如何使每页有五个方程式？

Question

我想在每页显示 5 个二次方程，并在左侧显示方程编号，该怎么做？

\documentclass[preview,border=12pt]{standalone}
\usepackage{amsmath}
\begin{document}
\begin{gather}
-10 x^2+23 x-12=0 \\
 56 x^2-28 x=0 \\
 28 x^2+8 x-36=0 \\
 -3 x^2+13 x-4=0 \\
 -9 x^2+27 x-20=0 \\
 -5 x^2+9 x-4=0 \\
 2 x^2-12 x+16=0 \\
 -14 x^2+48 x+32=0 \\
 -45 x^2-36 x=0 \\
 -45 x^2-66 x-24=0 \\
 -14 x^2+40 x-24=0 \\
 24 x^2+5 x-36=0 \\
 9 x^2+38 x+8=0 \\
 20 x-35 x^2=0 \\
 -72 x^2-77 x-20=0 \\
 -3 x^2+9 x+12=0 \\
 -12 x^2-24 x=0 \\
 -56 x^2-11 x+12=0 \\
 28 x^2+20 x-8=0 \\
 10 x^2+4 x-32=0 \\
 -14 x^2-36 x-16=0 \\
 -4 x^2-28 x+32=0 \\
 5 x^2+29 x+36=0 \\
 24 x^2-59 x+36=0 \\
 -6 x^2-18 x+24=0 \\
 -12 x^2-11 x+36=0 \\
 -35 x^2-68 x-32=0 \\
 -8 x^2-60 x-28=0 \\
 64 x^2+16 x-24=0 \\
 -21 x^2+19 x-4=0 \\
 24 x^2+44 x+16=0 \\
 15 x^2-5 x-20=0 \\
 49 x^2+35 x+4=0 \\
 4 x^2+12 x-16=0 \\
 4 x^2-8 x-12=0 \\
 8 x^2-37 x+20=0 \\
 -10 x^2-37 x+36=0 \\
 28 x^2+4 x-24=0 \\
 -24 x^2+2 x+12=0 \\
 6 x^2-15 x-36=0 \\
 -36 x^2+24 x+12=0 \\
 16 x^2+8 x-24=0 \\
 -10 x^2-43 x-28=0 \\
 -6 x^2-26 x+20=0 \\
 12 x^2+16 x-16=0 \\
 9 x^2+32 x-16=0 \\
 4 x^2-4 x-8=0 \\
 -24 x^2+60 x-36=0 \\
 -5 x^2+21 x+20=0 \\
 -5 x^2-x+4=0 \\
 40 x^2+44 x-24=0 \\
 3 x^2-10 x-8=0 \\
 -42 x^2-17 x+4=0 \\
 -15 x^2+32 x-16=0 \\
 14 x^2+12 x-32=0 \\
 20 x-25 x^2=0 \\
 -30 x^2+4 x+16=0 \\
 36 x^2-65 x-36=0 \\
 9 x^2-12 x=0 \\
 -2 x^2-13 x-20=0 \\
 18 x^2+30 x-28=0 \\
 -3 x^2+4 x+32=0 \\
 56 x^2-25 x-4=0 \\
 48 x^2+74 x+28=0 \\
 -8 x^2-30 x+8=0 \\
 3 x^2-10 x+8=0 \\
 18 x^2-73 x-36=0 \\
 -49 x^2+28 x+32=0 \\
 -18 x^2+80 x-32=0 \\
 -4 x^2+24 x-32=0 \\
 18 x^2+x-4=0 \\
 -4 x^2+12 x-8=0 \\
 -35 x^2+36 x+32=0 \\
 20 x^2+21 x+4=0 \\
 20 x^2-68 x+24=0 \\
 -16 x^2+28 x-12=0 \\
 -24 x^2-52 x+32=0 \\
 -18 x^2-30 x-12=0 \\
 -18 x^2-28 x+16=0 \\
 48 x^2+16 x-32=0 \\
 -54 x^2-60 x-16=0 \\
 28 x^2-64 x+36=0 \\
 14 x^2+24 x-8=0 \\
 40 x^2+28 x-24=0 \\
 5 x^2-x-4=0 \\
 27 x^2+48 x+16=0 \\
 9 x^2+13 x+4=0 \\
 -x^2+8 x-16=0 \\
 6 x^2-14 x-12=0 \\
 20 x-30 x^2=0 \\
 27 x^2-84 x+32=0 \\
 -32 x^2-8 x+12=0 \\
 10 x^2+46 x+24=0 \\
 -42 x^2+52 x-16=0 \\
 -35 x^2+48 x-16=0 \\
 9 x^2-41 x-20=0 \\
 -24 x^2+8 x+16=0 \\
 42 x^2-3 x-12=0 \\
 45 x^2+47 x+12=0 \\
 -32 x^2+24 x+20=0 \\
72 x^2+4 x-16=0 \\
 -24 x^2+2 x+12=0 \\
 -15 x^2-33 x+36=0 \\
 5 x^2+23 x+12=0 \\
 -18 x^2+3 x+36=0 \\
 28 x^2+12 x-16=0 \\
 10 x^2-2 x-36=0 \\
 54 x^2+6 x-20=0 \\
 2 x^2-14 x+20=0 \\
 54 x^2-24=0 \\
 10 x^2-16 x-8=0 \\
 27 x^2+60 x+32=0 \\
 -36 x^2-42 x-12=0 \\
 -7 x^2-21 x+28=0 \\
 -63 x^2-46 x-8=0 \\
 10 x^2-14 x-12=0 \\
 -32 x^2-32 x+24=0 \\
 -27 x^2-30 x-8=0 \\
 12 x^2-34 x+24=0 \\
 -28 x^2-64 x-36=0 \\
 49 x^2+28 x-32=0 \\
 -24 x^2+60 x-36=0 \\
 54 x^2-30 x-24=0 \\
 -36 x^2+52 x-16=0 \\
 9 x^2-44 x+32=0 \\
 5 x^2-49 x+36=0 \\
 28 x^2-30 x+8=0 \\
 45 x^2-9 x-36=0 \\
 -32 x^2+8 x+12=0 \\
 20 x^2-31 x+12=0 \\
 56 x^2-32 x=0 \\
 18 x^2-54 x+28=0 \\
 36 x^2-42 x+12=0 \\
 10 x^2-18 x+8=0 \\
 45 x^2+92 x+32=0 \\
 12 x^2+22 x-20=0 \\
 32 x^2+40 x+8=0 \\
 -56 x^2-60 x-16=0 \\
 12 x^2+46 x-36=0 \\
 -45 x^2-71 x-28=0 \\
 -42 x^2-10 x+12=0 \\
 -8 x^2+20 x+12=0 \\
 -49 x^2+14 x+24=0 \\
 -2 x^2+11 x-12=0 \\
 -18 x^2+6 x+24=0 \\
 -40 x^2-60 x-20=0 \\
 36 x^2+12 x-24=0 \\
 -x^2-13 x-36=0 \\
 36 x^2+24 x-12=0 \\
 36 x-63 x^2=0 \\
 6 x^2+22 x+20=0 \\
 10 x^2-4 x-32=0 \\
 -8 x^2+16 x-8=0 \\
 24 x^2+5 x-36=0 \\
 -24 x^2+26 x+8=0 \\
 -6 x^2+29 x-20=0 \\
 -48 x^2+8 x+8=0 \\
 -24 x^2-20 x-4=0 \\
 45 x^2-31 x-4=0 \\
 -27 x^2+27 x+12=0 \\
 -12 x^2+2 x+24=0 \\
 -72 x^2+104 x-32=0 \\
 14 x^2+44 x+32=0 \\
 36 x^2-54 x+20=0 \\
 -16 x^2-32 x-12=0 \\
 -56 x^2-20 x+4=0 \\
 64 x^2-64 x+16=0 \\
 -60 x^2+46 x+28=0 \\
 8 x^2-6 x-20=0 \\
 36 x^2+16 x-20=0 \\
 12-12 x^2=0 \\
 -27 x^2-48 x-16=0 \\
 -28 x^2+23 x-4=0 \\
 -6 x^2-20 x+16=0 \\
 25 x^2-25 x+4=0 \\
 36 x^2+20 x-16=0 \\
 4 x^2-8 x-32=0 \\
 -8 x^2-34 x-36=0 \\
 28 x^2-9 x-4=0 \\
 24 x^2+32 x=0 \\
 27 x^2+60 x+32=0 \\
 -18 x^2-42 x+36=0 \\
 -12 x^2-48 x-36=0 \\
 -40 x^2+28 x+12=0 \\
 -4 x^2-9 x+28=0 \\
 63 x^2-8 x-16=0 \\
 -6 x^2+16 x+32=0 \\
 20 x^2-41 x+20=0 \\
 12 x^2+44 x+24=0 \\
 30 x^2-74 x+36=0 \\
 -36 x^2+8 x+28=0 \\
 -21 x^2-49 x-28=0 \\
 -45 x^2-101 x-36=0 \\
 -3 x^2+14 x-8=0 \\
 -28 x^2+4 x+32=0 \\
 -28 x^2+24 x+4=0 \\
 15 x^2-41 x+28=0 \\
 15 x^2+14 x-8=0 \\
 -24 x^2-44 x-16=0 \\
 30 x^2+14 x-8=0 \\
 35 x^2-x-12=0 \\
 48 x^2+32 x+4=0 \\
 9 x^2-36 x=0 \\
 9 x^2-6 x-24=0 \\
 9 x^2+5 x-4=0 \\
 56 x^2+18 x-8=0 \\
 18 x^2-54 x+36=0 \\
 36 x-63 x^2=0 \\
 64 x^2+40 x+4=0 \\
 -18 x^2-50 x-28=0 \\
 48 x^2+44 x+8=0 \\
 -8 x^2-36 x-28=0 \\
 45 x^2-16 x-16=0 \\
 -x^2-x+12=0 \\
 18 x^2+62 x+24=0 \\
 -56 x^2+95 x-36=0 \\
 30 x^2+34 x-36=0 \\
 48 x^2-44 x+8=0 \\
 -20 x^2-24 x-4=0 \\
 -30 x^2-16 x+32=0 \\
 16 x^2-16=0 \\
 21 x^2-54 x+24=0 \\
 16 x^2+20 x-24=0 \\
 81 x^2-36 x-32=0 \\
 36 x^2+78 x+36=0 \\
 -30 x^2+14 x+4=0 \\
 5 x^2-4 x=0 \\
 -2 x^2-2 x+24=0 \\
 -12 x^2+10 x+8=0 \\
 -8 x^2-76 x-36=0 \\
 -18 x^2+30 x+12=0 \\
 -6 x^2-16 x+32=0 \\
 64 x^2+8 x-20=0 \\
 27 x^2-12 x=0 \\
 -42 x^2-28 x=0 \\
 -35 x^2-43 x-12=0 \\
 32 x^2+24 x+4=0 \\
 18 x^2-9 x-20=0 \\
 -6 x^2+30 x-24=0 \\
 8 x^2+52 x+24=0 \\
 18 x^2+48 x+24=0 \\
 8 x^2-24 x-32=0 \\
 18 x^2+55 x-28=0 \\
 -45 x^2+66 x-24=0 \\
 -15 x^2-2 x+8=0 \\
 -14 x^2+57 x-28=0 \\
 -6 x^2+4 x+32=0 \\
 -36 x^2-18 x+28=0 \\
 -24 x^2-60 x+36=0 \\
 -72 x^2-95 x-28=0 \\
 -40 x^2+36 x+28=0 \\
 3 x^2+2 x-8=0 \\
 8 x^2+68 x-36=0 \\
 12-48 x^2=0 \\
 -49 x^2-70 x-24=0 \\
 -54 x^2+30 x+4=0 \\
 -15 x^2-20 x=0 \\
 -24 x^2-60 x-24=0 \\
 -24 x^2-4 x+8=0 \\
 -16 x^2+64 x+36=0 \\
 28 x^2+16 x=0 \\
 72 x^2+108 x+36=0 \\
 8 x^2+28 x+12=0 \\
 -9 x^2-27 x-20=0 \\
 -21 x^2-26 x-8=0 \\
 -54 x^2+69 x-20=0 \\
 -30 x^2+10 x+20=0 \\
 14 x^2-30 x+4=0 \\
 2 x^2+x-28=0 \\
 12 x^2-43 x+36=0 \\
 3 x^2-4 x=0 \\
 48 x^2-32 x-28=0 \\
 -35 x^2+36 x+32=0 \\
 -4 x^2+14 x+8=0 \\
 30 x^2+14 x-4=0 \\
 54 x^2-78 x+28=0 \\
 -7 x^2+24 x+16=0 \\
 -6 x^2+16 x+32=0 \\
 36 x^2-8 x-28=0 \\
 16 x^2+24 x+8=0 \\
 14 x^2+28 x=0 \\
 -8 x^2-8 x=0 \\
 -8 x^2+37 x-20=0 \\
 -63 x^2+85 x-28=0 \\
 18 x^2-18 x-20=0 \\
 27 x^2-75 x+28=0 \\
 32 x-72 x^2=0 \\
 -5 x^2-14 x+24=0 \\
 -6 x^2+52 x-32=0 \\
 -15 x^2-18 x+24=0 \\
 7 x^2+21 x-28=0 \\
 -24 x^2-20 x-4=0 \\
 30 x^2-6 x-24=0 \\
 8 x^2-12 x-20=0 \\
 -4 x^2+40 x-36=0 \\
 -35 x^2-36 x+32=0 \\
 8 x^2+28 x+20=0 \\
 6 x^2+28 x+32=0 \\
 30 x^2+2 x-12=0 \\
 25 x^2-20 x=0
\end{gather}
\end{document}

Answer 1

这里有一个建议，使用spreadlinesfrommathtools以及align来更好地对齐方程式。您需要使用命令\allowdisplaybreaks才能将方程式拆分到各个页面上。

行间距设置为\textheight/5-\baselineskip。因此，文本高度除以 5，减去一行的高度。

要获取左边的方程编号，请使用选项leqno。

更新：由于文档以公式开头，因此在公式开始前有一些额外的垂直空间（请参阅如何将 amsmath 方程式置于页面顶部而忽略 \topskip？）。但\noindent在文档开头添加可以解决这个问题。

\documentclass[a4paper]{article}
\usepackage[margin=2cm,showframe]{geometry}

\usepackage[leqno]{mathtools}  % <----This loads amsmath
\allowdisplaybreaks

\begin{document}
\noindent
\begin{spreadlines}{\textheight/5-\baselineskip}
\begin{align}
-10 x^2+23 x-12=0 \\
 56 x^2-28 x=0 \\
 28 x^2+8 x-36=0 \\
 -3 x^2+13 x-4=0 \\
 -9 x^2+27 x-20=0 \\
 -5 x^2+9 x-4=0 \\
 2 x^2-12 x+16=0 \\
 -14 x^2+48 x+32=0 \\
 -45 x^2-36 x=0 \\
 -45 x^2-66 x-24=0 \\
 -14 x^2+40 x-24=0 \\
 24 x^2+5 x-36=0 \\
 9 x^2+38 x+8=0 \\
 20 x-35 x^2=0 \\
 -72 x^2-77 x-20=0 \\
 -3 x^2+9 x+12=0 \\
 -12 x^2-24 x=0 \\
 -56 x^2-11 x+12=0 \\
 28 x^2+20 x-8=0 \\
 10 x^2+4 x-32=0 \\
 -14 x^2-36 x-16=0 \\
 -4 x^2-28 x+32=0 \\
 5 x^2+29 x+36=0 \\
 24 x^2-59 x+36=0 \\
 -6 x^2-18 x+24=0 \\
 -12 x^2-11 x+36=0 \\
 -35 x^2-68 x-32=0 \\
 -8 x^2-60 x-28=0 \\
 64 x^2+16 x-24=0 \\
 -21 x^2+19 x-4=0 \\
 24 x^2+44 x+16=0 \\
 15 x^2-5 x-20=0 \\
 49 x^2+35 x+4=0 \\
 4 x^2+12 x-16=0 \\
 4 x^2-8 x-12=0 \\
 8 x^2-37 x+20=0 \\
 -10 x^2-37 x+36=0 \\
 28 x^2+4 x-24=0 \\
 -24 x^2+2 x+12=0 \\
 6 x^2-15 x-36=0 \\
 -36 x^2+24 x+12=0 \\
 16 x^2+8 x-24=0 \\
 -10 x^2-43 x-28=0 \\
 -6 x^2-26 x+20=0 \\
 12 x^2+16 x-16=0 \\
 9 x^2+32 x-16=0 \\
 4 x^2-4 x-8=0 \\
 -24 x^2+60 x-36=0 \\
 -5 x^2+21 x+20=0 \\
 -5 x^2-x+4=0 \\
 40 x^2+44 x-24=0 \\
 3 x^2-10 x-8=0 \\
 -42 x^2-17 x+4=0 \\
 -15 x^2+32 x-16=0 \\
 14 x^2+12 x-32=0 \\
 20 x-25 x^2=0 \\
 -30 x^2+4 x+16=0 \\
 36 x^2-65 x-36=0 \\
 9 x^2-12 x=0 \\
 -2 x^2-13 x-20=0 \\
 18 x^2+30 x-28=0 \\
 -3 x^2+4 x+32=0 \\
 56 x^2-25 x-4=0 \\
 48 x^2+74 x+28=0 \\
 -8 x^2-30 x+8=0 \\
 3 x^2-10 x+8=0 \\
 18 x^2-73 x-36=0 \\
 -49 x^2+28 x+32=0 \\
 -18 x^2+80 x-32=0 \\
 -4 x^2+24 x-32=0 \\
 18 x^2+x-4=0 \\
 -4 x^2+12 x-8=0 \\
 -35 x^2+36 x+32=0 \\
 20 x^2+21 x+4=0 \\
 20 x^2-68 x+24=0 \\
 -16 x^2+28 x-12=0 \\
 -24 x^2-52 x+32=0 \\
 -18 x^2-30 x-12=0 \\
 -18 x^2-28 x+16=0 \\
 48 x^2+16 x-32=0 \\
 -54 x^2-60 x-16=0 \\
 28 x^2-64 x+36=0 \\
 14 x^2+24 x-8=0 \\
 40 x^2+28 x-24=0 \\
 5 x^2-x-4=0 \\
 27 x^2+48 x+16=0 \\
 9 x^2+13 x+4=0 \\
 -x^2+8 x-16=0 \\
 6 x^2-14 x-12=0 \\
 20 x-30 x^2=0 \\
 27 x^2-84 x+32=0 \\
 -32 x^2-8 x+12=0 \\
 10 x^2+46 x+24=0 \\
 -42 x^2+52 x-16=0 \\
 -35 x^2+48 x-16=0 \\
 9 x^2-41 x-20=0 \\
 -24 x^2+8 x+16=0 \\
 42 x^2-3 x-12=0 \\
 45 x^2+47 x+12=0 \\
 -32 x^2+24 x+20=0
\end{align}
\end{spreadlines}
\end{document}