<div>Paul,</div><div><br></div><div>Thanks!</div><div>I have read Williams's book some time ago and I will have a look at it again.</div><div><br></div><div>Perhaps the world's best specialist on Greek and Roman table abaci is Alain Schärlig (University of Lausanne, retired). He has written several books on the subject (two are mentioned in my blog post).</div><div><br></div><div>In my book "Milestones in Analog and Digital Computing" (English translation in preparation) you find a (mostly) comprehensive list of medieval (and later) table abaci with beautiful pictures. Most of them are preserved in Switzerland, some in Germany, France and other countries. There are also step-by-step instructions for their usage. The book includes a list of museums with information where which artifact has survived (e.g. Darius vase, Salamis tablet, original Roman abaci in Italy and France, etc.).</div><div><br></div><div>Best,</div><div>Herbert</div><div><br></div><div><br></div><div><br></div><div>
<p align="left" style="margin: 0px; text-align: left;"><b style="mso-bidi-font-weight:
normal"><span style='margin: 0px; font-family: "Arial","sans-serif"; font-size: 10pt;'>Meilensteine der Rechentechnik, Band 1</span></b></p>
<p align="left" style="margin: 0px; text-align: left;"><span lang="DE-CH" style="margin: 0px;"><a href="https://www.degruyter.com/view/product/480555"><span lang="DE" style='margin: 0px; font-family: "Arial","sans-serif"; font-size: 10pt;'><font color="#0000ff">https://www.degruyter.com/view/product/480555</font></span></a></span><span style='margin: 0px; font-family: "Arial","sans-serif"; font-size: 10pt;'></span></p>
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<p align="left" style="margin: 0px; text-align: left;"><b style="mso-bidi-font-weight:
normal"><span style='margin: 0px; font-family: "Arial","sans-serif"; font-size: 10pt;'>Meilensteine der Rechentechnik, Band 2</span></b></p>
<p align="left" style="margin: 0px; text-align: left;"><span lang="DE-CH" style="margin: 0px;"><a href="https://www.degruyter.com/view/product/503373"><span lang="DE" style='margin: 0px; font-family: "Arial","sans-serif"; font-size: 10pt;'><font color="#0000ff">https://www.degruyter.com/view/product/503373</font></span></a></span><span style='margin: 0px; font-family: "Arial","sans-serif"; font-size: 10pt;'></span></p>
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<p style="margin: 0px;"><b style="mso-bidi-font-weight:normal"><span style='margin: 0px; font-family: "Arial","sans-serif"; font-size: 10pt;'>Amazon</span></b></p>
<p style="margin: 0px;"><span lang="DE-CH" style="margin: 0px;"><a href="https://tinyurl.com/y9upwagp"><span style='margin: 0px; font-family: "Arial","sans-serif"; font-size: 10pt;'><font color="#0000ff">https://tinyurl.com/y9upwagp</font></span></a></span><span lang="DE-CH" style='margin: 0px; color: black; font-family: "Arial","sans-serif"; font-size: 10pt;'> </span></p>
<b></b><i></i><u></u><sub></sub><sup></sup><strike></strike><font size="3"></font><font face="Times New Roman"></font><br></div><div><b></b><i></i><u></u><sub></sub><sup></sup><strike></strike><br></div><div><br></div><signature id="signaturefinder_x-mail-compose1550743056341">--<br><div>Bruderer Informatik</div><div>Seehaldenstraße 26</div><div>Postfach 47</div><div>CH-9401 Rorschach</div><div>Schweiz/Switzerland</div><div>Telefon +41 71 855 77 11<br></div></signature><blockquote style="margin-right: 0px; margin-left:15px;">----Ursprüngliche Nachricht----<br>Von : pedwards@stanford.edu<br>Datum : 20/02/2019 - 23:00 (MZ)<br>An : herbert.bruderer@bluewin.ch<br>Cc : members@sigcis.org, members@lists.sigcis.org<br>Betreff : Re: [SIGCIS-Members] History of Rome. How did they calculate?<br><br>The THROBAC and Jim’s MacAbacus are great - but more seriously, there is a useful discussion on the origins of the abacus in Williams, M. R. 1985. A History of Computing Technology. Englewood Cliffs: Prentice-Hall, Inc. - pp 53-66.
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Williams focuses mainly on the table abacus used by the Greeks and Romans - not the hand abacus discussed in this intriguing blog post, which I did not know about.
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On p 56, Williams reproduces a drawing of the Greek abacus in use, copied from an ancient vase. Williams is referring to the obvious table abacus in the drawing — but the man in that same drawing is holding something in one hand that might conceivably be a hand abacus like the one Herbert identifies. No further information is given.
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Herbert, please let us know what you find out!
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Paul
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On Feb 20, 2019, at 12:36,
<a style="cursor:pointer; text-decoration:underline; color:blue" onclick="javascript:handleMailto('mailto:herbert.bruderer@bluewin.ch');"> herbert.bruderer@bluewin.ch</a> wrote:
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<p><b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="margin: 0.0px;"><font face="trebuchet ms,sans-serif">How did the Romans calculate?</font></span></b></p>
<p><span lang="EN-US" style="margin: 0.0px;"><font face="trebuchet ms,sans-serif"><a href="https://cacm.acm.org/blogs/blog-cacm/234881-how-did-the-romans-calculate/fulltext"><font color="#0000ff">https://cacm.acm.org/blogs/blog-cacm/234881-how-did-the-romans-calculate/fulltext</font></a> </font></span></p>
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<p>Hi all:</p>
<p>Does anyone know how the Romans calculated with the Roman numeral system?</p>
<p>What is the meaning of the right-most slot of the Roman hand abacus?</p>
<p>Do you have Roman hand abaci (original devices or replicas) in your collection? </p>
<p>Thank you very much for your help.</p>
<p>Best wishes,</p>
<p>Herbert Bruderer</p> _______________________________________________
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___________________________
<br> Paul N. Edwards
<br> William J. Perry Fellow in International Security
<br>
<a href="http://cisac.fsi.stanford.edu/">Center for International Security and Cooperation</a>
<br> Stanford University
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<br> Professor of
<a href="http://www.si.umich.edu/">Information</a> and
<a href="http://www.lsa.umich.edu/history/">History</a> (Emeritus)
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University of Michigan
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<br> Contact:
<br> m:
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<br> t: @AVastMachine
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