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="id002054">
                <pb pagenum="114" xlink:href="015/01/133.jpg"/>
              ea tradenda ſunt, quæ oppreſsis ſint auxilio: ea ſunt, quę ſubtilibus
                <lb/>
                <expan abbr="conſtãt">conſtant</expan>
              rationibus, et multiplicata
                <expan abbr="amittũt">amittunt</expan>
              uim ut quaſi
                <expan abbr="pręſtẽt">pręſtent</expan>
              pau
                <lb/>
              ca multis, & exigua magnis. </s>
              <s id="id002055">In cęteris obſcurare ita decet cuncta,
                <expan abbr="q̃">quae</expan>
                <lb/>
              obeſſe poſſunt, aut quouis modo puerti ad malos uſus
                <expan abbr="queãt">queant</expan>
              , ut di­
                <lb/>
              cta
                <expan abbr="nõ">non</expan>
              dicta eſſe
                <expan abbr="putẽt">putent</expan>
              , hoc eſt
                <expan abbr="officiũ">officium</expan>
                <expan abbr="nõ">non</expan>
              ſolum probi, ſed
                <expan abbr="etiã">etiam</expan>
              pruden
                <lb/>
              tis uiri.</s>
            </p>
            <p type="margin">
              <s id="id002056">
                <margin.target id="marg409"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="main">
              <s id="id002057">Propoſitio centeſima decima octaua.</s>
            </p>
            <p type="main">
              <s id="id002058">Quanta proportione decedat ictus in obliquum parietem ab eo,
                <lb/>
              qui eſt ad perpendiculum declarare.</s>
            </p>
            <figure id="id.015.01.133.1.jpg" xlink:href="015/01/133/1.jpg" number="124"/>
            <p type="main">
              <s id="id002059">Sit paries b d e, ex a
                <expan abbr="ferat̃">feratur</expan>
              in dictus, qui ſi
                <lb/>
                <arrow.to.target n="marg410"/>
                <lb/>
              eſſet in c d
                <expan abbr="parietẽ">parietem</expan>
              eſſe ad perpendiculum, &
                <lb/>
              ualidiſsimus, ſin uero in f g abraderet, &
                <expan abbr="nõ">non</expan>
                <lb/>
                <expan abbr="cõquaſſaret">conquaſſaret</expan>
              . </s>
              <s id="id002060">Quæritur ergo ex b d e muro
                <lb/>
              qualis excipietur? </s>
              <s id="id002061">erit ergo proportio anguli c d a ad
                <expan abbr="angulũ">angulum</expan>
              b d a,
                <lb/>
              ueluti ictus a d in d c ad
                <expan abbr="ictũ">ictum</expan>
              in b d,
                <expan abbr="manifeſtũ">manifeſtum</expan>
              eſt
                <expan abbr="aũt">aut</expan>
              ſequi proportio­
                <lb/>
              nem,
                <expan abbr="quoniã">quoniam</expan>
              maxima uarietate
                <expan abbr="cõſtat">conſtat</expan>
              dum ex angulo b d a acuto fit
                <lb/>
              acutior,
                <expan abbr="quoniã">quoniam</expan>
              ſi b d c ſit
                <expan abbr="q̃druplus">quadruplus</expan>
              b d a erit reſiduus ad
                <expan abbr="dimidiũ">dimidium</expan>
              b
                <lb/>
              d a nonuplus ipſi dimidio, & ad
                <expan abbr="quartã">quartam</expan>
                <expan abbr="partẽ">partem</expan>
              habebit proportionem
                <lb/>
                <expan abbr="decemnouẽ">decem nouem</expan>
              ad
                <expan abbr="unũ">unum</expan>
              . </s>
              <s id="id002062">Si ergo
                <expan abbr="etiã">etiam</expan>
              in
                <expan abbr="idẽ">idem</expan>
              tenderent,
                <expan abbr="nõ">non</expan>
              efficerent mille
                <lb/>
              ictus q̊d tres, cuius demonſtratio hęc eſt. </s>
              <s id="id002063">Supponamus
                <expan abbr="proportionẽ">proportionem</expan>
                <lb/>
              b d c ad
                <expan abbr="q̃rtam">quartam</expan>
                <expan abbr="partẽ">partem</expan>
              a d b ad dito reſiduo ad b d c eſſe
                <expan abbr="ſolũ">ſolum</expan>
                <expan abbr="decuplã">decuplam</expan>
              :
                <lb/>
                <expan abbr="tũc">tunc</expan>
              ex duob. </s>
              <s id="id002064">ictibus centupla erit in d c ad
                <expan abbr="eã">eam</expan>
              , quę in b e,
                <expan abbr="etiã">etiam</expan>
              tribus
                <lb/>
              millecupla: nam
                <expan abbr="cõquaſſata">conquaſſata</expan>
              turri in primo ictu, id d decuplo magis
                <lb/>
              ad perpendiculum <08> in b d e
                <expan abbr="ſumat̃">ſumatur</expan>
              decima pars in ambitu d, & illa
                <lb/>
              erit ergo
                <expan abbr="tã">tam</expan>
              diſſoluta, & infirma ex ſuppoſito, <08> eſt tota b e: ſed ex ſe
                <lb/>
              cundo ictu decuplo magis
                <expan abbr="cõquaſſabit̃">conquaſſabitur</expan>
              illa pars, <08> b e ergo tota d c
                <lb/>
              centuplo magis
                <expan abbr="quaſſabit̃">quaſſabitur</expan>
              ex duob. </s>
              <s id="id002065">ictibus c d turris, <08> b e, & ita in
                <lb/>
              tribus: ex
                <expan abbr="decẽ">decem</expan>
              millibus ergo ictibus
                <expan abbr="etiã">etiam</expan>
              ad amuſsim directis,
                <expan abbr="cũ">cum</expan>
              ta
                <lb/>
                <expan abbr="mẽid">men id</expan>
              uix fieri poſsit in
                <expan abbr="tãta">tanta</expan>
              multitudine
                <expan abbr="nõ">non</expan>
              plus
                <expan abbr="cõminuet̃">comminuetur</expan>
              b d e, <08>
                <lb/>
              ex decë c d
                <expan abbr="p̃ter">pnter</expan>
                <expan abbr="quã">quam</expan>
                <expan abbr="exiguũ">exiguum</expan>
                <expan abbr="quippiã">quippiam</expan>
              in ſuperficie. </s>
              <s id="id002066">Imo ut
                <expan abbr="declaratũ">declaratum</expan>
                <lb/>
              eſt multo minus repetita ratione multiplicis. </s>
              <s id="id002067">Ob id in arce
                <expan abbr="Medio­lanẽſi">Medio­
                  <lb/>
                lanenſi</expan>
              exterius lapidibus uiuis in
                <expan abbr="rotundũ">rotundum</expan>
              diducta ſuperficie inter­
                <lb/>
                <figure id="id.015.01.133.2.jpg" xlink:href="015/01/133/2.jpg" number="125"/>
                <lb/>
              uallo que
                <expan abbr="q̃">quae</expan>
              drato hunc in
                <expan abbr="modũ">modum</expan>
              munitę ſunt altiores tur
                <lb/>
              res. </s>
              <s id="id002068">Fiat ergo murus cuius proportio a d c ad b d a ſit ſex
                <lb/>
              quitertia, erit que angulus b d c
                <expan abbr="dodrãs">dodrans</expan>
              recti, &
                <expan abbr="parũ">parum</expan>
              incli
                <lb/>
              natis,
                <expan abbr="ſiquidẽ">ſiquidem</expan>
              b d c erit quarta pars recti, & ſit tantę ma­
                <lb/>
              gnitudinis, at que duritiei, ac adeò benè coniunctus fer­
                <lb/>
                <arrow.to.target n="table16"/>
                <lb/>
              reis cathenis, ac ſtolonibus, ut poſsit reſiſtere
                <expan abbr="machinarũ">machinarum</expan>
                <expan abbr="fe­rentiũ">fe­
                  <lb/>
                rentium</expan>
                <expan abbr="ſphęrã">ſphęram</expan>
                <expan abbr="librarũ">librarum</expan>
              ducentarum (quæ ſanè maximæ ſunt)
                <lb/>
                <figure id="id.015.01.133.3.jpg" xlink:href="015/01/133/3.jpg" number="126"/>
              quinquaginta:
                <expan abbr="tũc">tunc</expan>
              cum proportio ſexquitertia nouies repeti­
                <lb/>
              ta, ut in numeris uides, efficiat quinquies replicatis nouem
                <lb/>
              ictibus, fiet proportio decupla quinquies producta, quę eſt cen
                <lb/>
                <expan abbr="tũ">tum</expan>
              millium ad
                <expan abbr="unũ">unum</expan>
              in quadraginta quin que ictibus. </s>
              <s id="id002069">
                <expan abbr="Antequã">Antequam</expan>
                <lb/>
              ergo peruenit ad quinquaginta ictus rectos neceſſe erit, ut </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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