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w:rsidRPr="00316841"><w:rPr><w:b/><w:sz w:val="24"/></w:rPr><w:t>Placa BM 13901</w:t></w:r><w:bookmarkEnd w:id="1"/></w:p><w:p w:rsidR="00000000" w:rsidRPr="00316841" w:rsidRDefault="00AE64BB"><w:pPr><w:spacing w:before="120" w:line="360" w:lineRule="auto"/><w:ind w:right="-568" w:firstLine="0"/><w:jc w:val="both"/><w:rPr><w:b/><w:sz w:val="24"/></w:rPr></w:pPr><w:r><w:rPr><w:b/><w:noProof/><w:sz w:val="24"/><w:lang w:eastAsia="pt-PT"/></w:rPr><w:drawing><wp:anchor distT="0" distB="0" distL="114300" distR="114300" simplePos="0" relativeHeight="251659776" behindDoc="1" locked="0" layoutInCell="1" allowOverlap="1"><wp:simplePos x="0" y="0"/><wp:positionH relativeFrom="margin"><wp:posOffset>-165735</wp:posOffset></wp:positionH><wp:positionV relativeFrom="margin"><wp:posOffset>2948305</wp:posOffset></wp:positionV><wp:extent cx="1421130" cy="2333625"/><wp:effectExtent l="19050" t="0" r="7620" b="0"/><wp:wrapSquare wrapText="bothSides"/><wp:docPr id="22" name="Imagem 1" descr="http://uploads.siteduzero.com/files/408001_409000/408170.png"/><wp:cNvGraphicFramePr><a:graphicFrameLocks noChangeAspect="1" xmlns:a="http://schemas.openxmlformats.org/drawingml/2006/main"/></wp:cNvGraphicFramePr><a:graphic xmlns:a="http://schemas.openxmlformats.org/drawingml/2006/main"><a:graphicData uri="http://schemas.openxmlformats.org/drawingml/2006/picture"><pic:pic xmlns:pic="http://schemas.openxmlformats.org/drawingml/2006/picture"><pic:nvPicPr><pic:cNvPr id="0" name="Imagem 1" descr="http://uploads.siteduzero.com/files/408001_409000/408170.png"/><pic:cNvPicPr><a:picLocks noChangeAspect="1" noChangeArrowheads="1"/></pic:cNvPicPr></pic:nvPicPr><pic:blipFill><a:blip r:embed="rId14" cstate="print"/><a:srcRect/><a:stretch><a:fillRect/></a:stretch></pic:blipFill><pic:spPr bwMode="auto"><a:xfrm><a:off x="0" y="0"/><a:ext cx="1421130" cy="2333625"/></a:xfrm><a:prstGeom prst="rect"><a:avLst/></a:prstGeom><a:noFill/></pic:spPr></pic:pic></a:graphicData></a:graphic></wp:anchor></w:drawing></w:r></w:p><w:p w:rsidR="00AE64BB" w:rsidRDefault="00AE64BB"><w:pPr><w:spacing w:before="120" w:line="360" w:lineRule="auto"/><w:ind w:right="-568" w:firstLine="425"/><w:jc w:val="both"/><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr></w:p><w:p w:rsidR="00000000" w:rsidRPr="00316841" w:rsidRDefault="0095609D"><w:pPr><w:spacing w:before="120" w:line="360" w:lineRule="auto"/><w:ind w:right="-568" w:firstLine="425"/><w:jc w:val="both"/><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t>Através do estudo destas placas, podemos dizer que os babilónicos eram apaix</w:t></w:r><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">onados pela matemática, a placa </w:t></w:r><w:hyperlink r:id="rId15" w:history="1"><w:r w:rsidRPr="00316841"><w:rPr><w:rStyle w:val="Hiperligao"/><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/><w:color w:val="auto"/></w:rPr><w:t>BM 13901</w:t></w:r></w:hyperlink><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve"> é um exemplo desse fascínio. </w:t></w:r></w:p><w:p w:rsidR="00000000" w:rsidRPr="00316841" w:rsidRDefault="0095609D"><w:pPr><w:spacing w:before="120" w:line="360" w:lineRule="auto"/><w:ind w:right="-568" w:firstLine="425"/><w:jc w:val="both"/><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">Nesta placa, existe um problema, cujo método aplicado pelo escriba é idêntico ao nosso </w:t></w:r><w:r 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Math"/></w:rPr><m:t>bx</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>=</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:oMath><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t>;</w:t></w:r></w:p><w:p w:rsidR="00000000" w:rsidRPr="00316841" w:rsidRDefault="0095609D"><w:pPr><w:pStyle w:val="PargrafodaLista"/><w:numPr><w:ilvl w:val="0"/><w:numId w:val="2"/></w:numPr><w:spacing w:before="120"/><w:ind w:left="0" w:right="-568" w:firstLine="0"/><w:contextualSpacing/><w:jc w:val="both"/><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">De seguida, multiplica-se por </w:t></w:r><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/><w:i/></w:rPr><w:t>a</w:t></w:r><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve"> em ambos os membros: </w:t></w:r><m:oMath><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>a</m:t></m:r></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>x</m:t></m:r></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>abx</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>=</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>ac</m:t></m:r></m:oMath><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t>;</w:t></w:r></w:p><w:p w:rsidR="00000000" w:rsidRPr="00316841" w:rsidRDefault="0095609D"><w:pPr><w:pStyle w:val="PargrafodaLista"/><w:numPr><w:ilvl w:val="0"/><w:numId w:val="2"/></w:numPr><w:spacing w:before="120"/><w:ind w:left="0" w:right="-568" w:firstLine="0"/><w:contextualSpacing/><w:jc w:val="both"/><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">Adiciona-se </w:t></w:r><m:oMath><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:d><m:dPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:dPr><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:d></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup></m:oMath><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve"> </w:t></w:r><w:proofErr w:type="gramStart"/><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t>em</w:t></w:r><w:proofErr w:type="gramEnd"/><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve"> ambos os membros de forma a obter o produto notável no 1º memb</w:t></w:r><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">ro: </w:t></w:r><m:oMath><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:d><m:dPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:dPr><m:e><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>ax</m:t></m:r></m:e></m:d></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>abx</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:d><m:dPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:dPr><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:d></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t xml:space="preserve"> </m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>=</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>ac</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:d><m:dPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:dPr><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:d></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>⇔</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:d><m:dPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:dPr><m:e><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>ax</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:d></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>=</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>ac</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:d><m:dPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:dPr><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:d></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup></m:oMath><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t>;</w:t></w:r></w:p><w:p w:rsidR="00000000" w:rsidRPr="00316841" w:rsidRDefault="0095609D"><w:pPr><w:pStyle w:val="PargrafodaLista"/><w:numPr><w:ilvl w:val="0"/><w:numId w:val="2"/></w:numPr><w:spacing w:before="120" w:line="360" w:lineRule="auto"/><w:ind w:left="0" w:right="-568" w:firstLine="0"/><w:contextualSpacing/><w:jc w:val="both"/><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">Resolve-se a equação: </w:t></w:r><m:oMath><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>ax</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>=</m:t></m:r><m:rad><m:radPr><m:degHide m:val="on"/><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:radPr><m:deg/><m:e><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>ac</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:d><m:dPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:dPr><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:d></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup></m:e></m:rad><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>⇔</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>x</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" 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w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:d></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup></m:e></m:rad><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>-</m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>b</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:eastAsiaTheme="minorEastAsia" w:hAnsi="Cambria Math"/></w:rPr><m:t>a</m:t></m:r></m:den></m:f><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" 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w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">O processo descrito em cima descreve os passos dados pelo escriba, contudo não foi o único, </w:t></w:r><w:hyperlink r:id="rId17" w:history="1"><w:r w:rsidRPr="00316841"><w:rPr><w:rStyle w:val="Hiperligao"/><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/><w:color w:val="auto"/></w:rPr><w:t>Diofanto de Alexandria</w:t></w:r></w:hyperlink><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve"> também o utilizou. O escriba resolve uma equação semelhante, </w:t></w:r><m:oMath><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>x</m:t></m:r></m:e><m:sup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>+</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>bx</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>=</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:hAnsi="Cambria Math"/></w:rPr><m:t>a</m:t></m:r></m:oMath><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t>,</w:t></w:r><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve"> </w:t></w:r><w:proofErr w:type="gramStart"/><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t>por</w:t></w:r><w:proofErr w:type="gramEnd"/><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve"> processos geométricos usando a regra do “corta e cola”, como mostra na figura seguinte:</w:t></w:r></w:p><w:p w:rsidR="00000000" w:rsidRPr="00316841" w:rsidRDefault="0095609D"><w:pPr><w:spacing w:before="120" w:line="360" w:lineRule="auto"/><w:ind w:right="-568" w:firstLine="1134"/><w:jc w:val="both"/><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr><w:r w:rsidRPr="00316841"><w:pict><v:shape id="_x0000_s1026" type="#_x0000_t202" style="position:absolute;left:0;text-align:left;margin-left:18.05pt;margin-top:0;width:371.25pt;height:11.75pt;z-index:251654656" stroked="f"><v:textbox style="mso-next-textbox:#_x0000_s1026" inset="0,0,0,0"><w:txbxContent><w:p w:rsidR="00000000" w:rsidRDefault="0095609D"><w:pPr><w:pStyle w:val="Legenda"/><w:ind w:firstLine="0"/><w:jc w:val="center"/><w:rPr><w:noProof/></w:rPr></w:pPr><w:r><w:t>Resolução</w:t></w:r><w:r><w:t xml:space="preserve"> geométrica do escriba</w:t></w:r></w:p></w:txbxContent></v:textbox><w10:wrap type="topAndBottom"/></v:shape></w:pict></w:r></w:p><w:p w:rsidR="00000000" w:rsidRPr="00316841" w:rsidRDefault="0095609D"><w:pPr><w:spacing w:before="120" w:line="360" w:lineRule="auto"/><w:ind w:right="-568" w:firstLine="708"/><w:jc w:val="both"/><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:eastAsiaTheme="minorEastAsia" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">O passo algébrico nº 3 corresponde à situação em que é acrescentado o quadrado azul-escuro ao </w:t></w:r><w:hyperlink r:id="rId18" w:history="1"><w:r w:rsidRPr="00316841"><w:rPr><w:rStyle w:val="Hiperligao"/><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/><w:color w:val="auto"/></w:rPr><w:t>gnómon</w:t></w:r></w:hyperlink><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve"> da parte 2 da figura. Através deste problema podemos afirmar que os escri</w:t></w:r><w:r w:rsidRPr="00316841"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">bas limitavam-se a “completar quadrados”. 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