tag:blogger.com,1999:blog-26098309872961013582024-03-13T14:58:30.689-04:00Mathematical TreasuresHistorical mathematical materials, including texts, documents, and artifacts from the collections of David Eugene Smith and George Arthur Plimpton. These treasures are online through the cooperation of Columbia University Libraries and The Mathematical Association of America.
See the full index of Mathematical Treasures on the MAA Mathematical Sciences Digital Library.
This blog is updated every Saturday.Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.comBlogger64125tag:blogger.com,1999:blog-2609830987296101358.post-36379515352805020752012-12-29T12:00:00.000-05:002012-12-29T12:00:01.649-05:00Enjoy Mathematical Treasures!<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.maa.org/pubs/FOCUSdec12-jan13.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="http://digital.ipcprintservices.com/publication/?i=139063" border="0" height="320" src="http://www.maa.org/pubs/FOCUSdec12-jan13.jpg" title="http://digital.ipcprintservices.com/publication/?i=139063" width="248" /></a></div>
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Read about <a href="http://digital.ipcprintservices.com/publication/?i=139063" target="_blank">Mathematical Treasures</a> in the December 2012/January 2013 issue of <i>MAA FOCUS, </i>the newsmagazine of the Mathematical Association of America. </div>
Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-21274582754283192822012-12-22T12:00:00.000-05:002012-12-22T12:00:02.497-05:00Lilavati of Bhaskara<span style="font-family: inherit;"><br /></span>
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<span style="font-family: inherit;">This is a page from a manuscript of the <em>Lilavati</em> of Bhaskara II (1114-1185). This manuscript dates from 1650. The rule for the problem illustrated here is in verse 151, while the problem itself is in verse 152:</span></div>
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<span style="font-family: inherit;">151: The square of the pillar is divided by the distance between the snake and its hole; the result is subtracted from the distance between the snake and its hole. The place of meeting of the snake and the peacock is separated from the hole by a number of <em>hastas</em> equal to half that difference.</span></div>
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<span style="font-family: inherit;">152: There is a hole at the foot of a pillar nine <em>hastas</em> high, and a pet peacock standing on top of it. Seeing a snake returning to the hole at a distance from the pillar equal to three times its height, the peacock descends upon it slantwise. Say quickly, at how many <em>hastas</em> from the hole does the meeting of their two paths occur? (It is assumed here that the speed of the peacock and the snake are equal.) </span></div>
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<span style="font-family: inherit;">These verses and much else from the <em>Lilavati</em> may be found in Kim Plofker, "Mathematics in India", in Victor Katz, ed., <i>The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook</i> <em> </em> (Princeton: Princeton University Press, 2007), pp. 385-514.</span></div>
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<span style="line-height: 16.78333282470703px;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=2588" target="_blank">Lilavati of Bhaskara</a></span></div>
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Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-181865480835123692012-12-01T10:00:00.000-05:002012-12-21T15:02:33.972-05:00Francesco Ghaligai's Practica D'Arithmetica <div class="separator" style="clear: both; text-align: center;">
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<span style="font-family: inherit; margin-left: 1em; margin-right: 1em;"> <img border="0" height="240" src="http://mathdl.maa.org/images/upload_library/46/Plimpton-Smith/080080142-2.jpg" width="400" /></span></div>
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<span style="font-family: inherit;">These pages are from the <span style="background-color: white; line-height: 16.78333282470703px;">1552 edition of the </span><em style="background-color: white; line-height: 16.78333282470703px;">Practica d'Arithmetica</em><span style="background-color: white; line-height: 16.78333282470703px;"> of Francesco Ghaligai (d. 1536). On these pages, </span><span style="background-color: white; line-height: 16.78333282470703px;">Ghaligai proposes a new notation for powers of the unknown. Notice on the left hand page that his notation for the second power (censo) is just a square, but the other notations never caught on with other authors. On the right hand page, Ghaligai illustrates the notation by calculating the powers of 2 up to the fifteenth power.</span></span></div>
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<span style="font-family: inherit;"><em style="background-color: white; line-height: 16.78333282470703px;">Practica d'Arithmetica </em><span style="background-color: white; line-height: 16.78333282470703px;">was originally published in 1521, but this printing, like several other printings, is identical with the original. Its intended audience was merchants, so there are many practical problems dealing with issues of trade. In the sections on algebra, Ghaligai introduces his own notation.</span></span></div>
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<span style="font-family: inherit;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3811" target="_blank">Francesco Ghaligai's Practica D'Arithmetica</a></span></div>
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<br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-77897660749817922612012-11-17T09:00:00.000-05:002012-11-17T09:00:04.377-05:00Austran weights <div class="separator" style="clear: both; text-align: center;">
<a href="http://mathdl.maa.org/images/upload_library/46/Plimpton-Smith/080080167-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img border="0" height="198" src="http://mathdl.maa.org/images/upload_library/46/Plimpton-Smith/080080167-1.jpg" width="320" /></span></a></div>
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<span style="font-family: inherit;">Nest of Austrian weights of the 18<sup>th</sup> century. Selected by D.E.Smith for his collection to illustrate the ancient, “Problem of Weights”. One example of this problem is given by Claude Bachet as:</span></div>
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<span style="font-family: inherit;"><em>What is the least number of weights that can be used on a scale pan to weigh any in</em><em>tegral number of pounds from </em>1<em> to </em>40 <em>inclusive, if the weights can be placed in ei</em><em>ther of the scale pans?</em></span></div>
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<span style="font-family: inherit;">This particular set of weights is elaborately decorated and is one of the best specimens of the weight maker’s art of the period. It bears at least ten official seals, one of which contains the date 1787.</span></div>
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<span style="font-family: inherit;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3890" target="_blank">Austran weights</a> </span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-21122009264693495962012-11-10T08:00:00.000-05:002012-11-10T08:00:05.513-05:00Thomas Digges' Pantometria <div class="separator" style="clear: both; text-align: center;">
<span style="font-family: inherit; margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="http://3.bp.blogspot.com/-dk6W_ABemWI/UJ16t0XNngI/AAAAAAAAFsc/qEpPP7Tng2w/s640/pantrica.jpg" width="452" /></span></div>
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<span style="background-color: white; font-family: inherit; line-height: 16.78333282470703px;">This is the </span><a href="http://mathdl.maa.org/images/upload_library/46/Plimpton-Smith/8081Diggesgeometry.tif" style="background-color: white; color: blue; font-family: inherit; line-height: 16.78333282470703px;" target="_blank" title="title page">title page</a><span style="background-color: white; font-family: inherit; line-height: 16.78333282470703px;"> of </span><em style="background-color: white; font-family: inherit; line-height: 16.78333282470703px;">A Geometrical Practise Named Pantometria</em><span style="background-color: white; font-family: inherit; line-height: 16.78333282470703px;">, a guide to applied geometry published by </span><a href="http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Digges.html" style="background-color: white; color: blue; font-family: inherit; line-height: 16.78333282470703px;" target="_blank" title="Thomas Digges">Thomas Digges</a><span style="background-color: white; font-family: inherit; line-height: 16.78333282470703px;"> (1546-1595) in 1571. </span><em style="background-color: white; font-family: inherit; line-height: 16.78333282470703px;">Pantometria</em><span style="background-color: white; font-family: inherit; line-height: 16.78333282470703px;"> was completed by Thomas from a manuscript left by his father, Leonard Digges, who died when Thomas was 13 years old. After his father's death, Thomas became the ward of </span><a href="http://www-history.mcs.st-and.ac.uk/Biographies/Dee.html" style="background-color: white; color: blue; font-family: inherit; line-height: 16.78333282470703px;">John Dee</a><span style="background-color: white; font-family: inherit; line-height: 16.78333282470703px;"> (1527-1609), sometime scientific advisor to Queen Elizabeth I. Thomas was greatly influenced by Dee, and remained friends with him throughout his life. Thomas Digges became a recognized astronomer and the leader of the English Copernicans.</span><br />
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<span style="font-family: inherit;">See more pages from <a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3437" target="_blank">Thomas Digges' <i>Pantometria</i> </a></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-76069962090984812542012-09-30T12:00:00.000-04:002012-10-03T10:32:45.785-04:00Francesco Barozzi's Procli Diadochi <div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-tuQgRNsjhEg/UGxMZTWp8xI/AAAAAAAAFUA/S4jTHV7XDro/s1600/Screen+shot+2012-10-03+at+10.34.52+AM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-tuQgRNsjhEg/UGxMZTWp8xI/AAAAAAAAFUA/S4jTHV7XDro/s320/Screen+shot+2012-10-03+at+10.34.52+AM.png" width="219" /></a></div>
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This is the frontispiece of Procli Diadochi by Francesco Barozzi, published in Venice, 1560. Barozzi (1537 - 1604) was a Venetian nobleman, a mathematician, astronomer and humanist. A correspondent of Christopher Clavius, he was well known in the Italian mathematical community of the time. He was a translator of and commentator on ancient mathematical classics and was particularly active in the 16th century movement to revive an interest in Euclidean geometry. His book is a translation of and commentary on Proclus Diadochus’ ( 411 - 485 ) edition of Euclid's Elements. The portrait depicts Barozzi.<br />
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3608" target="_blank">Francesco Barozzi's Procli Diadochi</a><br />
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Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-33449755505713838012012-06-30T12:00:00.000-04:002012-06-30T12:00:08.590-04:00Van Heuraet's Rectification of Curves<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-L7j4TexORoE/T-d5Sqc8TmI/AAAAAAAAEp4/yIU5Akl2Os4/s1600/Van+Heuraet's+Rectification+of+Curves.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="251" src="http://3.bp.blogspot.com/-L7j4TexORoE/T-d5Sqc8TmI/AAAAAAAAEp4/yIU5Akl2Os4/s400/Van+Heuraet's+Rectification+of+Curves.jpg" width="400" /></a></div>
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<span style="font-family: inherit;"><span style="background-color: white;">These pages are from t</span><span style="background-color: white; line-height: 16px;">he brief work </span><em style="background-color: white; line-height: 16px;">On the Transformation of Curves into Straight Lines</em><span style="background-color: white; line-height: 16px;">, by </span>Hendrick van Heuraet<span style="background-color: white; line-height: 16px;"> (1634 - 1660), published in the 1659 Latin edition of Descartes's </span><em style="background-color: white; line-height: 16px;">Geometry</em><span style="background-color: white; line-height: 16px;">, edited by van Schooten. Although van Heuraet was not the first to accomplish a rectification, a task that Descartes had said could not be done, this is the first publication of a general procedure, a procedure very close to our standard calculus procedure for finding the length of a curve.</span></span><br />
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<span style="font-family: inherit;"><span style="line-height: 16px;">On </span>these two pages<span style="line-height: 16px;">, van Heuraet describes his general procedure for rectification, one which tranforms the length into an integral, that is, the area under a curve. He then illustrates the procedure by calculating the length of the semi-cubical parabola, </span><em style="line-height: 16px;">y</em><sup style="line-height: 16px;">2</sup><span style="line-height: 16px;"> = </span><em style="line-height: 16px;">x</em><sup style="line-height: 16px;">3</sup><span style="line-height: 16px;">/</span><em style="line-height: 16px;">a. </em><span style="line-height: 16px;"> (We can take </span><em style="line-height: 16px;">a</em><span style="line-height: 16px;"> = 1 for simplicity.) Note that since the procedure for finding arc length involved first finding </span><em style="line-height: 16px;">dy</em><span style="line-height: 16px;">/</span><em style="line-height: 16px;">dx</em><span style="line-height: 16px;"> (or the tangent to the curve)</span><em style="line-height: 16px;">,</em><span style="line-height: 16px;"> van Heuraet accomplishes this by using Descartes's normal method and Hudde's rule for finding a double root. Note also that van Heuratet uses Descartes's symbol for "equal" rather than our modern equal sign.</span></span><br />
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3601" target="_blank"><span style="font-family: inherit;">Van Heuraet's Rectification of Curves</span></a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-68816619458156873772012-06-23T12:00:00.000-04:002012-06-24T16:29:08.404-04:00Zhoubi suanjing<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/--cGWDmxzXW8/T-d4cO4YTuI/AAAAAAAAEps/A87fx8urXIo/s1600/Zhoubi+suanjing.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="http://4.bp.blogspot.com/--cGWDmxzXW8/T-d4cO4YTuI/AAAAAAAAEps/A87fx8urXIo/s400/Zhoubi+suanjing.jpg" width="293" /></a></div>
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<span style="font-family: verdana, helvetica, arial, sans-serif; font-size: 12px; line-height: 16px;">This pages is from the </span><em style="font-family: verdana, helvetica, arial, sans-serif; font-size: 12px; line-height: 16px;">Zhoubi suanjing</em><span style="font-family: verdana, helvetica, arial, sans-serif; font-size: 12px; line-height: 16px;"> (</span><em style="font-family: verdana, helvetica, arial, sans-serif; font-size: 12px; line-height: 16px;">Arithmetical Classic of the Gnomon and the Circular Paths of Heaven</em><span style="font-family: verdana, helvetica, arial, sans-serif; font-size: 12px; line-height: 16px;">), a Chinese book on astronomy and mathematics dated to approximately 100 BCE. </span><span style="background-color: white; font-size: 12px; line-height: 16px;"><span style="font-family: verdana, helvetica, arial, sans-serif;">This diagram illustrates a square of side 4 fitting into a square of side 5.</span></span><br />
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3434" target="_blank">Zhoubi suanjing</a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-56256772930098796762012-06-16T12:00:00.000-04:002012-06-16T12:00:02.804-04:00Christopher Clavius's Edition of Euclid's Elements<span style="font-family: inherit;"><br /></span><br />
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<span style="font-family: inherit;">Euclid’s propositions I-46 and I-47 as given in Christopher Clavius’<span style="background-color: white; line-height: 16px; text-align: left;"> ( 1538-1612) </span><em style="background-color: white; line-height: 16px; text-align: left;">Elements</em><span style="background-color: white; line-height: 16px; text-align: left;"> published in Rome in 1574.</span><span style="background-color: white; line-height: 16px; text-align: left;"> </span><span style="background-color: white; line-height: 16px; text-align: left;">Note that Clavius indicates his volume contains 15 books of Euclid.</span><span style="background-color: white; line-height: 16px; text-align: left;"> </span><span style="background-color: white; line-height: 16px; text-align: left;">Many medieval authors erroneously attributed two extra books to Euclid's </span><em style="background-color: white; line-height: 16px; text-align: left;">Elements.</em><span style="background-color: white; line-height: 16px; text-align: left;"></span><span style="background-color: white; line-height: 16px; text-align: left;">Book XIV extends Euclid discussion in book XIII on the comparison of the regular solids inscribed in a sphere.</span><span style="background-color: white; line-height: 16px; text-align: left;"> </span><span style="background-color: white; line-height: 16px; text-align: left;">This work is now believed to have been composed by </span>Hypsicles<span style="background-color: white; line-height: 16px; text-align: left;"> of Alexandria (ca.190 BCE—ca 120 BCE).</span><span style="background-color: white; line-height: 16px; text-align: left;"> </span><span style="background-color: white; line-height: 16px; text-align: left;">Book XV also deals with the properties of regular solids and is believed to have been compiled by </span>Isidore of Miletus<span style="background-color: white; line-height: 16px; text-align: left;"> (fl.ca. 532), who was the architect responsible for the Cathedral of Holy Wisdom in Constantinople, later to become the Hagia Sophia.</span></span><br />
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3636" target="_blank"><span style="font-family: inherit;">Christopher Clavius's edition of Euclid's Elements</span></a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-9903975307800449312012-06-09T12:00:00.000-04:002012-06-11T10:09:23.742-04:00Jan de Witt's Elements of Curves<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-0UveDiKGJsY/T8kjYFX-wAI/AAAAAAAAEiI/dBvBSqqXVvs/s1600/Jan+de+Witt's+Elements+of+Curves.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="http://1.bp.blogspot.com/-0UveDiKGJsY/T8kjYFX-wAI/AAAAAAAAEiI/dBvBSqqXVvs/s400/Jan+de+Witt's+Elements+of+Curves.jpg" width="292" /></a></div>
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<span style="font-family: inherit;">This image is page 263 of </span><em style="background-color: white; font-family: inherit; line-height: 16px; text-align: left;">Elements of Linear Curves </em><span style="background-color: white; font-family: inherit; line-height: 16px; text-align: left;">by </span><a href="http://www-history.mcs.st-andrews.ac.uk/history/Biographies/De_Witt.html" style="background-color: white; color: blue; font-family: inherit; line-height: 16px; text-align: left;">Jan de Witt</a><span style="background-color: white; font-family: inherit; line-height: 16px; text-align: left;"> (1625 - 1672). De Witt was a student of Frans van Schooten, who published this work in his 1661 edition of Descartes' </span><em style="background-color: white; font-family: inherit; line-height: 16px; text-align: left;">Geometry</em><span style="background-color: white; font-family: inherit; line-height: 16px; text-align: left;">. (This copy is from the 1683 edition. And, in fact, de Witt himself probably finished the work by 1646.) The first of the two books of this treatise was devoted to developing the properties of the conic sections using synthetic methods based on the work of Apollonius. But in the second book, de Witt produced a complete algebraic treatment of the conics, beginning with equations in two variables, based on the work of Fermat and Descartes.</span><br />
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<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px; text-align: left;">On this page, de Witt shows how to rotate the axes to turn a complicated second degree equation in two variables into the standard one displayed earlier. Unlike in modern treatises, de Witt does not use trigonometry, but gives the equations of the new axes in terms of the old ones. That is, he uses a transformation of coordinates based on the form of the given equation.</span>
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3722" target="_blank"><span style="font-family: inherit;">More pages from Jan de Witt's Elements of Curves </span></a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-30441735936145980122012-06-02T12:00:00.000-04:002012-06-02T12:00:07.304-04:00Francisco Feliciano's Libro di Arithmetica<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px; text-align: left;">This page is from the 1536 edition of the </span><em style="background-color: white; line-height: 16px; text-align: left;">Libro di Arithmetica i Geometria</em><span style="background-color: white; line-height: 16px; text-align: left;"> of Francesco Feliciano (first half of 16th century). Not much is known about Feliciano, except that he was born in Lazisa, near Verona and was still living in 1563. This book is basically a revision of Feliciano's earlier </span><em style="background-color: white; line-height: 16px; text-align: left;">Libro de Abaco</em><span style="background-color: white; line-height: 16px; text-align: left;">, which appeared in 1517. The book contains much commercial arithmetic, but also a treatment of roots, the rule of false position, some algebra, and a section on practical geometry. The book had a good deal of influence on the teaching of elementary mathematics, appearing in numerous editions including one in 1669, 143 years after the original edition.</span></span><br />
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<a href="http://1.bp.blogspot.com/-AozuihokLeA/T8kh9ZV5cdI/AAAAAAAAEiA/39T7LiUgjBc/s1600/Francisco+Feliciano's+Libro+di+Arithmetica.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img border="0" height="400" src="http://1.bp.blogspot.com/-AozuihokLeA/T8kh9ZV5cdI/AAAAAAAAEiA/39T7LiUgjBc/s400/Francisco+Feliciano's+Libro+di+Arithmetica.jpg" width="272" /></span></a></div>
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<span style="font-family: inherit;">On this page, <span style="background-color: white; line-height: 16px; text-align: left;">Feliciano shows how to calculate the circumference and area of a circle. Note that he approximates pi by 22/7 to calculate the circumference and area of a circle of diameter 14.</span></span><br />
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<span style="font-family: inherit;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3735" target="_blank">More pages from Francisco Feliciano's Libro di Arithmetica</a></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-48611732688574554492012-05-26T12:00:00.000-04:002012-06-01T16:05:09.202-04:00Johann Boschenstein's Rechenbuch<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-aHllGHW5oN0/T8kgEWlbYuI/AAAAAAAAEh4/MPWg3gjN97c/s1600/Johann+Boschenstein's+Rechenbuch.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="http://1.bp.blogspot.com/-aHllGHW5oN0/T8kgEWlbYuI/AAAAAAAAEh4/MPWg3gjN97c/s400/Johann+Boschenstein's+Rechenbuch.jpg" width="245" /></a></div>
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<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px; text-align: left;">This is the </span>title page<span style="background-color: white; line-height: 16px; text-align: left;"> of </span><em style="background-color: white; line-height: 16px; text-align: left;">Ain neu geordnet Rechenbiechlin</em><span style="background-color: white; line-height: 16px; text-align: left;"> (1514) by </span>Johann Böschenstein <span style="background-color: white; line-height: 16px; text-align: left;">(1472-1540). Böschenstein was best known as a professor of Hebrew in several German universities. In fact, Martin Luther studied Hebrew with him at one time. This rechenbuch introduced students to the basic principles of arithmetic, with application to various business problems. The engraving on the title page shows someone working on an arithmetic problem.</span>
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3736" target="_blank"><span style="font-family: inherit;">Johann Boschenstein's Rechenbuch</span></a><br />
<br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-15969431531941426402012-05-19T12:00:00.000-04:002012-06-01T16:05:39.007-04:00Christian Wolff's Treatise of Algebra<span style="font-family: inherit;"><br /></span><br />
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<a href="http://3.bp.blogspot.com/-8ZZA05fXMD8/T61kHUpBzMI/AAAAAAAAEa0/IM8cNC7lqug/s1600/Christian-Wolff's-Treatise-of-Algebra.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img border="0" height="285" src="http://3.bp.blogspot.com/-8ZZA05fXMD8/T61kHUpBzMI/AAAAAAAAEa0/IM8cNC7lqug/s400/Christian-Wolff's-Treatise-of-Algebra.jpg" width="400" /></span></a></div>
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<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px; text-align: left;">Pages 202-203 (click to enlarge) of </span><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3737" target="_blank">Christian Wolff's <i>Treatise of Algebra</i></a><i>.</i> On these pages<span style="background-color: white; line-height: 16px; text-align: left;">, Wolff discusses some elements of the theory of equations. Note that he mentions Descartes' rule of signs, without attribution to Descartes. In fact, he attributes it to Thomas Harriot and claims further that no one had yet proven it. The first published proof of the result was due to </span>Jean Paul de Gua de Malves<span style="background-color: white; line-height: 16px; text-align: left;"> (1713 - 1785), who gave two proofs in 1741 in a paper in the </span><em style="background-color: white; line-height: 16px; text-align: left;">Memoires </em><span style="background-color: white; line-height: 16px; text-align: left;">of the Paris Academy.</span></span><br />
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3737" target="_blank"><span style="font-family: inherit;">Christian Wolff's <i>Treatise of Algebra</i></span></a><br />
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<span style="background-color: white; line-height: 16px; text-align: left;"><span style="font-family: inherit;">Wolff was a student of Leibniz and is most famous for his work in philosophy. His school of philosophy, in fact, was the most prominent in Germany prior to Kant. This book was originally written in Latin in 1713. It first appeared in English in 1739, though this copy is of the second edition on 1765. <a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3737" target="_blank">Read more</a>. </span></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-57363132992301966402012-05-12T12:00:00.000-04:002012-05-12T12:00:06.233-04:00Michael Stifel's Arithmetica Integra<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-fc3Mq1EE5DA/T61ic0bKu_I/AAAAAAAAEas/xVjZu_PJ1FU/s1600/Michael-Stifel's-Arithmetica-Integra.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img border="0" height="400" src="http://4.bp.blogspot.com/-fc3Mq1EE5DA/T61ic0bKu_I/AAAAAAAAEas/xVjZu_PJ1FU/s400/Michael-Stifel's-Arithmetica-Integra.jpg" width="267" /></span></a></div>
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<span style="font-family: inherit;"><span style="line-height: 16px; text-align: left;">This diagram from</span><span style="line-height: 16px; text-align: left;"> </span><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3752" target="_blank">Michael Stifel's<i> Arithmetica Integra</i></a> <span style="line-height: 16px; text-align: left;">represents the solution to the pair of simultaneous equations</span></span><br />
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<span style="font-family: inherit;">x<sup>2</sup> + y<sup>2</sup> - (x + y) = 78, xy + (x + y) = 39.</span></div>
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<span style="font-family: inherit;">Here, the two unknowns are represented by AC and BC, while the sum AB is called "B" by Stifel. Also, the script z is Stifel's notation for the square of the (first) unknown, namely x<sup>2</sup>. Note that therefore the smaller square (on the upper right) is labeled with the script z, the two rectangles are labeled 39 - 1B (since their areas are each xy, which is equal to 30 - (x + y)), and the larger square, which is equal to y<sup>2</sup>, is labeled 78 + B - z, that is 78 + (x + y) - x<sup>2</sup>. Stifel completes the problem as follows: The sum of the areas of all four regions of the diagram is equal to 156 - B, and this equals B<sup>2</sup>. It follows that B = 12. Therefore the larger square has area 90 - x<sup>2</sup>, and the two rectangles each have area 27. But either of those rectangles is the mean proportional between the larger square and the smaller square. Therefore, (90 - x<sup>2</sup>):27 = 27:x<sup>2</sup>. It follows that 90x<sup>2</sup> - x<sup>4</sup> = 729. So x<sup>2</sup> = 9 and x = 3. Then y = 9 and the problem is solved.</span></div>
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3752" target="_blank"><span style="font-family: inherit;">Michael Stifel's <i>Arithmetica Integra</i></span></a><br />
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<span style="font-family: inherit;"><a href="http://en.wikipedia.org/wiki/Michael_Stifel" style="background-color: white; color: blue; line-height: 16px; text-align: left;" target="_blank">Michael Stifel</a><span style="background-color: white; line-height: 16px; text-align: left;"> (1487-1567), one of the best-known German cossists of the sixteenth century. Stifel's work covered the basics of algebra, using the German symbols for powers of the unknown and also considering negative exponents for one of the first times in a European book. He also presented the Pascal triangle as a tool for finding roots of numbers and was one of the first to present one combined form of the algorithm for solving quadratic equations.</span></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-4927165993304480022012-05-05T12:00:00.000-04:002012-05-05T12:00:06.349-04:00Richard Sault's New Treatise of Algebra<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: inherit;"><em style="background-color: white; line-height: 16px;">A New Treatise of Algebra</em><span style="background-color: white; line-height: 16px;"> by</span><a href="http://en.wikipedia.org/wiki/Richard_Sault" style="background-color: white; color: blue; line-height: 16px;" target="_blank"> Richard Sault</a><span style="background-color: white; line-height: 16px;"> (d. 1702). Not much is known about Sault, except that he ran a mathematical school in London in the 1690s near the Royal Exchange and was an editor of and contributor to the </span><a href="http://en.wikipedia.org/wiki/The_Athenian_Mercury" style="background-color: white; color: blue; line-height: 16px;" target="_blank"><em>Athenian Mercury</em></a><span style="background-color: white; line-height: 16px;">, a literary journal that was published between 1690 and 1697. The</span><em style="background-color: white; line-height: 16px;">Treatise of Algebra </em><span style="background-color: white; line-height: 16px;">was published as an appendix to William Leybourne's </span><em style="background-color: white; line-height: 16px;">Pleasure with Profit</em><span style="background-color: white; line-height: 16px;">, and included a chapter by Joseph Raphson on converging series.</span></span></div>
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<a href="http://2.bp.blogspot.com/-mFyzjeA8uDU/T5rn5s6PXII/AAAAAAAAEVs/k7LKy9hd6hI/s1600/080080137-3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img border="0" height="640" src="http://2.bp.blogspot.com/-mFyzjeA8uDU/T5rn5s6PXII/AAAAAAAAEVs/k7LKy9hd6hI/s640/080080137-3.jpg" width="426" /></span></a></div>
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<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px;">This image is </span><a href="http://mathdl.maa.org/images/upload_library/46/Plimpton-Smith/8137-3Sault19.tif" style="background-color: white; color: blue; line-height: 16px;" target="_blank">page 19</a>. Notice that<span style="background-color: white; line-height: 16px;"> Sault describes in some detail, with an example, how to convert a word problem into algebraic notation. Note that he generalizes his problem by using arbitrary constants, instead of just the given numbers.</span></span></div>
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<a href="http://mathdl.maa.org/jsp/search/searchResults.jsp?url=http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591" target="_blank"><span style="font-family: inherit;">Richard Sault's New Treatise of Algebra</span></a></div>
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<br /></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com1tag:blogger.com,1999:blog-2609830987296101358.post-82266628439661884032012-04-28T12:00:00.000-04:002012-04-28T12:00:07.658-04:00Simon Stevin's Oeuvres Mathematiques<div class="separator" style="clear: both; text-align: center;">
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This is the title page of the <i>Oeuvres Mathematiques</i> of Simon Stevin (1548-1620), edited by Albert Girard (1595 - 1632) and published in 1634. More pages are available on <a href="http://mathdl.maa.org/jsp/search/searchResults.jsp?url=http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591" target="_blank">MathDL</a>.</div>
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<a href="http://4.bp.blogspot.com/-tpOiFigO4SI/T5rnHizos8I/AAAAAAAAEVk/9AcKhKbZ5P0/s1600/080080139-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="http://4.bp.blogspot.com/-tpOiFigO4SI/T5rnHizos8I/AAAAAAAAEVk/9AcKhKbZ5P0/s640/080080139-1.jpg" width="425" /></a></div>
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<a href="http://mathdl.maa.org/jsp/search/searchResults.jsp?url=http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591" target="_blank">Simon Stevin's <i>Oeuvres Mathematiques</i></a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-89549277184477714312012-04-21T10:00:00.000-04:002012-04-21T10:00:07.232-04:00Gerolamo Cardano's Practica Arithmetice<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: inherit; margin-left: 1em; margin-right: 1em;"><a href="http://3.bp.blogspot.com/-yhapOlAVYzU/T4Ml05mjrfI/AAAAAAAAERw/FIZ05o3ZZGg/s1600/Gerolamo-Cardano's-Practica-Arithmetice.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://3.bp.blogspot.com/-yhapOlAVYzU/T4Ml05mjrfI/AAAAAAAAERw/FIZ05o3ZZGg/s400/Gerolamo-Cardano's-Practica-Arithmetice.jpg" width="270" /></a></span></div>
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<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px;">This is the title page of the </span><em style="background-color: white; line-height: 16px;">Practica Arithmetice </em><span style="background-color: white; line-height: 16px;">of </span>Gerolamo Cardano<span style="background-color: white; line-height: 16px;"> (1501-1576), published in 1539. It was a comprehensive work on arithmetical questions, with numerous practical problems and even some elementary algebra and geometry.</span></span>
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<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px;">More pages: </span></span><span style="line-height: 16px;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3796" target="_blank">Gerolamo Cardano's Practica Arithmetice</a></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-86058431410053562552012-04-14T10:00:00.000-04:002012-04-14T10:00:04.404-04:00John Ward's Compendium of Algebra<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-5mNa99ufUC4/T4Mk4PNvKuI/AAAAAAAAERo/7EyA5TvWLJc/s1600/John-Ward's-Compendium-of-Algebra.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img border="0" height="328" src="http://4.bp.blogspot.com/-5mNa99ufUC4/T4Mk4PNvKuI/AAAAAAAAERo/7EyA5TvWLJc/s400/John-Ward's-Compendium-of-Algebra.jpg" width="400" /></span></a></div>
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<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px;">This is the </span>title page<span style="background-color: white; line-height: 16px;"> of </span><em style="background-color: white; line-height: 16px;">A Compendium of Algebra</em><span style="background-color: white; line-height: 16px;"> (1724), written by John Ward, an English mathematicians about whom very little is known. He was born in 1648 and died sometime around 1730. It is known that he taught mathematics in Chester and is famous for another mathematics work, the </span><em style="background-color: white; line-height: 16px;">Young Mathematician's Guide</em><span style="background-color: white; line-height: 16px;">, first published in 1703. That work was imported in large quantities to New England and was used for a time as a textbook at Harvard University. It contains a very interesting method of calculating pi.</span></span>
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<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px;">More pages: </span></span><span style="line-height: 16px;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3882" target="_blank">John Ward's Compendium of Algebra</a></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-59615806458208391212012-04-07T12:00:00.000-04:002012-04-07T12:00:07.937-04:00Gemma Frisius's Arithmeticae Methodus Facilis<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-xx50TNVr9Hg/T2D2wGxCm9I/AAAAAAAAEMA/CG9AbIqQ-uU/s1600/Gemma+Frisius's+Arithmeticae+Methodus+Facilis.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://1.bp.blogspot.com/-xx50TNVr9Hg/T2D2wGxCm9I/AAAAAAAAEMA/CG9AbIqQ-uU/s400/Gemma+Frisius's+Arithmeticae+Methodus+Facilis.jpg" width="353" /></a></div>
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<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="background-color: white; line-height: 16px;">An example of the use of double false position to solve a problem in two unknowns found in the </span><em style="background-color: white; line-height: 16px;">Arithmeticae Practicae Methodus Facilis </em><span style="background-color: white; line-height: 16px;">(1540), by </span>Gemma Frisius<span style="background-color: white; line-height: 16px;"> (originally Regnier Gemma) (1508-1555). Gemma Frisius was best known for his work in astronomy and map-making; he worked closely with Gerardus Mercator in making an early globe. He also suggested a method for determining longitude at sea.</span> </span><br />
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<span style="font-family: Georgia, 'Times New Roman', serif;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3883" target="_blank">Gemma Frisius's Arithmeticae Methodus Facilis</a></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-14303935204691634082012-03-31T12:00:00.000-04:002012-03-31T12:00:09.330-04:00Antichissimo di Algorismo<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="background-color: white; line-height: 16px;">One of two illustrations from the fourteenth century Italian codex, </span></span>
<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3886" target="_blank"><span style="font-family: Georgia, 'Times New Roman', serif;"><i>Antichissimo di Algorismo</i></span></a><span style="font-family: Georgia, 'Times New Roman', serif;"><span style="background-color: white; line-height: 16px;">. This is one of many algorisms written at this time. They were arithmetics designed to introduce the Hindu-Arabic numerals, their operational algorithms and demonstrate their use in problem solving. The majority of the problems considered in this codex are commercial in nature. A few might be categorized as “recreational problems”. A special feature of this codex is that it contains 42 illustrations, many of which supplement problems. </span></span><br />
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<a href="http://4.bp.blogspot.com/-KJGK9JJOdjE/T2D13nHgW2I/AAAAAAAAEL4/ETIpZLtMOmc/s1600/Antichissimo+di+Algorismo.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Georgia, 'Times New Roman', serif;"><img border="0" height="400" src="http://4.bp.blogspot.com/-KJGK9JJOdjE/T2D13nHgW2I/AAAAAAAAEL4/ETIpZLtMOmc/s400/Antichissimo+di+Algorismo.jpg" width="327" /></span></a></div>
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<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="background-color: white; line-height: 16px;">The illustration on </span>folio 60<span style="background-color: white; line-height: 16px;"> presents the situation where three couples wish to cross a stream. The small boat they have will only accommodate two persons at a time. How can they all get to the other shore if no man is to cross with another’s wife? This is a variation of the puzzle-type </span>“River Crossing Problem<span style="background-color: white; line-height: 16px;">” that has been posed over the centuries in many guises.</span> </span><br />
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3886" target="_blank"><span style="font-family: Georgia, 'Times New Roman', serif;">Antichissimo di Algorismo</span></a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-13119995329040230572012-03-24T12:00:00.000-04:002012-03-24T12:00:06.584-04:00German protractor<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-x0US5qxClOU/T2D0wuVlaeI/AAAAAAAAELw/JGj-aO_6IGI/s1600/German+protractor.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-x0US5qxClOU/T2D0wuVlaeI/AAAAAAAAELw/JGj-aO_6IGI/s1600/German+protractor.jpg" /></a></div>
<span style="font-family: Georgia, 'Times New Roman', serif;">Brass protractor<span style="background-color: white; line-height: 16px;"> from about 1700 of German manufacture. Its base plate contains some Baroque decoration. Note its similarity to a present day student protractor.</span> </span><br />
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3889" target="_blank"><span style="font-family: Georgia, 'Times New Roman', serif;">German protractor</span></a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-81959934422557268652012-03-17T12:00:00.000-04:002012-03-17T12:00:00.934-04:00Simon Jacob's Rechenbuch<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-4BNHXbeIYiM/T2DzMHqFaDI/AAAAAAAAELo/m-XX79w4mcs/s1600/Simon-Jacob's-Rechenbuch.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-4BNHXbeIYiM/T2DzMHqFaDI/AAAAAAAAELo/m-XX79w4mcs/s320/Simon-Jacob's-Rechenbuch.jpg" width="277" /></a></div>
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<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="background-color: white; line-height: 16px;">This is the </span>title page<span style="background-color: white; line-height: 16px;"> of the "New and Fully Revised" Rechenbuch of </span>Simon Jacob<span style="background-color: white; line-height: 16px;"> (d. 1564), one of the best-known Rechenmeisters of the sixteenth century. The book was first published in 1560, but this illustration is from the 1565 edition. </span> </span><br />
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<a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=2779" target="_blank"><span style="font-family: Georgia, 'Times New Roman', serif;">Simon Jacob's Rechenbuch</span></a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-3959330312258553522012-03-10T12:00:00.000-05:002012-03-14T15:31:52.086-04:00English tally sticks<br />
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<a href="http://4.bp.blogspot.com/-RAf93DDJObg/T2Dxwma582I/AAAAAAAAELg/mq_tjY1ubk4/s1600/English-tally-sticks.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="245" src="http://4.bp.blogspot.com/-RAf93DDJObg/T2Dxwma582I/AAAAAAAAELg/mq_tjY1ubk4/s400/English-tally-sticks.jpg" width="400" /></a></div>
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<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="background-color: white; line-height: 16px;">Notched pieces of wood or bone were used by many ancient peoples to record numbers. The most common type of these </span>“tally sticks”<span style="background-color: white; line-height: 16px;"> was made of wood. Tally sticks served as records or receipts for financial transactions such as the payment of taxes, debts and fines. From the 12th century onward tally sticks were </span>officially employed<span style="background-color: white; line-height: 16px;"> by the Exchequer of England to collect the King’s taxes. Local sheriffs were given the task of actually collecting the taxes. The depth and series of notches on these sticks represented the value of the transaction. In recording a debt, wooden sticks were often split horizontally into two parts: the lender receiving one part, the </span><em style="background-color: white; line-height: 16px;">stock</em><span style="background-color: white; line-height: 16px;">; and the debtor, the other part, the </span><em style="background-color: white; line-height: 16px;">foil</em><span style="background-color: white; line-height: 16px;">. </span>This box<span style="background-color: white; line-height: 16px;"> contains sticks that date from the year 1296 and were found in the Chapel of the Pyx, Westminster Abbey in 1808. England abolished the use of tally sticks in 1826.The accumulation of tally sticks in the Office of the Exchequer were burned in 1834 resulting in a fire that destroyed the Parliament Building.</span> </span></div>
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<span style="font-family: Georgia, 'Times New Roman', serif;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3893" target="_blank">English tally sticks</a></span></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-9081039689658240462012-03-03T10:00:00.000-05:002012-03-05T11:24:46.373-05:00Korean Sangi rods<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-281pxEzd_z0/T1ToUw3FB4I/AAAAAAAAEJY/CjEMcqZF0_Y/s1600/Korean+Sangi+rods.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="170" src="http://3.bp.blogspot.com/-281pxEzd_z0/T1ToUw3FB4I/AAAAAAAAEJY/CjEMcqZF0_Y/s400/Korean+Sangi+rods.jpg" width="400" /></a></div>
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<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="background-color: white; line-height: 16px; text-align: -webkit-auto;">This </span>set of late 19th century <em>sangi</em><span style="background-color: white; line-height: 16px; text-align: -webkit-auto;">, wooden computing rods, originated in Korea. They are contained in their cloth carrying case. Sangi were also used in Japan up until about 1700. These computing rods or sticks, and their resulting numeration system, were originally derived from </span><em style="background-color: white; line-height: 16px; text-align: -webkit-auto;">suanzi</em><span style="background-color: white; line-height: 16px; text-align: -webkit-auto;">, rods used in China from ancient times through the Yuan Dynasty (1271-1368). The Chinese rods were replaced by the </span><em style="background-color: white; line-height: 16px; text-align: -webkit-auto;">suanpan</em><span style="background-color: white; line-height: 16px; text-align: -webkit-auto;">, or bead abacus, which was then adapted with variations throughout Asia.</span>
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<span style="font-family: Georgia, 'Times New Roman', serif;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3894" target="_blank">Korean Sangi rods</a></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-2609830987296101358.post-6688881009726429652012-02-25T15:00:00.000-05:002012-02-25T15:00:01.584-05:00Italian armillary sphere<span style="font-family: Verdana, sans-serif;"><br /></span><br />
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<a href="http://3.bp.blogspot.com/-7jYzQ1foF7c/T0fLjtjmybI/AAAAAAAAEF4/U1ZYj90W0TU/s1600/Italian-armillary-sphere.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-7jYzQ1foF7c/T0fLjtjmybI/AAAAAAAAEF4/U1ZYj90W0TU/s320/Italian-armillary-sphere.jpg" width="266" /></a></div>
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<span style="font-family: Georgia, 'Times New Roman', serif;"><span style="background-color: white; line-height: 16px;">An </span>armillary sphere<span style="background-color: white; line-height: 16px;"> is a mechanical model of the universe. The metal bands within the spheres represented the circular orbits of the planets revolving around a central Earth or the sun, depending on the particular scientific theory depicted; pre or post Copernican. When devised, they were among the most complex mechanical devices of their time. Renaissance personages frequently had themselves portrayed in paintings standing next to an armillary sphere indicating their association with wisdom and knowledge.</span></span>
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<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 16px;"><a href="http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591&bodyId=3902" target="_blank">Italian armillary sphere</a></span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0