Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.002794">
                <pb pagenum="164" xlink:href="009/01/164.jpg"/>
              quidem minus etiam oſtendemus eſſe ipſo D A. </s>
              <s id="s.002795">Nam quoniam duo latera
                <lb/>
              B D, & D K, trianguli B D K, duobus lateribus B D, & D E,
                <expan abbr="triãguli">trianguli</expan>
              B E D,
                <lb/>
              æqualia ſunt, ſed minor eſt angulus B D K, angulo B D E: minor igitur erit
                <lb/>
              baſis B K, baſe B E, per 24. primi, quod demonſtrandum erat</s>
            </p>
            <p type="main">
              <s id="s.002796">Præterea, quod Ariſt. ratiocinando ſumit tantum ſpatium conficere na­
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              uigium, quantum remi manubrium, ambiguum eſt. </s>
              <s id="s.002797">Nam remi manubrium
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              duabus fertur motionibus: vna propria,
                <expan abbr="circulariq́">circularique</expan>
              ; ſuper ſcalmo: altera
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              verò, qua vnà fertur cum ipſo nauigio. </s>
              <s id="s.002798">ſpatium igitur, quod omninò decur­
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              ſum eſt à remi manubrio, eo quod à nauigio confectum eſt, maius erit. </s>
              <s id="s.002799">At
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              ſi paria ſpatia decurſa eſſe intelligat à remi manubrio motu proprio, & à
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              nauigio,
                <expan abbr="neq;">neque</expan>
              hoc difficultate caret. </s>
              <s id="s.002800">Nam nauigium interdum maius ſpa­
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              tium percurret, interdum minus, iuxta remigum vires, & prout mari remi
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              palmula immerſa fuerit: remi verò manubrium tametſi ab exiguis viribus
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              moueatur haud minorem tamen ambitum deſcribet, quàm ſi à multo ma­
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              iore virtute moueretur. </s>
              <s id="s.002801">Quapropter, vt huiuſmodi Ariſt. ſententiam exa­
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              minaremus, Theoremata, quæ ſequuntur, demonſtrauimus.</s>
            </p>
            <p type="head">
              <s id="s.002802">
                <emph type="italics"/>
              PROPOSITIO PRIMA.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="s.002803">Si Remiges nauigium mouere poſſunt, maius ſemper ſpa­
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              tium remi manubrium percurrit, quàm nauigium.</s>
            </p>
            <p type="main">
              <s id="s.002804">Sit enim remus A C, manubrium A, ſcalmus B, qui propter nauigij
                <lb/>
              motum ſpatium percurrat à B, in D, in quo loco ipſe remus A C, ſi­
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                <figure id="id.009.01.164.1.jpg" place="text" xlink:href="009/01/164/1.jpg" number="92"/>
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              tum rectitudinis habeat E F. </s>
              <s id="s.002805">Spatium
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              itaque, quod A, conficit, curua linea
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              ſit A E, cui recta linea reſpondeat A Z, in re­
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              ctam E F, perpendicularis. </s>
              <s id="s.002806">Nauigium verò
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              idem ſpatium conficiet, quod ſcalmus B: aio
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              igitur ipſam A Z, rectam lineam, recta B D,
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              maiorem eſſe. </s>
              <s id="s.002807">ſecet enim recta A C, rectam
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              E F, in G: æquiangula ſunt igitur bina trian­
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              gula A G Z, & B G D, quapropter ſicut A G,
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              ad B G, ſie A Z, ad B D, per. </s>
              <s id="s.002808">4. 6. libri Eucli­
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              dis: maior eſt autem A G, ipſa B G, & maior
                <lb/>
              igitur erit A Z, quam B D. & proinde maius
                <lb/>
              ſpatium remi manubrium percurrit, quam
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              nauigium, quod demonſtrandum erat.</s>
            </p>
            <p type="main">
              <s id="s.002809">Quod ſi à puncto B, rectam lineam vtrinque
                <lb/>
              ducamus H K, ad remi menſuram, rectos facientem angulos cum B D,
                <expan abbr="re-ctamq́">re­
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                ctamque</expan>
              ; A Z, ſecantem in I, manifeſtè intelligemus ipſam rectam A Z, con­
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              ſtare ex A I, & I Z, quarum prior reſpondet curuæ A H, quæ motu proprio
                <lb/>
              manubrij deſcripta eſt; poſterior verò æqualis eſt rectæ B D, quæ motu na­
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              uigij decurſa eſt.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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