Basic Structure of Formula Encoding

Formulas are first tagged with an empty <formula/> element. In a second capturing step, the formulas can be transcribed according to the TeX notation and enclosed using <formula>[...]</formula>. The <formula> element gets an attribute @notation, in which the notation ("TeX" or "MathML") is specified. In another attribute @facs, a graphical representation of the corresponding formula can be referenced.

The formulas include:
  • mathematical and physical formulas and equations,
  • fractions (with fraction line; if not available as Unicode entity),
  • chemical compounds,
  • expressions of logic.
Pure variables are not encoded as <formula>.

Formulas can be either within a line (inline) or separated from the continuous text. In the latter case, the line break is specified before and after the formula using <lb/>. If there is a punctuation mark immediately after a formula, it is included. Layout information (e. g. centering) is not taken into account.

Encoding of Formulas (1)

<formula notation="TeX">
  \lambda_T = \frac{1}{\pi ns^2}\int\limits_0^\infty\frac{4x^2e^{-x^2}dx}{\psi(x)+\frac{n_1\sigma^2}{ns^2}\psi\left(x\sqrt\frac{m_1}{m}\right)}
</formula>

Source: Boltzmann, Ludwig: Vorlesungen über Gastheorie. Bd. 1. Leipzig, 1896. [Facsimile 87]

Encoding of Formulas (2)

<formula notation="TeX">
  U=u_1 \, \left ( \frac{z_1}{z_2} \cdot \frac{z_3}{z_4} - 1 \right )
</formula>

Source: Fischer, Hermann: Die Werkzeugmaschinen. Bd. 1: Die Metallbearbeitungs-Maschinen. [Textband]. Berlin, 1900. [Facsimile 181]

Encoding of Formulas (3)

<p>Wir setzen wieder<lb/>
  <formula notation="TeX">\frac{\cos kr}{r} = f_r + \frac{1}{r}</formula>,<lb/>
  <formula notation="TeX">\Psi = \Psi' + \Psi''</formula>,<lb/>
  <formula notation="TeX">\Psi' = \int pf_rd\omega</formula>,<lb/>
  <formula notation="TeX">\Psi'' = \int p\frac{1}{r}d\omega</formula>.
</p><lb/>

Source: Helmholtz, Hermann von: Theorie der Luftschwingungen in Röhren mit offenen Enden. In: Journal für die reine und angewandte Mathematik 57 (1860), Heft 1, S. 1-72. [Facsimile 31]