[Tex/LaTex] LyX change font to smooth-looking vector font

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I don't like the way Lyx typesets my documents. Letters look jagged around the edges. When I click Document>Settings>Fonts the only options I have available are Default, Roman, Sans Serif and Typewriter. Any suggestions?

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In 2.0 (beta) you’ll simply have to change the font in the respective drop down menus for ‘roman’, ‘sans serif’ and ‘typewriter’. I don’t know if it is the same in earlier versions.

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[Tex/LaTex] How to know if a math font fits well with the text font

The Elements of Typographic Style is generally a very good source for typographical ideas. However it tells little about math fonts.

Here is some my personal opinions on math fonts.

First the weight should match the text fonts. You won't want the math, especially the inline math looks too bold or too light compared to the text fonts. The colour of the whole page should be even. By colour, we mean distribution of the black ink across the page. This is perhaps the most basic but yet most difficult part of all typographical work. (This is also why we need micro typography, etc.) In short, if you have a glance at the page, there should be neither holes nor black island due the improper weights of the math fonts.
Second, the math font should distinguish itself from the text. When the reader read the text with some inline math, he or she expect to recognise those math symbols easily. That is a math letter should stands like a math letter, rather than a normal text. This is perhaps the reason why we typeset math in italics at the first place. However, a math fonts too different from the text font surely is not a good choice. A math font with modest slope of italics while having similar strokes, serifs, etc. is usually a good choice. Often this is the case when the math fonts and text fonts come from the same family or similar design. On the other hand, this does not mean a font with little slope or even an upright fonts cannot be used as math fonts. For example, the Euler math blends perfect with Palatino. But if there is a Euler text fonts, I personally don't believe it will be a good combination, because the math and text are almost the same.
Third, there are some subtile considerations, for example the shapes of letter v in math should distinguish itself from the greek letter nu, etc. The completeness and subtle perfection of a math font is a difficult task. This is why there are very few good math fonts out there. mathdesign, the one you use has lots symbols, but the details of its letter forms is not tuned well. Personally I will prefer a font with tuned detailed of every glyph it has, rather than a fonts with lots symbols, but many of them looks ugly. However, any fonts serves the purpose of writing after all, so if you absolutely need a symbol from a certain fonts, you should use it anyway.
Fourth, the math fonts and text fonts should have similar x height. Though this can be done with scaling, it should be noted that scaling a fonts down will decrease its weight, scaling it up will increase the weight. It is a simple math, if you scale up the fonts by a factor 2, then the area of the letter occupying is increased by a factor 4. So the x-height and the weight (my first opinion) cannot be considered separately.

There are some other sources you can turn to learn about math fonts design and thus its choice.

Understanding the æsthetics of math typesetting

Fonts for mathematics

Designing math fonts

For your other questions, I believe they are actually the same as the math font problem. The key is the weight, which affect the colour the page most directly. Then you can consider other things. For example, you may want they looks differently so they can serve different purpose.

[Tex/LaTex] Is it possible to change the font of line numbers in a code listing

The key is numberstyle:

\lstset{numberstyle=\ttfamily}

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[Tex/LaTex] How to know if a math font fits well with the text font

[Tex/LaTex] Is it possible to change the font of line numbers in a code listing

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