screenshot from p.196 of the pdf file download from archive.org, using maximal resolution, 0% saturation, maximal b/w contrast
<p>
The diagram is intended as Schopenhauer's proof "by intuition"<sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup> of (a special case of) the Pythargorean theorem.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup> Using the names from the image annotations, and taking for granted that <i>abd</i>, <i>adf</i>, <i>dfg</i>, <i>bdg</i>, <i>acf</i>, and <i>beg</i> are all congruent triangles which therefore all have the same area,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup> we have <span style="text-decoration:overline;"><i>ab</i></span><sup>2</sup> = A(<i>abd</i>)+A(<i>adf</i>)+A(<i>dfg</i>)+A(<i>bdg</i>) = 4*A(<i>abd</i>), while <span style="text-decoration:overline;"><i>ad</i></span><sup>2</sup> = A(<i>adf</i>)+A(<i>acf</i>) = 2*A(<i>abd</i>) and <span style="text-decoration:overline;"><i>bd</i></span><sup>2</sup> = A(<i>bdg</i>)+A(<i>bge</i>) = 2*A(<i>abd</i>).
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Notes:
</p><div class="reflist" style="list-style-type: decimal;">
<ol class="references"><li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a href="//commons.wikimedia.org/wiki/File:On_the_Fourfold_Root,_and_On_the_Will_in_Nature.djvu" title="File:On the Fourfold Root, and On the Will in Nature.djvu">File:On the Fourfold Root, and On the Will in Nature.djvu</a>, p.160</span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">in §39, p.164</span>
</li>
<li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">denoted by "A(.)"</span>
</li>
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<bdi><a href="https://en.wikipedia.org/wiki/en:Arthur_Schopenhauer" class="extiw" title="w:en:Arthur Schopenhauer"><span title="German philosopher (1788–1860)">Arthur Schopenhauer</span></a>
</bdi>
1903
<a rel="nofollow" class="external text" href="https://archive.org/details/onthefourfoldroo00schouoft">Djvu file</a> of Arthur Schopenhauer's essay <i>On the Fourfold Root of the Principle of Sufficient Reason</i> at archive.org