+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
+\end{align}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formula Numbering
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+numbering
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro see
+status open
+
+\begin_layout Plain Layout
+Formula numbering
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+General
+\end_layout
+
+\begin_layout Standard
+Numbered formulas can be created with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Numbered
+\begin_inset space ~
+\end_inset
+
+Formula
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcuts"
+arg "command-sequence math-display; math-number-toggle;"
+\end_inset
+
+).
+ Existing formulas can be numbered with the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Number
+\begin_inset space ~
+\end_inset
+
+Whole
+\begin_inset space ~
+\end_inset
+
+Formula
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-toggle"
+\end_inset
+
+).
+ The formula number is displayed in \SpecialChar LyX
+ behind the formula as a number in parentheses.
+
+\change_deleted 232239728 1611410645
+The number sign is replaced in the output by the formula number.
+\change_deleted 5863208 1612727075
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\change_inserted 232239728 1611410697
+LyX appears to put the actual formula number in the raw file now
+\change_unchanged
+
+\end_layout
+
+\end_inset
+
+
+\change_unchanged
+
+\end_layout
+
+\begin_layout Standard
+When numbering is turned on in multiline formulas,
+ all formulas will be numbered.
+ But the numbering can be controlled with the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Number
+\begin_inset space ~
+\end_inset
+
+This
+\begin_inset space ~
+\end_inset
+
+Line
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-line-toggle"
+\end_inset
+
+) for every formula.
+\end_layout
+
+\begin_layout Standard
+Except for inline formulas,
+ all formulas can be numbered with two different styles,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Cross-References
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Cross-references
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+to formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All labeled formulas can be cross-referenced.
+ A label is added with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Label
+\family default
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "label-insert"
+\end_inset
+
+.
+ The cursor must be inside a displayed formula.
+ Alternatively you can right-click on the formula and choose
+\family sans
+Equation Label
+\family default
+.
+ A dialog pops up displaying the prefix
+\series bold
+eq:
+
+\series default
+ in a text field.
+ The label is inserted behind the prefix.
+ The predefined prefix means
+\begin_inset Quotes eld
+\end_inset
+
+equation
+\begin_inset Quotes erd
+\end_inset
+
+ and makes it easier to find labels in large documents because it marks it as a formula label to distinguish it from e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+section labels.
+ To change a label,
+ the menu
+\family sans
+Insert\SpecialChar menuseparator
+Label
+\family default
+ is used again or you can right-click on a formula and then on
+\family sans
+Equation Label
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The name of the label is displayed in \SpecialChar LyX
+ within parentheses behind the formula number.
+ A formula with a label is always numbered.
+\end_layout
+
+\begin_layout Standard
+Cross-references are inserted via the menu
+\family sans
+Insert\SpecialChar menuseparator
+Cross-Reference
+\family default
+ or with the toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show-new-inset ref"
+\end_inset
+
+.
+ A formula cross-reference appears in the output as formula number.
+ When in the cross-reference dialog window the format
+\series bold
+(<reference>)
+\series default
+ is chosen,
+ the cross-reference appears in the output as formula number in parentheses.
+\begin_inset Newline newline
+\end_inset
+
+By right-clicking on a cross-reference in \SpecialChar LyX
+,
+ one jumps to the formula that is referenced.
+\end_layout
+
+\begin_layout Standard
+Here are as examples cross-references to formulas of the following subsections:
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Note the different cross-reference types.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The equations
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:tag"
+nolink "false"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:c"
+nolink "false"
+
+\end_inset
+
+ are equivalent.
+ In (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:Lat"
+nolink "false"
+
+\end_inset
+
+) big Latin letters are used for the numbering in contrary to (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:Rom"
+nolink "false"
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+When the argument of
+\series bold
+
+\backslash
+tag
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+tag
+\series default
+ is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:User-defined-Numbering"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series default
+ contains a box like in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Paragraph-Boxes"
+nolink "false"
+
+\end_inset
+
+,
+ the formula cannot be referenced.
+\end_layout
+
+\begin_layout Subsection
+Subnumbering
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+subnumbering
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas can be numbered as subequations.
+ To activate this feature,
+ add the module
+\family sans
+Subequations
+\family default
+ to the document in the menu
+\family sans
+Document\SpecialChar menuseparator
+Settings\SpecialChar menuseparator
+Modules
+\family default
+.
+ To insert subequations use the menu
+\family sans
+Insert\SpecialChar menuseparator
+Custom Insets\SpecialChar menuseparator
+Subequations
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The equations to be subnumbered are put into the
+\family sans
+Subequations
+\family default
+ inset.
+ An example:
+\begin_inset Formula
+\begin{equation}
+A=C-B
+\end{equation}
+
+\end_inset
+
+
+\begin_inset VSpace -5mm
+\end_inset
+
+
+\begin_inset Flex Subequations
+status open
+
+\begin_layout Plain Layout
+\begin_inset Formula
+\begin{equation}
+B=C-A\label{eq:b}
+\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{equation}
+C=A+B\label{eq:c}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Every formula in the
+\family sans
+Subequations
+\family default
+ inset will be subnumbered with a,
+ b,
+ c,
+ \SpecialChar ldots
+ in the output.
+ For multiline formulas every line will be subnumbered.
+\end_layout
+
+\begin_layout Standard
+Referencing subequations works like normal equations:
+
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:b"
+nolink "false"
+
+\end_inset
+
+,
+
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:c"
+nolink "false"
+
+\end_inset
+
+.
+ If you want to reference the subequations collectively,
+ insert a label as first thing in the
+\family sans
+Subequations
+\family default
+ inset.
+ Formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:Here-is-an"
+plural "false"
+caps "false"
+noprefix "false"
+nolink "false"
+
+\end_inset
+
+ is an example.
+\end_layout
+
+\begin_layout Standard
+When inserting subequations,
+ vertical space is added before the equation.
+ To remove this,
+ insert -5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm vertical space right before the
+\family sans
+Subequations
+\family default
+ inset.
+ If the formula style
+\series bold
+Indented
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+For formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used,
+ insert -7
+\begin_inset space \thinspace{}
+\end_inset
+
+mm space instead.
+\end_layout
+
+\begin_layout Standard
+To get another subnumber instead of small Latin letters,
+ insert this command as \SpecialChar TeX
+ code before the equations in the
+\family sans
+Subequations
+\family default
+ inset:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+theparentequation -
+\backslash
+roman{equation}}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+theparentequation
+\series default
+ creates the parent number and
+\series bold
+
+\backslash
+roman{equation}
+\series default
+ adds a small Roman number as subnumber.
+ For more information about the customization of the numbering,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Numbering-with-Roman"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Here is an example of a multiline formula where the numbering is customized and turned off for the second line:
+\begin_inset Flex Subequations
+status open
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "eq:Here-is-an"
+
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+theparentequation -
+\backslash
+roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\begin{eqnarray}
+A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
+ & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
+ & = & B^{2}-2BZ+Z^{2}
+\end{eqnarray}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Numbering with Roman Numbers and Letters
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Numbering-with-Roman"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+with letters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+with Roman numbers
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas can also be numbered with Roman numbers and Latin letters.
+ To number with small Roman numbers,
+ the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\begin_layout Standard
+is inserted before the formula in \SpecialChar TeX
+ mode.
+
+\series bold
+
+\backslash
+renewcommand
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+renewcommand
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ redefines the predefined command
+\series bold
+
+\backslash
+theequation
+\series default
+ to the command
+\series bold
+
+\backslash
+roman{equation}
+\series default
+.
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+The command
+\series bold
+
+\backslash
+renewcommand
+\series default
+ has the same scheme as the command
+\series bold
+
+\backslash
+newcommand
+\series default
+ described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:The-Command-newcommand"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series bold
+equation
+\series default
+ is the formula counter.
+ When the command
+\series bold
+
+\backslash
+the
+\series default
+ is used as prefix for a counter,
+ the value of the counter is output as Arabic number.
+ When a formula is numbered,
+ \SpecialChar LaTeX
+ sets internally the command
+\series bold
+
+\backslash
+theequation
+\series default
+ behind the formula.
+
+\series bold
+
+\backslash
+roman{equation}
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+R
+\end_layout
+
+\end_inset