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>
            <pb pagenum="229" xlink:href="015/01/248.jpg"/>
            <p type="main">
              <s id="id003888">Dixi quod in hipomochlio parua uarietas fit in motu: igitur à
                <lb/>
                <arrow.to.target n="marg749"/>
                <lb/>
              leui cauſa magnum nauigium impellitur aut uariatur. </s>
              <s id="id003889">Cum enim a
                <lb/>
                <expan abbr="trãsfertur">transfertur</expan>
              ad b, fit minima uarietas in e, igitur a parua poterit tranſ­
                <lb/>
                <figure id="id.015.01.248.1.jpg" xlink:href="015/01/248/1.jpg" number="241"/>
                <lb/>
              ferri, tum uero quod debuit
                <expan abbr="trãsferri">transferri</expan>
              ad c, transfertur ad
                <lb/>
              d, nam motus ipſe ab alia cauſa fit, uelut
                <expan abbr="uẽto">uento</expan>
              aut remis,
                <lb/>
              ita non eſt difficultas niſi propter motum aquæ, ſcilicet
                <lb/>
              ut tabula ſcindat illam. </s>
              <s id="id003890">Ad hoc autem contulit illud
                <lb/>
              quod intra nauim prominet ut uectis rationem habeat,
                <lb/>
              & ob id facilius uerti.</s>
            </p>
            <p type="margin">
              <s id="id003891">
                <margin.target id="marg749"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003892">Similiter uarietas in puppi exigua eſt cauſa magnæ
                <lb/>
              uarietatis in prora, quod autem poteſt fieri paucioribus
                <lb/>
              & faciliori modo id debet fieri, hac igitur cauſa in pup­
                <lb/>
              pi temonem conſtituere oportet ſeu guberna culum.</s>
            </p>
            <p type="main">
              <s id="id003893">Cum autem impellatur à mari, neceſſe eſt, ut à latere excipiat
                <lb/>
              aquam ita ut tantum pendeat in unam partem, quantum nauis in
                <lb/>
              aduerſam, nam ſi nauis non penderet, gubernaculum rectè dirige­
                <lb/>
                <figure id="id.015.01.248.2.jpg" xlink:href="015/01/248/2.jpg" number="242"/>
                <lb/>
              retur. </s>
              <s id="id003894">Vt ergo ex duobus obliquis
                <expan abbr="unũ">unum</expan>
              rectum conſtitui
                <lb/>
              tur, ita ex naui & gubernaculo, nam ſint a b & c b & im­
                <lb/>
              pellatur ad d, impelletur per mediam lineam b e & non
                <lb/>
              per a b neque c b, igitur oportet temonem pendere ex ad
                <lb/>
              uerſo inclinationis nauis. </s>
              <s id="id003895">Eſt etiam alia ratio, quoniam
                <lb/>
              nauis ſecurior redditur, nam quemadmodum quod in
                <lb/>
              medio eſt, facilius impellitur tranſuerſim, quàm quod pendet in
                <lb/>
              contrarium, ita & in gubernaculo. </s>
              <s id="id003896">Eſt & id ob neceſsitatem, quoni­
                <lb/>
              am motus aquæ plerumque eſt in partem, uelut & uentus ad la­
                <lb/>
              tus eius ſitus, ſecundum quem moueri debet nauis. </s>
              <s id="id003897">Sicut igitur &
                <lb/>
              uela & malus inclinantur, ut motum directum efficiant, quia aliò
                <lb/>
              dirigitur nauis quam qui mouet uentus, ita de temone compara­
                <lb/>
              tione aquæ.</s>
            </p>
            <p type="main">
              <s id="id003898">Propoſitio ducenteſima prima.</s>
            </p>
            <p type="main">
              <s id="id003899">Si duæ lineæ non ſecantes circuli peripheriam in
                <expan abbr="unũ">unum</expan>
                <expan abbr="punctũ">punctum</expan>
              , ex
                <lb/>
              ea coëant, exterius neceſſe eſt illas peripheria
                <expan abbr="cõtenta">contenta</expan>
              eſſe maiores.</s>
            </p>
            <p type="head">
              <s id="id003900">LEMMA PRIMVM.</s>
            </p>
            <p type="main">
              <s id="id003901">Si fuerit proportio primi ad ſecundum maior quàm tertij ad
                <lb/>
              quartum, erit primi ad tertium maior quàm ſecundi ad quartum.
                <lb/>
                <arrow.to.target n="marg750"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003902">
                <margin.target id="marg750"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003903">Quamuis hoc demonſtretur à Campano, quia </s>
            </p>
            <p type="main">
              <s id="id003904">
                <arrow.to.target n="marg751"/>
                <lb/>
              tamen facile eſt hic adijcietur. </s>
              <s id="id003905">Sit igitur maior a
                <lb/>
              ad b quam c ad d, dico maiorem eſſe a ad c quam
                <lb/>
                <figure id="id.015.01.248.3.jpg" xlink:href="015/01/248/3.jpg" number="243"/>
                <lb/>
                <arrow.to.target n="marg752"/>
                <lb/>
              b ad d, quia enim maior eſt a ad b quam c ad d fiat e ad b ut c ad e
                <lb/>
                <arrow.to.target n="marg753"/>
                <lb/>
              eritque e minuſ quam a, e igitur ad c ut b ad d ſed maior a ad c quam
                <lb/>
              e ad e igitur maior a ad c quam b ad d.
                <lb/>
                <arrow.to.target n="marg754"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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