123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184 |
- <HTML>
- <HEAD>
- <meta http-equiv=Content-Type content="text/html; charset=ISO-8859-1">
- <TITLE>Euclid and the US Constitution -- Reading Revolutions -- Intellectual History</TITLE>
- </HEAD>
- <BODY bgcolor="#FFFFFF" marginwidth="0" marginheight="0" topmargin="0" leftmargin="0">
- <table border="0" cellspacing="0" width="100%" id="AutoNumber1" cellpadding="0" height="667">
- <tr>
- <td width="110" height="102">
- <img border="0" src="wlefttopcorner.jpg" width="108" height="106"></td>
- <td width="100%" background="wwtopcenter.jpg" height="106"> </td>
- <td width="109" height="102">
- <img border="0" src="wrighttopcorner.jpg" width="105" height="106"></td>
- </tr>
- <tr>
- <td width="110" background="wleftcenter.jpg" height="456"> </td>
- <td width="33%" height="456">
- <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.
- The Babylonians and Egyptians as well as other cultures used mathematics in
- astronomy, building, and calculation. In this example from an Egyptian
- papyrus from 1700 BC the problem illustrates a simple linear equation.
- </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.
- They dealt with the specific problems. All that changed with the
- Greeks. They began to ask why things happened in astronomy, medicine,
- mathematics, and the world around them. 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. 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. 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"> </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. By then, Euclid's <i>Elements </i>
- had not only influenced mathematics but all other branches of knowledge.
- The idea of proof, evidence and the use of reason and logic to approach the
- world underlay science and medicine as well as philosophy. </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:
- 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. 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. Euclid not only established modern mathematics but
- gave us a new way to think about our social affairs. It is not
- sufficient to assert a position, one must prove it based on fundamental
- principles. </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. It is
- the first English translation made from a Greek manuscript. Previous
- translations had been based on Arabic documents. </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"> </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>
- <center><table border="6" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="80%" id="decorative" bgcolor="#cccccc">
- <tr>
- <td width="100%"><center><table border="6" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" id="credits" bordercolor="#111111" bgcolor="#cccccc">
- <tr>
- <td width="100%"><blockquote><font face="Verdana,Arial,Helvetica" size="-1"><br>Citation:<br><br>"Euclid's Elements and the Declaration of Independence." Summary of a lecture by Mike Molinsky.
- University of Maine at Farmington, September 7, 2005. Retrieved _______. <http://hua.umf.maine.edu/Reading_Revolutions/euclid.html>.<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>
- </blockquote></td></tr></table></center>
- </td></tr></table></center>
- </td>
- <td width="110" background="wrightcenter.jpg" height="456"> </td>
- </tr>
- <tr>
- <td width="110" height="105">
- <img border="0" src="wleftbottcorner.jpg" align="top" width="108" height="105"></td>
- <td width="100%" background="wbottcenter.jpg" height="105"> </td>
- <td width="109" height="105">
- <img border="0" src="wrightbotcorner.jpg" align="top" width="105" height="105"></td>
- </tr>
- </table>
- </body>
- </html>
|