Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002619">
                <pb pagenum="148" xlink:href="015/01/167.jpg"/>
              hic additus ad 14 conſtituit 14 25/36 quadratum 3 5/6. Et ita 14 eſt diffe­
                <lb/>
              rentia duorum quadratorum, ſcilicet 25/36 & 14 25/36.
                <lb/>
                <arrow.to.target n="marg518"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002620">
                <margin.target id="marg518"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id002621">Ex hoc habebis duo quadrata in datis terminis quæ different
                <lb/>
              dato numero, & eſt pulchrum. </s>
              <s id="id002622">Velut uolo duo quadrata quæ dif­
                <lb/>
              ferant in 2, & <02> minoris ſit inter 1 & 2, tunc capies per regulam i­
                <lb/>
              pſam 2, & auferes
                <expan abbr="numerũ">numerum</expan>
              quadratum ita quòd reſiduum diuiſum
                <lb/>
              per duplum radicis efficiat
                <expan abbr="numerũ">numerum</expan>
              inter 1 & 2. Veluti capio 4/9 qua­
                <lb/>
              dratum, aufero ex 2, relinquitur 1 5/9 diuido per duplum 2/13 radicis 4/9 &
                <lb/>
              eſt 1 1/3 & exit 1 1/6, & hic eſt minor numerus cuius quadratum eſt 1 13/36
                <lb/>
              cui ſi addantur 2, fient 3 13/36 numerus quadratus 1 5/6.</s>
            </p>
            <p type="main">
              <s id="id002623">
                <arrow.to.target n="marg519"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002624">
                <margin.target id="marg519"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              _{m}. 3.</s>
            </p>
            <p type="main">
              <s id="id002625">Cum autem uolueris duo quadrata quæ differant in 100, tunc
                <lb/>
              per regulam datam ſi auferes 1, peruenires ad numeros magnos &
                <lb/>
              fractos, & ideo melius eſt quia numerus eſt par, ut detrahas nume­
                <lb/>
              rum parem quadratum, ita quod reſiduum poſsit diuidi per
                <expan abbr="duplũ">duplum</expan>
                <lb/>
              radicis, ut in hoc non detraho neque quia remanet impar, nec 16 quia
                <lb/>
              84
                <expan abbr="reſiduũ">reſiduum</expan>
              non
                <expan abbr="põt">pont</expan>
              diuidi per 8 ita ut exeat integer numerus, ergo
                <lb/>
                <expan abbr="detrahã">detraham</expan>
              4 &
                <expan abbr="relinquet̃">relinquetur</expan>
              96, diuido per
                <expan abbr="duplũ">duplum</expan>
              radicis quod eſt 4 exit
                <lb/>
              24, cuius quadratum qua eſt 576 addito 100 facit 676
                <expan abbr="quadratũ">quadratum</expan>
              26.
                <lb/>
              Et ita ex 433 non auferam ſed 9, quia relinquetur 24 qui poteſt diui­
                <lb/>
              di per ſe, duplum <02> 9 & exit 4 cuius
                <expan abbr="quadratũ">quadratum</expan>
              eſt 16, addito 33 fit 49.</s>
            </p>
            <p type="main">
              <s id="id002626">Secunda regula, cum uolueris propoſito uno numero quadra­
                <lb/>
              to illum diuidere infinitis modis in duos numeros quadratos, cape
                <lb/>
              quemuis numerum quadratum per primum exemplum regulę pri
                <lb/>
              mæ, & cum eo diuide numerum propoſitum, & qui proueniet erit
                <lb/>
              quadratus,
                <expan abbr="hũc">hunc</expan>
              ergo duces in partes numeri quadrati quę ſunt nu­
                <lb/>
              meri
                <expan abbr="q̃drati">quadrati</expan>
              , & fient duo quadrati numeri, & illi
                <expan abbr="componẽt">component</expan>
                <expan abbr="numerũ">numerum</expan>
                <lb/>
                <expan abbr="quadratũ">quadratum</expan>
                <expan abbr="priorẽ">priorem</expan>
              quem diuiſiſti. </s>
              <s id="id002627">quia multiplicatio fit per
                <expan abbr="eoſdẽ">eoſdem</expan>
              nu­
                <lb/>
              meros qui ſunt partes diuiſoris. </s>
              <s id="id002628">Velut uolo facere de 4 duas partes
                <lb/>
              quę ſint
                <expan abbr="q̃drati">quadrati</expan>
              numeri, capio
                <expan abbr="numerũ">numerum</expan>
                <expan abbr="q̃dratũ">quadratum</expan>
              qui
                <expan abbr="cõponat̃">componatur</expan>
              ex duo­
                <lb/>
              bus
                <expan abbr="q̃dratis">quadratis</expan>
              , uelut 25, diuido 4 per 25 exit 4/25
                <expan abbr="hũc">hunc</expan>
              duco per 9 & 16
                <expan abbr="q̃dra­tos">quadra­
                  <lb/>
                tos</expan>
              numeros
                <expan abbr="cõponentes">componentes</expan>
              25
                <expan abbr="fiũt">fiunt</expan>
              1 11/25 & 2 14/25
                <expan abbr="q̃drati">quadrati</expan>
              1 2/5 & 1 3/5 Et hi
                <expan abbr="q̃drati">quadrati</expan>
                <lb/>
                <expan abbr="cõponunt">componunt</expan>
              4. Et ita poſſes diuidere infinitis modis, puta per 17 13/36 &
                <lb/>
              per 169. Tertia regula cum unus numerus additus
                <lb/>
                <figure id="id.015.01.167.1.jpg" xlink:href="015/01/167/1.jpg" number="174"/>
                <lb/>
              primo & detractis à
                <expan abbr="ſecũdo">ſecundo</expan>
              facit ambo quadrata,
                <expan abbr="idẽ">idem</expan>
                <lb/>
              numerus coniunctus cum differentia illorum nume­
                <lb/>
              rorum & detractus à primo & additus ſecundo facit
                <lb/>
              eoſdem numeros quadratos, ueluti capio 10 primum
                <lb/>
              3 ſecundum 6 additus ad 10 & detractus à 7 efficit 6
                <lb/>
              & 1 quadratos dico quod iunctus 16 cum 3 differen­
                <lb/>
              tia 10 & 7 fit 9, qui detractus à 10 & additus ad 7 effi­
                <lb/>
              cit 1 & 16 numeros quadratos priores.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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