broken links euclid's elements

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@@ -115,7 +115,7 @@ title: BookOfProofs - Mathematics, Physics, and Computer Sciences
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             <div class="w3-display-topleft w3-black w3-padding">Euclid's Elements</div>
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diff --git a/docs/branches/algebra/isomorphism-of-rings.html b/docs/branches/algebra/isomorphism-of-rings.html
@@ -46,7 +46,7 @@ <h3 class='navigation'><a href='https://bookofproofs.github.io/branches/algebra/
 <hr>
 
 <h1>Theorem: Isomorphism of Rings</h1>
-<p>Let $(R, + ,\cdot)$ and $(S,\ast,\circ)$ be two <a href="https://bookofproofs.github.io/branches/algebra/ring.html" title="Algebra / Definition: (Unit) Ring">rings</a> and $f:R\to S$ a <a href="https://bookofproofs.github.io/branches/algebra/ring-homomorphism.html" title="Algebra / Definition: Ring Homomorphism">ring homomorphism</a>. Then the <a href="https://bookofproofs.github.io/branches/set-theory/partial-total-maps.html" title="Set Theory / Definition: Partial and Total Maps (Functions)">function</a> $$g:R/\ker{(f)}\to\operatorname{im}(f),\quad g([x])=f(x)$$ a an <a href="https://bookofproofs.github.io/branches/algebra/isomorphism.html" title="Algebra / Definition: Isomorphism">isomorphism</a>, called a <strong>ring isomorphism</strong>.</p>
+<p>Let $(R, + ,\cdot)$ and $(S,\ast,\circ)$ be two <a href="https://bookofproofs.github.io/branches/algebra/ring.html" title="Algebra / Definition: (Unit) Ring">rings</a> and $f:R\to S$ a <a href="https://bookofproofs.github.io/branches/algebra/ring-homomorphism.html" title="Algebra / Definition: Ring Homomorphism">ring homomorphism</a>. Then the <a href="https://bookofproofs.github.io/branches/set-theory/partial-total-maps.html" title="Set Theory / Definition: Partial and Total Maps (Functions)">function</a> $$g:R/\ker{(f)}\to\operatorname{im}(f),\quad $g([x])=f(x)$$ a an <a href="https://bookofproofs.github.io/branches/algebra/isomorphism.html" title="Algebra / Definition: Isomorphism">isomorphism</a>, called a <strong>ring isomorphism</strong>.</p>
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@@ -62,4 +62,4 @@ <h1>Theorem: Isomorphism of Rings</h1>
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diff --git a/docs/branches/geometry/elements-euclid/book--1-plane-geometry/acute-angle.html b/docs/branches/geometry/elements-euclid/book--1-plane-geometry/acute-angle.html
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+<meta name="description" content="1.12: ACUTE ANGLE &amp;#9733; bring your math skills to the graduate level &amp;#10004; step by step &amp;#10010; by the axiomatic method &amp;#10140; visit BookOfProofs now!">
+<meta name="keywords" content="acute,acute angle,angle,acute angle definition">
+<title>1.12: Acute Angle</title>
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+<h3 class='navigation'><a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--1-plane-geometry/obtuse-angle.html'>&#x25C0;</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--1-plane-geometry/definitions-from-book-1.html'>&#x25B2;</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--1-plane-geometry/boundary.html'>&#x25B6;</a><a href='https://bookofproofs.github.io/branches/branches.html'>Branches</a> / <a href='https://bookofproofs.github.io/branches/geometry/geometry.html'>Geometry</a> / <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/elements-euclid.html'>Elements-euclid</a> / <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--1-plane-geometry/book--1-plane-geometry.html'>Book--1-plane-geometry</a> / Definition: 1.12: Acute Angle</h3>
+
+<hr>
+
+<h1>Definition: 1.12: Acute Angle</h1>
+<blockquote>
+<p>And an <strong>acute angle</strong> (is) one less than a <a href="https://bookofproofs.github.io/branches/geometry/elements-euclid/book--1-plane-geometry/right-angle-perpendicular-straight-lines.html" title="Geometry / Elements Euclid / Book  1 Plane Geometry / Definition: 1.10: Right Angle, Perpendicular Straight Lines">right angle</a>.</p>
+</blockquote>
+<h3>Modern Definition</h3>
+<p>Euclid's definition corresponds to today's formulation.</p>
+<h3>Example</h3>
+<p>The angle \(\angle{PQR}\) (marked dark-green) is acute. </p>
+<p><img alt="angle" src="https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/examples/angle.jpg?raw=true" /></p>
+<h3 class='navigation'>Mentioned in:</h3>
+
+<p>Definitions: <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--1-plane-geometry/right-triangle-obtuse-triangle-acute-triangle.html' title='Geometry / Elements Euclid / Book  1 Plane Geometry / Definition: 1.21: Right Triangle, Obtuse Triangle, Acute Triangle'>1</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--1-plane-geometry/square-rectangle-rhombus-rhomboid-trapezium.html' title='Geometry / Elements Euclid / Book  1 Plane Geometry / Definition: 1.22: Square, Rectangle, Rhombus, Rhomboid, Trapezium'>2</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book-11-elementary-stereometry/inclination-of-a-plane-to-a-plane.html' title='Geometry / Elements Euclid / Book 11 Elementary Stereometry / Definition: Def. 11.06: Inclination of a Plane to a Plane'>3</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book-11-elementary-stereometry/cone.html' title='Geometry / Elements Euclid / Book 11 Elementary Stereometry / Definition: Def. 11.18: Cone'>4</a> <br>Proofs: <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--2-geometric-algebra/law-of-cosines-for-acute-angles-proof.html' title='Geometry / Elements Euclid / Book  2 Geometric Algebra / Proof: By Euclid (related to Proposition: 2.13: Law of Cosines (for Acute Angles))'>5</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--3-circles/line-at-right-angles-to-diameter-of-circle-at-its-ends-touches-the-circle-proof.html' title='Geometry / Elements Euclid / Book  3 Circles / Proof: By Euclid (related to Proposition: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle)'>6</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--3-circles/relative-sizes-of-angles-in-segments-proof.html' title='Geometry / Elements Euclid / Book  3 Circles / Proof: By Euclid (related to Proposition: 3.31: Relative Sizes of Angles in Segments)'>7</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--3-circles/construction-of-segment-on-given-line-admitting-given-angle-proof.html' title='Geometry / Elements Euclid / Book  3 Circles / Proof: By Euclid (related to Proposition: 3.33: Construction of Segment on Given Line Admitting Given Angle)'>8</a> <br>Propositions: <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--2-geometric-algebra/law-of-cosines-for-acute-angles.html' title='Geometry / Elements Euclid / Book  2 Geometric Algebra / Proposition: 2.13: Law of Cosines (for Acute Angles)'>9</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--3-circles/line-at-right-angles-to-diameter-of-circle-at-its-ends-touches-the-circle.html' title='Geometry / Elements Euclid / Book  3 Circles / Proposition: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle'>10</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--3-circles/relative-sizes-of-angles-in-segments.html' title='Geometry / Elements Euclid / Book  3 Circles / Proposition: 3.31: Relative Sizes of Angles in Segments'>11</a> <a href='https://bookofproofs.github.io/branches/geometry/elements-euclid/book--3-circles/construction-of-segment-on-given-line-admitting-given-angle.html' title='Geometry / Elements Euclid / Book  3 Circles / Proposition: 3.33: Construction of Segment on Given Line Admitting Given Angle'>12</a> <br></p>
+<hr>
+<p><span class='navigation'>Thank you to the contributors under <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a>!</span>  <a class='improve' title='improve this site' href='https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/branches/geometry/elements-euclid/book--1-plane-geometry/acute-angle.md'><img src='https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/edit-black.png?raw=true' alt=''></a>  <a class='improve' title='improvement history' href='https://github.com/bookofproofs/bookofproofs.github.io/commits/main/_sources/branches/geometry/elements-euclid/book--1-plane-geometry/acute-angle.md'><img src='https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/calendar-black.png?raw=true' alt=''></a><br><dl></dd><dt><span class='navigation'>Github:</span></dt><dd> <a title='github user bookofproofs' href='https://github.com/bookofproofs'><img src='https://github.com/bookofproofs.png?size=32' alt='bookofproofs'/></a><br></dd><dt><span class='navigation'>non-Github:</span></dt><dd></dd><dd>@Fitzpatrick<br></dl><br></p>
+<hr>
+<h3>References</h3>
+<h4>Adapted from (subject to copyright, with kind permission)</h4>
+<ol>
+<li><strong>Fitzpatrick, Richard</strong>: <a href='https://farside.ph.utexas.edu/Books/Euclid/Euclid.html'>Euclid's "Elements of Geometry"</a></li>
+</ol>
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