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>
            <pb pagenum="149" xlink:href="015/01/168.jpg"/>
            <p type="head">
              <s id="id002629">SCHOLIVM</s>
            </p>
            <p type="main">
              <s id="id002630">Sunt & alij modi plures faciendi huiuſmodi, ſed
                <expan abbr="nõ">non</expan>
              ſunt ad eò ge
                <lb/>
              nerales, & nihilo minus ſunt magis confuſi, & non aliquid plus.</s>
            </p>
            <p type="main">
              <s id="id002631">Quarta regula,
                <expan abbr="cũ">cum</expan>
              uolueris
                <expan abbr="numerũ">numerum</expan>
              aliquem non quad. </s>
              <s id="id002632">qui bifa
                <lb/>
                <expan abbr="riã">riam</expan>
                <expan abbr="componat̃">componatur</expan>
              ex duob. </s>
              <s id="id002633">
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002634">uelut 10 ex 25, & 25 & 49 & 1,
                <lb/>
                <figure id="id.015.01.168.1.jpg" xlink:href="015/01/168/1.jpg" number="175"/>
                <lb/>
              &
                <expan abbr="ſumat̃">ſumatur</expan>
              a b numerus quad. </s>
              <s id="id002635">diuiſus in
                <expan abbr="ſupplemẽta">ſupplementa</expan>
              , ita quae c
                <lb/>
              d ſit portio minor eiuſmodi, ut adiecta illi
                <expan abbr="æq̃li">æquali</expan>
              c d gnomo
                <lb/>
              cir
                <expan abbr="cũſcriptus">cunſcriptus</expan>
              c k l
                <expan abbr="cũ">cum</expan>
                <expan abbr="fq̃drato">fquadrato</expan>
              , ſit
                <expan abbr="ęq̃lis">ęqualis</expan>
              a b
                <expan abbr="q̃drato">quadrato</expan>
              , detractis
                <lb/>
                <expan abbr="igit̃">igitur</expan>
              c e & e d,
                <expan abbr="æq̃libus">æqualibus</expan>
              erunt duo
                <expan abbr="ſupplemẽta">ſupplementa</expan>
              c k l
                <expan abbr="cũf">cunf</expan>
              qua­
                <lb/>
              drato ęqualia duob. </s>
              <s id="id002636">
                <expan abbr="ſupplemẽtis">ſupplementis</expan>
              a b
                <expan abbr="cũ">cum</expan>
                <expan abbr="q̃drato">quadrato</expan>
              h g. </s>
              <s id="id002637">Maio­
                <lb/>
              ra
                <expan abbr="aũt">aunt</expan>
                <expan abbr="ſupplemẽta">ſupplementa</expan>
                <expan abbr="excedũt">excedunt</expan>
              minora in duplo quad. </s>
              <s id="id002638">c d
                <expan abbr="igit̃">igitur</expan>
              detractis
                <lb/>
              minoribus ſupplementis
                <expan abbr="cõmunibus">communibus</expan>
              , erit
                <expan abbr="duplũ">duplum</expan>
              quad. </s>
              <s id="id002639">c d
                <expan abbr="cũ">cum</expan>
              f qua­
                <lb/>
              drato ęqualia h g
                <expan abbr="q̃drato">quadrato</expan>
              . </s>
              <s id="id002640">Ergo propoſito numero, putà 3 ducam in ſe
                <lb/>
              fit 9,
                <expan abbr="ducã">ducam</expan>
              2
                <expan abbr="minorẽ">minorem</expan>
              in ſe fit 4, duplicabo fit 8, detraho ex 9,
                <expan abbr="relinquit̃">relinquitur</expan>
                <lb/>
              1 numerus
                <expan abbr="q̃dratus">quadratus</expan>
              ,
                <expan abbr="igit̃">igitur</expan>
                <expan abbr="dicã">dicam</expan>
              q̊d 3
                <expan abbr="cũ">cum</expan>
              duplo 2, & erit
                <expan abbr="totũ">totum</expan>
              7, eſt unus
                <lb/>
              numerus, alter <02> 1. 1. 1, &
                <expan abbr="horũ">horum</expan>
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002641">
                <expan abbr="cõponunt">componunt</expan>
              50,
                <expan abbr="duplũ">duplum</expan>
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002642">5. Et ſimi
                <lb/>
              liter capio 6
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002643">36
                <expan abbr="duplũ">duplum</expan>
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002644">4. 32 differentia 4, numerus
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002645">2, ideo
                <lb/>
              6
                <expan abbr="cũ">cum</expan>
              duplo 4, & eſt 14, eſt unus numerus, alter 2,
                <expan abbr="quorũ">quorum</expan>
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002646">ſunt 200,
                <lb/>
                <expan abbr="dimidiũ">dimidium</expan>
              eſt 100
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002647">10
                <expan abbr="cõpoſiti">compoſiti</expan>
              ex 6 & 4. Et ita capio 9,
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002648">eius 81 du
                <lb/>
                <expan abbr="plũ">plum</expan>
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002649">6. 72 differentia 9 numerus
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002650">
                <expan abbr="igit̃">igitur</expan>
              cum duplo 6, & eſt 21, eſt
                <lb/>
              unus
                <expan abbr="illorũ">illorum</expan>
              , alter 3
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002651">450,
                <expan abbr="duplũ">duplum</expan>
              225
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002652">15, qui conſtat ex 9 & 6. Et
                <lb/>
              ita capio 11
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002653">cuius eſt 121,
                <expan abbr="duplũ">duplum</expan>
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002654">6 eſt 72 differentia, 72 & 21 eſt
                <lb/>
              49 numerus
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002655">7,
                <expan abbr="igit̃">igitur</expan>
              23 qui conſtat ex 11, & duplo 6 numeri mino
                <lb/>
              ris eſt unus numerus, alter eſt 7
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002656">
                <expan abbr="quorũ">quorum</expan>
              ſunt 578.
                <expan abbr="duplũ">duplum</expan>
              289,
                <expan abbr="q̃d">quad</expan>
              .
                <lb/>
              </s>
              <s id="id002657">17, qui conſtat ex 11 & 6. Quinta regula, per hoc inueniemus infini
                <lb/>
              tos numeros
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002658">
                <expan abbr="cõponentes">componentes</expan>
              32, nam
                <expan abbr="cũ">cum</expan>
              32 ſit duplus
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002659">
                <expan abbr="diuidã">diuidam</expan>
              per
                <lb/>
              unum
                <expan abbr="aggregatũ">aggregatum</expan>
              ex inuentis puta 578, & quia ambo ex ſuppoſito
                <lb/>
              ſunt dupli ad
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002660">qui proueniet erit
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002661">ſcilicet 16/289, duc in numeros
                <expan abbr="q̃­dratos">qua­
                  <lb/>
                dratos</expan>
              qui componunt 578, & ſunt 529 & 49, & fient 2 206/289 & 29 83/289,
                <lb/>
              & hi iuncti
                <expan abbr="fiũt">fiunt</expan>
              32, quia ſunt multiplicatæ partes numeri, per quem
                <lb/>
              eſt diuiſus numerus. </s>
              <s id="id002662">Et ita poteris diuidere 32 in infinitos alios
                <expan abbr="q̃d">quad</expan>
              .</s>
            </p>
            <p type="main">
              <s id="id002663">Sexta regula, ponamus modò quod uelim diuidere 10,
                <expan abbr="cõpoſitũ">compoſitum</expan>
              ex
                <lb/>
              duob. </s>
              <s id="id002664">
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002665">9 & 1, & non
                <expan abbr="duplũ">duplum</expan>
              numero
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002666">ita quod ſit diuiſus in alios
                <lb/>
              duos:
                <expan abbr="ducã">ducam</expan>
              10 in 25
                <expan abbr="cõpoſitũ">compoſitum</expan>
              ex duob. </s>
              <s id="id002667">
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002668">fit 250/25, at 250
                <expan abbr="cõponit̃">componitur</expan>
              aliter
                <lb/>
              ex duob. </s>
              <s id="id002669">quad. </s>
              <s id="id002670"><08> 225/25 & 25/25, ſcilicet 169/25 & 81/25, id eſt 6 19/25 & 3 6/25, qui ſunt
                <expan abbr="q̃d">quad</expan>
              .
                <lb/>
              </s>
              <s id="id002671">2 3/5 & 1 4/5, & ita uolo diuidere 13 in duo alia
                <expan abbr="q̃drata">quadrata</expan>
              <08> 9 & 4, duco 13 in
                <lb/>
              25 & fit 325/25, qui neceſſario
                <expan abbr="cõponit̃">componitur</expan>
              ex 225/25 & 100/25, ſed ego uolo q̊d
                <expan abbr="cõpo">compo</expan>
                <lb/>
                <expan abbr="nat̃">natur</expan>
              aliter, uelut ex 289/25 & 63/25, & ita ex 11 14/25 & 1 11/25, qui ſunt numeri
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002672">com
                <lb/>
              ponentes 13, & <02> ſunt 3 2/5 & 1 1/5, & in his opus eſt induſtria, ſcilicet ut
                <lb/>
                <expan abbr="multiplicet̃">multiplicetur</expan>
              per numeros
                <expan abbr="q̃d">quad</expan>
              . </s>
              <s id="id002673">ut proueniant numeri illi
                <expan abbr="bifariã">bifariam</expan>
              comp
                <lb/>
              ſiti ex
                <expan abbr="q̃dratis">quadratis</expan>
              . </s>
              <s id="id002674">Vt uerò uideamus
                <expan abbr="reſiduũ">reſiduum</expan>
              , proponamus quae uelim diui
                <lb/>
              dere 6 in duos numeros
                <expan abbr="q̃d">quad</expan>
              ,
                <expan abbr="primũ">primum</expan>
              ſcire debes q̊d non poſſunt eſſe </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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