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="id003731">
                <pb pagenum="221" xlink:href="015/01/240.jpg"/>
              conſtat. </s>
              <s id="id003732">Demonſtrandum eſt ergo a b & g q maiores eſſe
                <foreign lang="grc">αζ</foreign>
              &
                <foreign lang="grc">ζβ</foreign>
              ,
                <lb/>
              nam
                <foreign lang="grc">αγ</foreign>
              &
                <foreign lang="grc">γζ</foreign>
              ſunt æquales &
                <foreign lang="grc">ζδ</foreign>
              &
                <foreign lang="grc">δβ</foreign>
              ex ſuppoſito, quare
                <foreign lang="grc">αζ</foreign>
              &
                <foreign lang="grc">ζβ</foreign>
                <lb/>
              æquales ſunt poteſtate quadrato,
                <foreign lang="grc">αβ</foreign>
              igitur ambæ iunctæ lineæ me­
                <lb/>
                <arrow.to.target n="marg700"/>
                <lb/>
              diæ inter duplum
                <foreign lang="grc">αβ</foreign>
              & ipſam
                <foreign lang="grc">αβ</foreign>
              , quadratum enim
                <foreign lang="grc">αζ</foreign>
              &
                <foreign lang="grc">ζβ</foreign>
              coniun­
                <lb/>
              ctarum eſt duplum quadratis uniuſcuiusque earum pariter acceptis,
                <lb/>
                <arrow.to.target n="marg701"/>
                <lb/>
              uelut & quadratum mediæ inter duplum
                <foreign lang="grc">αβ</foreign>
              & ipſam
                <foreign lang="grc">αβ</foreign>
              , at quadra­
                <lb/>
              tum coniunctæ ex a b & a c eſt æquale duplo quadrati a b cum qua
                <lb/>
                <arrow.to.target n="marg702"/>
                <lb/>
              drato a c, igitur ſuperat duplum quadrati
                <foreign lang="grc">α β</foreign>
              in quadrato a c, ſed
                <lb/>
                <arrow.to.target n="marg703"/>
                <lb/>
              quod poteſt in duplum quadrati
                <foreign lang="grc">αβ</foreign>
              eſt aggregatum
                <foreign lang="grc">αζ</foreign>
              &
                <foreign lang="grc">ζβ</foreign>
              , igitur
                <lb/>
              a b & a d ſunt longiores iunctæ
                <foreign lang="grc">αζ</foreign>
              &
                <foreign lang="grc">ζβ</foreign>
              quia poſſunt eo plus quan­
                <lb/>
                <arrow.to.target n="marg704"/>
                <lb/>
              tum eſt quadratum a c.</s>
            </p>
            <p type="margin">
              <s id="id003733">
                <margin.target id="marg698"/>
              Q
                <emph type="italics"/>
              uæſt.
                <emph.end type="italics"/>
              25.</s>
            </p>
            <p type="margin">
              <s id="id003734">
                <margin.target id="marg699"/>
              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="id003735">
                <margin.target id="marg700"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              47.
                <emph type="italics"/>
              pri­
                <lb/>
              mi &
                <emph.end type="italics"/>
              4.
                <emph type="italics"/>
              ſe­
                <lb/>
              cundi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003736">
                <margin.target id="marg701"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003737">
                <margin.target id="marg702"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              4.
                <emph type="italics"/>
              ſecun
                <lb/>
              di
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003738">
                <margin.target id="marg703"/>
              P
                <emph type="italics"/>
              er eandem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003739">
                <margin.target id="marg704"/>
              P
                <emph type="italics"/>
              er eandem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003740">Propoſitio centeſima nonageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id003741">Si duo circuli ſuper eodem centro eodem motu transferuntur,
                <lb/>
              æquale ſpatium ſuperant.</s>
            </p>
            <p type="main">
              <s id="id003742">Sint duo circuli a b, c d ſuper eodem centro e qui transferantur
                <lb/>
                <figure id="id.015.01.240.1.jpg" xlink:href="015/01/240/1.jpg" number="235"/>
                <lb/>
                <arrow.to.target n="marg705"/>
                <lb/>
              ſuper axe per
                <expan abbr="ſpatiũ">ſpatium</expan>
              c g dum reſoluitur c d,
                <lb/>
              tum ergo a erit in f, quia c d contingit pla­
                <lb/>
              num c g, igitur e c eſt ad
                <expan abbr="perpẽdiculum">perpendiculum</expan>
              c g,
                <lb/>
                <arrow.to.target n="marg706"/>
                <lb/>
              ergo punctum a eſt in f & a f æqualis c g,
                <lb/>
                <arrow.to.target n="marg707"/>
                <lb/>
              igitur a b circulus ſolum reuolutus eſt ſe­
                <lb/>
              mel, & tantum perambulauit ſpatij quan­
                <lb/>
              tum e d & æquali uelo citate, cùm tamen ſeorſum ſit proportio ſpa­
                <lb/>
              tij ad
                <expan abbr="ſpatiũ">ſpatium</expan>
              ut circuli ad circulum. </s>
              <s id="id003743">Hæc eſt ſubtiliſsima
                <expan abbr="quæſtionũ">quæſtionum</expan>
                <lb/>
                <arrow.to.target n="marg708"/>
                <lb/>
                <expan abbr="propoſitarũ">propoſitarum</expan>
              ab Ariſtotele in mechanicis, quam ſic quidam ſoluunt.
                <lb/>
              </s>
              <s id="id003744">Supponunt duo:
                <expan abbr="primũ">primum</expan>
              ſi quid ab aliquo mouetur nihil conferens
                <lb/>
                <figure id="id.015.01.240.2.jpg" xlink:href="015/01/240/2.jpg" number="236"/>
                <lb/>
              ad illum motum,
                <lb/>
              ex ſe ipſo per tan
                <lb/>
              tum mouebitur
                <lb/>
                <expan abbr="ſpatiũ">ſpatium</expan>
              , per quan­
                <lb/>
              tum ab illo mo­
                <lb/>
              tore mouebitur:
                <lb/>
              Secundum,
                <expan abbr="eadẽ">eadem</expan>
                <lb/>
              potentia in
                <expan abbr="eodẽ">eodem</expan>
                <lb/>
              tempore diuerſo
                <lb/>
              modo duo mobi
                <lb/>
              lia mouebit ęqua
                <lb/>
              lia, cum
                <expan abbr="unũ">unum</expan>
              mo­
                <lb/>
              tui aſſentietur aliud
                <expan abbr="nõ">non</expan>
              . </s>
              <s id="id003745">quod ſi hæc mobilia ſeiuncta fuiſſent, quod
                <lb/>
              aptitudinem haberet
                <expan abbr="ſeiunctũ">ſeiunctum</expan>
              uelocius moueretur, quàm dum con
                <lb/>
              iunctum eſt. </s>
              <s id="id003746">Cum ergo inquiunt circulus c d moueatur ab a b cir­
                <lb/>
              culo, nec conferat quic<08> ad motum, ideo tantum tranſibit ſpatium </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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