Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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        <div xml:id="echoid-div1" type="front" level="1" n="1">
          <div xml:id="echoid-div5" type="preface" level="2" n="1">
            <pb n="13" file="0013" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0013"/>
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        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div7" type="chapter" level="2" n="1">
            <head xml:id="echoid-head15" xml:space="preserve">IO. BAPTISTAE
              <lb/>
            BENEDICTI
              <lb/>
            PATRITII VENETI
              <lb/>
            SERENISS. CAR. EM.
              <lb/>
            ALLOBROGVM DVCIS
              <lb/>
            PHILOSOPHI.</head>
            <head xml:id="echoid-head16" style="it" xml:space="preserve">Theoremata Arithmetica.</head>
            <p>
              <s xml:id="echoid-s37" xml:space="preserve">
                <emph style="sc">PRaeclare</emph>
              multa veteres mathematici philoſophi de nu­
                <lb/>
              meris eorumq́ue effectibus excogitata poſteris tradide-
                <lb/>
              runt, quorum cum vix vllam rationem reddiderint, aut
                <lb/>
              certè per exiguam, occaſione diuerſorum problematum
                <lb/>
              mihi à Sereniſſimo Sabaudiæ Duce propoſitorum præbi-
                <lb/>
              ta, de ijs quæ ab antiquis propoſita fuerunt contemplanda
                <lb/>
              nonnulla occurrerunt, quæ poſteritati comendare non
                <lb/>
              inutile arbitratus fum, ne hæ meæ cogitationes intercide-
                <lb/>
              rent, & occaſionem præberem quamplurimis abſtruſa hęc
                <lb/>
              indagandi, quæ problematibus & thæorematibus inuoluta, vix aliquem qui euol-
                <lb/>
              ueret nacta funt.</s>
            </p>
            <p>
              <s xml:id="echoid-s38" xml:space="preserve">Inter cætera vero à me queſita, hoc fuit theorema.</s>
            </p>
            <div xml:id="echoid-div7" type="math:theorem" level="3" n="1">
              <head xml:id="echoid-head17" xml:space="preserve">THEOREMA PRIMVM.</head>
              <p>
                <s xml:id="echoid-s39" xml:space="preserve">
                  <emph style="sc">INterrogavit</emph>
                me Sereniſſimus Dux Sabaudiæ, qua ratione cognoſci poſ-
                  <lb/>
                ſet ſcientificè & ſpeculatiue (vt dicitur) productum ex duobus fractis numeris,
                  <lb/>
                quolibet producentium minus eſſe. </s>
                <s xml:id="echoid-s40" xml:space="preserve">Cui reſpondi, mente & cogitatione conci-
                  <lb/>
                piendum eſſe fractos producentes cum fractis productis, non vnius eiuſdemq́ue na-
                  <lb/>
                turæ eſſe, imò longè diuerfæ.</s>
              </p>
              <p>
                <s xml:id="echoid-s41" xml:space="preserve">Exempli gratia, fractis numeris propofitis
                  <var>.a.i.</var>
                et
                  <var>.a.c.</var>
                quorum integri ſint
                  <var>.a.
                    <lb/>
                  b.</var>
                et
                  <var>.a.d.</var>
                qui tanquam lineæ cogitentur, apertum fanè eſſet productum
                  <var>.c.i.</var>
                fu-
                  <lb/>
                perficiale futurum, quod nomen caperet à producto ſuperficiali
                  <var>.d.b.</var>
                generato ex
                  <lb/>
                vno in aliud totorum linearium, nam ſi conſtitueretur
                  <var>.a.i.</var>
                octauum ipſius
                  <var>.a.b.</var>
                et
                  <var>.a.
                    <lb/>
                  c.</var>
                dimidium
                  <var>.a.d.</var>
                multiplicato
                  <var>.a.i.</var>
                cum
                  <var>.a.c.</var>
                produceretur fextumdecimum ipſius
                  <var>.
                    <lb/>
                  d.b</var>
                . </s>
                <s xml:id="echoid-s42" xml:space="preserve">Quare
                  <var>.d.b.</var>
                eſſet totum
                  <reg norm="relatiuum" type="context">relatiuũ</reg>
                ipſius
                  <var>.c.i.</var>
                non aliquod totum producentium.
                  <lb/>
                </s>
                <s xml:id="echoid-s43" xml:space="preserve">Mirum itaque non eſt ſi productum
                  <var>.c.i.</var>
                minus videatur fuis producentibus, cum
                  <lb/>
                toto, diuerſæ naturæ à primis conferatur, fractum fiquidem ab integro eiuſdem
                  <lb/>
                naturæ, linearis, ſuperficialis, aut corporeæ denominatur.</s>
              </p>
              <p>
                <s xml:id="echoid-s44" xml:space="preserve">Quòd ſi amplioris cognitionis gratia ex ſcientiæ præceptis ſpeculari voluerit a@ </s>
              </p>
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