Indent itemized list with custom item names

How would I reproduce the typesetting in the screenshot below? In particular, I'm interested in the nicely indented list of hypotheses with the following features:

• The item names (H1, H2, H3) don't hang off into the left margin.
• The bodies of the three list items are aligned with each other and inset from the rest of the text

• Package enumitem is your friend here, I think – user31729 Jun 6 '16 at 17:52
• – Werner Jun 6 '16 at 18:07

It's easy with the enumitem package:

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{enumitem}
\usepackage{lipsum}

\begin{document}

\lipsum[1]
\begin{enumerate}[label=H\arabic*. , wide=0.5em,  leftmargin=*]
\item \lipsum[2]
\item \lipsum[3]
\item \lipsum[4]
\end{enumerate}

\end{document}


The package enumitem supports this out of the box, the only change required is the label, using label={H\arabic*.} as an option.

\documentclass{article}

\usepackage{blindtext}

\usepackage{enumitem}
\begin{document}
\section{Hypotheses and Hypotenuses}
\blindtext

\begin{enumerate}[font={\bfseries},label={H\arabic*.}]
\item \blindtext
\item \blindtext
\item \blindtext
\end{enumerate}

\end{document}