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<TITLE>Euclid and the US Constitution -- Reading Revolutions -- Intellectual History</TITLE>
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    <font face="Verdana,Arial,Helvetica" size="-1"><b><a href="lectures.html">INDEX</a></b><br><br><font size="+1"><center><i>Reading Revolutions:  Intellectual History</i><br><br><font size="+1">Euclid's Elements and the Declaration of Independence<br><br>
	<font size="+0">Mike Molinsky</center>

	<font face="Verdana,Arial,Helvetica" size="-1">
	<p>Following is a summary of Dr. Molinsky's talk with copies of his slides.</p>
	<p>The earliest documents we have in mathematics are 3 to 4,000 years old.&nbsp; 
	The Babylonians and Egyptians as well as other cultures used mathematics in 
	astronomy, building, and calculation.&nbsp; In this example from an Egyptian 
	papyrus from 1700 BC the problem illustrates a simple linear equation.&nbsp;
	</p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/3.jpg" width="450" height="349"></p>
	<p align="left">
    <font face="Verdana,Arial,Helvetica" size="-1">The Egyptians 
	did not try to provide an abstraction or create a theoretical model.&nbsp; 
	They dealt with the specific problems.&nbsp; All that changed with the 
	Greeks.&nbsp; They began to ask why things happened in astronomy, medicine, 
	mathematics, and the world around them.&nbsp; By the time of Euclid (325 - 
	265 BC) mathematics had changed drastically as compared to early Egyptian 
	attempts. </p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/DSCN0981w.jpg" width="400" height="300"></p>
	
	<p>Euclid's <i>Elements</i> comprises thirteen volumes.&nbsp; It 
	revolutionized mathematics by establishing definitions and postulates and 
	based on these going on to offer proofs of propositions.</p>
	
	<p align="center"><font face="Verdana,Arial,Helvetica" size="-1">
	<img border="0" src="pictures/Euclid/5.jpg" width="450" height="349"></font><br><br>
	<img border="0" src="pictures/Euclid/6.jpg" width="450" height="348"></p>
	
	<p align="left">Examples of definitions and postulates:</p>
	<p align="center">
	<img border="0" src="pictures/Euclid/DSCN0994w.jpg" width="400" height="287"></p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/8.jpg" width="450" height="349"></p>
	<p align="center">
	<img border="0" src="pictures/Euclid/9.jpg" width="450" height="350"></p>
	<p align="center">
	<img border="0" src="pictures/Euclid/10.jpg" width="450" height="350"></p>
	<p align="center">
	<img border="0" src="pictures/Euclid/11.jpg" width="450" height="349"></p>
	
	<p align="left"><font face="Verdana,Arial,Helvetica" size="-1">The 
	first proposition proves that the three sides of an equilateral triangle are 
	actually equal.&nbsp; Start by drawing a straight line.</p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/12.jpg" width="450" height="350"></p>
	
	<p align="left">Using the definition of a circle, draw a circle around point 
	A, then around point B:</p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/13.jpg" width="450" height="349"></p>
	<p align="center">
	<img border="0" src="pictures/Euclid/14.jpg" width="450" height="350"></p>
	
	<p align="left">Draw two more lines:</p>
	<p align="center">
	<img border="0" src="pictures/Euclid/15.jpg" width="450" height="351"></font></p>
	<p align="left">By definition, a straight line from the center of the circle 
	to the edge is equal to any other straight line drawn from the center of the 
	circle to the edge.</p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/16.jpg" width="450" height="350"></p>
	<p align="center">
	<img border="0" src="pictures/Euclid/17.jpg" width="450" height="350"></p>
	<p align="center">
	<img border="0" src="pictures/Euclid/18.jpg" width="450" height="350"></p>
	</font>
	<p align="left">Finally, it is shown that the three sides of the triangle 
	are equal and therefore the triangle is equilateral.</p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/19.jpg" width="450" height="349"></p>
	<p align="center">&nbsp;</p>
	<p align="center">
	<img border="0" src="pictures/Euclid/20.jpg" width="450" height="350"></p>
	<p align="left"><font face="Verdana,Arial,Helvetica" size="-1">Thomas 
	Jefferson lived 2000 years later.&nbsp; By then, Euclid's <i>Elements </i>
	had not only influenced mathematics but all other branches of knowledge.&nbsp; 
	The idea of proof, evidence and the use of reason and logic to approach the 
	world underlay science and medicine as well as philosophy.&nbsp; </font></p>
	<p align="center">
	<img border="0" src="pictures/Euclid/21.jpg" width="450" height="349"></p>
	
	<p align="left">The first lines of the Declaration of Independence propose 
	that before taking an action one has to show that it has cause and that it 
	needs to be explained.</p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/22.jpg" width="450" height="349"></p>
	
	<p align="left">The first step in the argument is to declare the postulates:&nbsp; 
	1) All men are created equal and have unalienable Rights, 2) Governments are 
	to secure those Rights, 3) Governments get their powers from the consent of 
	the governed, 4) It is the right of the governed to change Government if it 
	is destructive.</p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/23.jpg" width="450" height="349"></p>
	
	<p align="left">Proof of destructiveness must be submitted.&nbsp; Since the 
	Government has failed to secure the Rights of the governed it is neglecting 
	its duty.</p>
	
	<p align="center">
	<img border="0" src="pictures/Euclid/24.jpg" width="450" height="349"></p>
	
	<p align="left">By submitting proofs of the violation of Rights, Thomas 
	Jefferson completed the logic of the Declaration of Independence, making it 
	a document based on law -- universal law.</p>
	<p align="left">The form of logic used parallels Euclidian logic and the 
	system of proof.&nbsp; Euclid not only established modern mathematics but 
	gave us a new way to think about our social affairs.&nbsp; It is not 
	sufficient to assert a position, one must prove it based on fundamental 
	principles.&nbsp; </p>
	<p align="left">At the end of his talk, Dr. Molinsky invited the audience to 
	examine the edition of the Elements on loan to Mantor library.&nbsp; It is 
	the first English translation made from a Greek manuscript.&nbsp; Previous 
	translations had been based on Arabic documents.&nbsp; </p>
	<p align="center">
	<img border="0" src="pictures/Euclid/DSCN1066w.jpg" width="229" height="350"></p>
	<p align="center">Click on the images below for enlarged views of the 
	manuscript.</p>
	<p align="center"><a href="pictures/Euclid/DSCN1059wl.jpg">
	<img border="0" src="pictures/Euclid/DSCN1059w.jpg" width="350" height="259"></a></p>
	<p align="center">&nbsp;</p>
	<p align="center"><a href="pictures/Euclid/DSCN1049wl.jpg">
	<img border="0" src="pictures/Euclid/DSCN1049w.jpg" width="350" height="225"></a></p>
	<p align="left"><br>


	</p>


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          <td width="100%"><blockquote><font face="Verdana,Arial,Helvetica" size="-1"><br>Citation:<br><br>"Euclid's Elements and the Declaration of Independence."&nbsp; Summary of a lecture by Mike Molinsky.&nbsp; 
University of Maine at Farmington, September 7, 2005.&nbsp;  Retrieved _______.&nbsp; &lt;http://hua.umf.maine.edu/Reading_Revolutions/euclid.html&gt;.<br><br>URL:  <a href="http://hua.umf.maine.edu/Reading_Revolutions/index.html">http://hua.umf.maine.edu/Reading_Revolutions/index.html</a>  <br><br>Marilyn Shea, 2006<br><br>

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