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The source files I am playing with are in ordinary (AMS)TeX, not LaTeX. I find TeX fontography (is this a word?) to be rather confusing. In other document processing (like OpenOffice or MSWord, or what not), the names of fonts are intuitive, and furthermore you see them right away. But in TeX, Knuth seems to have wrapped it into several layers of riddles, puzzles and mysteries. Recently an editor told me to change my manuscript into "Times font" (I imagine she meant "Times New Roman"). What is the default font that TeX uses if you do not specify anything (as I did not)? So how would I do everything in "Times font" I have \magnification 1200 and that is the main text size I need.

In addition, I had some fonts like below for the titles that have then to be changed as well, except for their sizes...

\font\titlefontp=cmssdc10 at 15pt    %title fonts, bold
\font\titlefontd=cmssdc10 at 20pt
\font\titlefontt=cmssdc10 at 30pt
\font\titlefont=cmssdc10 at 40pt
\font\ninesl=cmsl9 at 15pt
\font\titlefontpa=cmr7 scaled \magstep4%  at 15pt
%\loadcmmib
\font\tencmmib=cmmib10 \skewchar\tencmmib='177   %italic bold in math

In a word -- how do I tell TeX to give me "Times font" output in those sizes?

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    You're basically asking to add support for Times in AMS-TeX: it can be done, but it requires at least some hours' work. There's no riddle, puzzle or mystery: just some patience and study are necessary. – egreg Dec 18 '15 at 21:08
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    why are you using a tex format that has not been maintained or really used since last century and then expecting that it has a natural interface to using current fonts? – David Carlisle Dec 18 '15 at 21:34
  • OK, I take it that you do not know the answer and/or that you believe if you knew the answer, it would take a long time to do. Unfortunately it confirms my lament about tex and fonts. I am still hoping there will be someone knowledgeable and able to do this. Crossing my fingers. – Rado Dec 18 '15 at 23:20
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In my opinion you can use the xetex engine, which permits to load also "non-TeX" fonts. You can load practically any font that is installed on your operating system.

Suppose you want to load Times New Roman at 10 pt. Then, assuming you have a font whose name is "Times New Roman" installed on your system, you can type \font\tentimes="Times New Roman" at 10 pt; or, if in your working directory you have a font file named, for example, "Times New Roman.otf", then you can simply type \font\tentimes="[Times New Roman.otf]" at 10pt.

I suggest you to look at the XeTeX manual, which in few pages explain the syntax for font loading.

But next you should also change the math fonts, because default computer modern math fonts look ugly with times. I suggest you to use the Math Times fonts, which can be loaded simply by \input mtp2.

An example file:

\input amstex
\input mtp2

\MTP{11pt}{7pt}{5.5pt}  % sets the sizes of math fonts
\font\eleventimes="Times New Roman" at 11pt
\eleventimes

This is some text.  And here is a formula:
$$
    \pmatrix 1&0&0\\0&1&0\\0&0&1\endpmatrix
$$

\bye

Of course you have to process it with xetex instead of tex or pdftex.

Notice that this is not a amstex-specific answers, but it can be used also in plain tex.

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    Thanks @user, I will look into your solution and report back when I get to it. – Rado Dec 19 '15 at 1:11
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    @Rado. It seems that mtp2 is not installed on your system. If you have texlive on linux you can follow cims.nyu.edu/~fennell/mtpro2/, otherwise I don't know. But, apart from that, if you remove \input mtp2 and the MTP line, does it work and display text in Times? – User Dec 23 '15 at 19:00
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    @Rado. Maybe you are interested in opmac (petr.olsak.net/opmac-e.html), a set of macros which add support for latex-like features to plain tex and so, with little modifications (tex.stackexchange.com/questions/279829/…), to amstex. With opmac loading Times is easy: just type \input ctimes. In addition opmac provides an easy to use font selection scheme, like the one you can find on Open Office. – User Dec 24 '15 at 9:43
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    this sounds promising. I will check it out and let you know what happens. – Rado Dec 26 '15 at 23:14
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    @Rado. Sorry, I use texlive and I do no nothing about other TeX platforms, so I can't help you. You should ask a new question, so that others can see and perhaps help you – User Jan 14 '16 at 8:38

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