi/cmsy/cmex);
- the fonts in AMS family "euler";
- the fonts from the MathTime series sold by Y&Y (for instance);
- and the Lucida family, also sold by Y&Y.

The first difficult problem is that the above mentionned fonts do not mix happily with most text faces. Two reason for this are "color" and "style". The weight and width (series in nfss terminology) of a peculiar font yield a given grey level or "color" of the printed page (which also relies on other parameters such as margins or baselineskips--bear in mind that the defaults in LaTeX are meant to work with cm fonts, and they may require modifications for typesetting in another font). Variations in color are however unavoidable in a mathematical text because of the very nature of many formulas that could not be imbedded in the normal text. However, in-line formulas should alter it minimally. For instance, using the standard math italics (cmmi, which is quite light) inside a document typeset with times.sty (Times-Roman, quite black) will be awfull. Conversely, using MathTimes (which makes rather a good job with Times) with lighter fonts like Plantin or Garamond will also be a disaster.

Regarding style, italics have usually the most idiosyncrasistic (?) shape in a font, which means that some letters from one italic font will be horrible next to the same letter from another one (just try to put side to side the italic p from Baskerville, Garamond, Times, Caslon or Computer Modern). This is unfortunately what happens nowadays in many mathematical journals, for instance in theorem statements... Sometimes, one find a "happy pair" by chance such as Charter and Euler you can see below.

Well, what about Cartan's book? It is unfortunately set in Baskerville, using old style digits for the numerals even in math mode. By luck, we are able to build virtual fonts thanks to the help of Alan Jeffrey whose package fontinst allows us to mix arbitrarily many fonts together. Also, the weight and dimensions of Baskerville are not too far from the ones of the cm fonts. We will be able to try out different levels of "hybridization". If I start from the first page of Henri Cartan's original book, I can see what would yield the defaults from LaTeX on the same text (whose header is here; notice I also tried to approximate the last page as it contains more maths). As this is a french text, we should try out the T1 version of the cm fonts, and the package french.sty. Spacing is better. LaTeX does an honorable job, but we are still quite far from the original layout! Let us try a piece of style. I admit it doesn't change things a lot. It is straightforward to only change the text fonts involved: bold Bodoni for the chapter headings, Baskerville for the text (in fact New Baskerville as I unfortunately have no Baskerville with old style digits). The result is acceptable but the two italic p's are definitely incompatible. We will try to overcome this little problem by creating with fontinst a new math italic font whose letters are taken from Baskerville italic, remaining symbols from cmmi. Simultaneously, we build the associated Baskerville oldstyle text font family and the support package widely inspired from macros due to S. Rahtz. Notice that there is no way to ask TeX to use the letters from an arbitrary font as "math italic", the TFM of such math fonts having special requirements.

I will stop with this approximation even if it is far from perfect. (The source is here.) But it is better in my opinion and I won't try to alter it for the sake of a better approximation. I conclude by saying that LaTeX is able to beat old style typography if one does the effort to ask it to do so.

I end up with four exotic versions for the same text:
- the first one relies on a combination of Minion for the text, math letters and digits; and cm for remaining symbols,
- the second one relies on a combination of Utopia for the text, math letters and digits; and Lucida for remaining symbols,
- the third one shows everything in Lucida (in fact here a clone of the former version which is distributed by Adobe),
- the last one demonstrates a possible usage of Euler for maths and Charter for text. This last example requires no additionnal work as the support file euler.sty is supplied by Frank Jensen and Frank Mittelbach.

Thierry Bouche
(non-english speaker)