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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page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id004042">
                <pb pagenum="237" xlink:href="015/01/256.jpg"/>
                <expan abbr="ctũ">ctum</expan>
              tamen b, quod
                <expan abbr="mouet̃">mouetur</expan>
              duobus motibus, non pertranſit niſi b c,
                <lb/>
              quæ poteſt eſſe minor b a: nam
                <expan abbr="cõſtat">conſtat</expan>
              quod
                <expan abbr="quãdo">quando</expan>
              m erit in a, o erit
                <lb/>
              in e, & quia m deſcendit in o, in eodem tempore, ergo o erit in c, &
                <lb/>
                <expan abbr="trãſiuit">tranſiuit</expan>
              ſemper per rectam b c: igitur m eſt minus
                <expan abbr="motũ">motum</expan>
              duobus mo
                <lb/>
              tibus quàm m l unico
                <expan abbr="tantũ">tantum</expan>
              . </s>
              <s id="id004043">Et quia aliquis dicere potuiſſet non eſt
                <lb/>
              mirum, quod m ſit minus motum duobus motibus quàm l m latus
                <lb/>
              unico tantum: quia m mouetur motu contrario motui lateris: nam
                <lb/>
              latus m o mouetur in latere b a aſcendendo, et punctum m uerſus o
                <lb/>
              in ipſo m o deſcendendo. </s>
              <s id="id004044">Dicit Philoſophus, hoc eſt mirum, quia
                <lb/>
              cum idem contingat in motu l, cuius latus mouetur per a c, & l per l
                <lb/>
              m recedendo in partem contrariam, nihilominus uelocius motum
                <lb/>
              eſt l, quàm latus l m, quia a d eſt longior a c. </s>
              <s id="id004045">Ex quo patet, quae quęſtio
                <lb/>
              Philoſophi eſt una tantum, & non duæ. </s>
              <s id="id004046">Et eſt cur motum duobus
                <lb/>
              motibus in rhombo, in uno mouetur uelocius latere tantum moto
                <lb/>
              uno motu, in alio tardius? </s>
              <s id="id004047">Et quia aliquis dicere poſſet, q̊d b c poſ­
                <lb/>
              ſet eſſe
                <expan abbr="lõgior">longior</expan>
              a c: Dicit Philoſophus, uerum eſt, ſed ego poſſum in­
                <lb/>
              uenire talem rhombum, qui etiam habeat a c longiorem, & tunc ni­
                <lb/>
              hilominus
                <expan abbr="ſequit̃">ſequitur</expan>
              quod dico. </s>
              <s id="id004048">Aliud
                <expan abbr="aũt">aunt</expan>
              , quod docet ex hac demon­
                <lb/>
              ſtratione, eſt quae ex duobus motibus rectis diuerſis poteſt fieri unus
                <lb/>
              motus rectus diuerſus: igitur idem punctum, puta formica poterit
                <lb/>
              ſimul, & ſemel moueri duobus motibus rectis diuerſis. </s>
              <s id="id004049">Et hoc eſt,
                <lb/>
              quia primus motus eſt rectus ſolum ſecundum formam, & non ſe­
                <lb/>
              cundum materiam: & alter ſecundus, ſcilicet miſtus eſt ſecundum
                <lb/>
              materiam & non ſecundum formam per rectam.</s>
            </p>
            <p type="margin">
              <s id="id004050">
                <margin.target id="marg790"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              24.
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004051">Ex hoc
                <expan abbr="ſequit̃">ſequitur</expan>
              aliud magis
                <expan abbr="mirũ">mirum</expan>
              , et eſt iuxta
                <expan abbr="noſtrũ">noſtrum</expan>
              motum rhom
                <lb/>
              bi l o in rhombo a d, fixo centro p in centro k, &
                <expan abbr="moueat̃">moueatur</expan>
              quomodo
                <lb/>
              libet, l, dico quod l f ſemper æqualis erit a f, quia
                <expan abbr="em̃">emm</expan>
              k l & k a ſunt æ­
                <lb/>
                <figure id="id.015.01.256.1.jpg" xlink:href="015/01/256/1.jpg" number="255"/>
                <lb/>
              quales,
                <expan abbr="cũ">cum</expan>
              eſſent una linea ante motum ducta, l a erit
                <lb/>
              angulus k l a, æqualis angulo k a l, ſed angulus k a c
                <lb/>
                <arrow.to.target n="marg791"/>
                <lb/>
              eſt æqualis angulo k l m, cum angulus k l m eſſet
                <expan abbr="idẽ">idem</expan>
                <lb/>
              angulo k a b, & angulus k a b eſt
                <expan abbr="æq̃lis">æqualis</expan>
              angulo k a c,
                <lb/>
                <arrow.to.target n="marg792"/>
                <lb/>
              igitur angulus k l m eſt æqualis angulo k a c,
                <expan abbr="igit̃">igitur</expan>
              reſi
                <lb/>
              duus fl a eſt æqualis reſiduo f a l, quare f a æqualis
                <lb/>
                <arrow.to.target n="marg793"/>
                <lb/>
              fl. </s>
              <s id="id004052">Si igitur quantum procedit latus m l in a c,
                <expan abbr="tãtum">tantum</expan>
                <lb/>
              deſcendat punctum in linea l m punctum perpetuo, erit in linea a c,
                <lb/>
              & per eam mouebitur. </s>
              <s id="id004053">Vnde ſequitur quod</s>
            </p>
            <p type="margin">
              <s id="id004054">
                <margin.target id="marg791"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              5.
                <emph type="italics"/>
              pri­
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004055">
                <margin.target id="marg792"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              34.
                <emph type="italics"/>
              pri­
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004056">
                <margin.target id="marg793"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              6.
                <emph type="italics"/>
              primi
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004057">Quod
                <expan abbr="punctũ">punctum</expan>
              l
                <expan abbr="mouebit̃">mouebitur</expan>
              duobus </s>
              <s id="id004058">motibus. </s>
              <s id="id004059">uno recto in linea, ſcilicet
                <lb/>
                <arrow.to.target n="marg794"/>
                <lb/>
              l m, & altero circulari. </s>
              <s id="id004060">ſ. </s>
              <s id="id004061">circa
                <expan abbr="centrũ">centrum</expan>
              k, &
                <expan abbr="tñ">tnm</expan>
                <expan abbr="mouebit̃">mouebitur</expan>
              uerè motu re­
                <lb/>
              cto
                <expan abbr="tm̃">tmm</expan>
              in alia linea, ſcilicet a c, & hoc eſt
                <expan abbr="primũ">primum</expan>
              admirabile. </s>
              <s id="id004062">Aliud eſt</s>
            </p>
            <p type="margin">
              <s id="id004063">
                <margin.target id="marg794"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id004064">Quod
                <expan abbr="punctũ">punctum</expan>
              l
                <expan abbr="mouebit̃">mouebitur</expan>
              duobus motibus, & per ipſos
                <expan abbr="mouebit̃">mouebitur</expan>
                <lb/>
                <arrow.to.target n="marg795"/>
                <lb/>
              ad
                <expan abbr="unguẽ">unguem</expan>
              uno motu ęquali uni
                <expan abbr="eorũ">eorum</expan>
              , ita q̊d alius motus nihil addet </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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