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="id001355">
                <pb pagenum="72" xlink:href="015/01/091.jpg"/>
              culei auxilio pluribus locis uela diſpoſita melius dirigunt iter, ut
                <lb/>
              quaſi craſſa minerua depictum, & poteſtate deformatum, ad amuſ­
                <lb/>
              ſim contrahant. </s>
              <s id="id001356">Motus ergo magnitudo non ſimpliciter conſtat,
                <lb/>
              ſed comparatione ſuperficiei ueli ad uelum longitudine quidem, </s>
            </p>
            <p type="main">
              <s id="id001357">
                <arrow.to.target n="marg285"/>
                <lb/>
              ac latitudine conflata per multiplicationem. </s>
              <s id="id001358">Altitudinis quo que ut
                <lb/>
                <arrow.to.target n="marg286"/>
                <lb/>
              infrà exponetur. </s>
              <s id="id001359">Ex quorum omnium ductu, quaſi cubica, uel tri­
                <lb/>
              plicata ratione, ut ſuperius oſtenſum eſt, ratio uelocitatis motus na
                <lb/>
              uium conflatur.</s>
            </p>
            <p type="margin">
              <s id="id001360">
                <margin.target id="marg285"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              86.</s>
            </p>
            <p type="margin">
              <s id="id001361">
                <margin.target id="marg286"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              42.</s>
            </p>
            <p type="main">
              <s id="id001362">Propoſitio octuageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id001363">Proportionem receſſus à recta uia ad obliquitatem inueſtigare.
                <lb/>
                <arrow.to.target n="marg287"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001364">
                <margin.target id="marg287"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001365">Sit nauis in a itura in b (uentus rectus ad c, medius ad e) per
                <expan abbr="ob­liquũ">ob­
                  <lb/>
                liquum</expan>
              , cum ergo tardius moueatur per a e quàm a c & per a b, quam
                <lb/>
              per a d, & ſint ad perpendiculum b e, b d quas conſtat eſſe breuiſsi­
                <lb/>
              mas earum, quæ ad a c & ad a d. </s>
              <s id="id001366">Queritur igitur quando uelocius
                <lb/>
                <figure id="id.015.01.091.1.jpg" xlink:href="015/01/091/1.jpg" number="85"/>
                <lb/>
              ferretur ad b, an cum per a c, c b, an cum per a d, d b,
                <lb/>
              an cum per a b ſimpliciter. </s>
              <s id="id001367">Et conſtat quod a d & d b
                <lb/>
              longiores ſunt a b, iſtud enim demonſtratum eſt ab
                <lb/>
              Euclide in primo Elementorum, dico modo a c, & </s>
            </p>
            <p type="main">
              <s id="id001368">
                <arrow.to.target n="marg288"/>
                <lb/>
              c b eſſe longiores a d & d b, nam quadrata a d & d b
                <lb/>
              & a c & c b ſunt æqualia quadrato a b per dicta ibi­
                <lb/>
                <arrow.to.target n="marg289"/>
                <lb/>
              dem, & ideo quadrata a c & c b ęqualia quadratis a d
                <lb/>
              & d b, ſed a d eſt longior a c, quia ducta c d angulus
                <lb/>
              d c a eſt obtuſus, igitur ad maiorem a c per decimam
                <lb/>
              nonam primi Elementorum: quare per communem
                <lb/>
              animi ſententiam quadratum a d maius eſt quadrato a c, quare rur­
                <lb/>
              ſus per communem animi ſententiam quadratum c b maius eſt
                <lb/>
              quadrato d b. </s>
              <s id="id001369">Cum ergo quadrata a d & d b æqualia ſint quadra­
                <lb/>
              tis a c & c b, & a d ſit maior a c & c b maior d b, ſequitur per nonam
                <lb/>
              ſecundi Elementorum, quod a c & c d ſint maiores a d & d b pari­
                <lb/>
              ter acceptis. </s>
              <s id="id001370">Si ergo maior fuerit exceſſus quàm proportio motus
                <lb/>
              per temonem cohibiti, ut ſupra uiſum eſt, tardius mouebitur per
                <lb/>
              a d, d b quàm a b per a c, c b quàm per a d, d b, ſed ſi contrà maior ſit
                <lb/>
              proportio motus cohibiti à temone ad motum liberum quàm ex­
                <lb/>
                <arrow.to.target n="marg290"/>
                <lb/>
              ceſſus ad exceſſum uelocius mouebitur per a d d b, quàm per a b,
                <lb/>
              & per a c quàm per a b. </s>
              <s id="id001371">Accedit huc e incommodo longioris uiæ,
                <lb/>
              quod uento a c non poterit ferri nauis ex c d in b, quoniam antea
                <lb/>
              ægre ferebatur: & nunc ægrius per c b quàm a b, plus enim diſtat
                <lb/>
              uentus a c ab itinere c a quàm à uento a b, ut uiſum eſt ſuperius, igi­
                <lb/>
              tur multo melius eſt (ni quid obſtet) ire per a b quàm per
                <expan abbr="ullã">ullam</expan>
              aliam
                <lb/>
                <arrow.to.target n="marg291"/>
                <lb/>
              uiam: niſi ſtationes ſint in c d, uel periculum immineat in a b. </s>
              <s id="id001372">Vbi ta
                <lb/>
              men uenti ſecundarent, tantum eſt uirium in recto curſu, & æquali </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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