Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

< >
[Figure 161]
Page: 256
[Figure 162]
Page: 256
[Figure 163]
Page: 262
[Figure 164]
Page: 270
[Figure 165]
Page: 276
[Figure 166]
Page: 278
< >
page |< < of 355 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.002820">
                <pb pagenum="166" xlink:href="009/01/166.jpg"/>
                <figure id="id.009.01.166.1.jpg" place="text" xlink:href="009/01/166/1.jpg" number="94"/>
                <lb/>
              decurſum motu proprio ſpatij B D, duplum
                <lb/>
              ſit: recta verò linea C H, curuæ reſpondeat
                <lb/>
              C G, quæ à remi palmula deſcripta eſt. </s>
              <s id="s.002821">Di­
                <lb/>
              co ipſas rectas lineas B D, & C H, æquales
                <lb/>
              eſſe. </s>
              <s id="s.002822">Nam in duobus triangulis B A E, &
                <lb/>
              C B Z, duæ rectæ lineæ A E, & C Z, æqua­
                <lb/>
              les ſunt. </s>
              <s id="s.002823">In parallelogrammo autem B H,
                <lb/>
              duæ B D, & H Z, æquales, atqui recta A E,
                <lb/>
              dupla eſt rectæ B D, per hypotheſim; dupla
                <lb/>
              eſt igitur, & C Z, rectæ H Z, quapropter
                <lb/>
              C H, & H Z, æquales erunt, Duæ igitur
                <lb/>
              C H, & B D, æquales per communem ſen­
                <lb/>
              tentiam.</s>
            </p>
            <p type="main">
              <s id="s.002824">Et quia nauigium tantum ſpatium de­
                <lb/>
              currit ſemper, quantum ſcalmus: ſi igitur
                <lb/>
              remi manubrium motu proprio duplum
                <lb/>
              confecerit ſpatium, quàm nauigium, tan­
                <lb/>
              tum prouehetur nauigium, quantum pal­
                <lb/>
              mula retroceſſerit, quod demonſtrandum
                <lb/>
              erat.</s>
            </p>
            <p type="head">
              <s id="s.002825">
                <emph type="italics"/>
              PROPOSITIO QVARTA.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="s.002826">Si nauigium minus ſpatium decurrat, quàm remi manu­
                <lb/>
              brium, ſed ſupra dimidium, magis prouehetur, quàm pal­
                <lb/>
              mula retrocedat; ſi verò citra dimidium, minus.</s>
            </p>
            <p type="main">
              <s id="s.002827">In deſcripta enim figura ponatur B D, minor quam A E, ſed eius dimi­
                <lb/>
              dio maior. </s>
              <s id="s.002828">Dico, quod ipſa B D, maior eſt quàm C H. </s>
              <s id="s.002829">Nam B D, &
                <lb/>
              H Z, æquales ſunt: Ad hæc A E, & C Z, æquales ſunt rectæ lineæ; ma­
                <lb/>
              ior igitur erit H Z, dimidio ipſius A E: quapropter reliqua C H, mi­
                <lb/>
              nor dimidio erit eiuſdem A E, & minor igitur erit C H, quàm B D. </s>
              <s id="s.002830">Spa­
                <lb/>
              tium autem B D, id eſt, quod nauigium conficit, ſpatium verò C H, remi
                <lb/>
              palmula in contrarium decurrit; idcircò prior pars Theorematis vera eſt.
                <lb/>
              </s>
              <s id="s.002831">Poſterior autem ſimiliter oſtendetur. </s>
              <s id="s.002832">ſi enim B D, minor eſt dimidio ipſius
                <lb/>
              A E: minor igitur erit, & H Z, dimidio eiuſdem A E; & quoniam A E, &
                <lb/>
              C Z, æquales ſunt: reliqua igitur C H, dimidio eiuſdem A E, maior erit: &
                <lb/>
              proinde minor erit B D, quàm C H. </s>
              <s id="s.002833">Nauigium igitur minus ſpatium de­
                <lb/>
              curret in anteriora, quam remi palmula in contrarium, quod demonſtran­
                <lb/>
              dum ſuſcepimus.</s>
            </p>
            <p type="head">
              <s id="s.002834">
                <emph type="italics"/>
              Corollarium.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.002835">Ex hac, & præcedenti infertur, quod ſi remi manubrium motu proprio
                <lb/>
              maius ſpatium decurrat, quàm nauigium, ſiue id ſit duplum, ſiue </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum