Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

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            <pb pagenum="165" xlink:href="009/01/165.jpg"/>
            <p type="head">
              <s id="s.002810">
                <emph type="italics"/>
              PROPOSITIO SECVNDA.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="s.002811">Si remi manubrium motu proprio, & nauigium, æqualia
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              ſpatia pertranſierint, fieri non poterit, vt palmula mo­
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              ueatur: ſed veluti centrum immota manebit.</s>
            </p>
            <p type="main">
              <s id="s.002812">Esto iterum remus A C, manubrium A, ſcalmus B: tantum autem ſpa­
                <lb/>
              tium conficiat nauigium; quantum motu proprio A. Dico, quod C,
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              remi palmula immota manebit. </s>
              <s id="s.002813">Nam ſi a loco ſuo dimota fuerit:
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              ſpatium igitur permeet C D, ad poſteriora: quo quidem decurſo,
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              remus A C, poſitionem rectitudinis habeat F D, ſcalmus
                <expan abbr="itaq;">itaque</expan>
              B, tranſlatus
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              erit in G. </s>
              <s id="s.002814">Excitetur autem à puncto B, in
                <expan abbr="vtramq;">vtramque</expan>
              partem linea E B R, ad
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                <figure id="id.009.01.165.1.jpg" place="text" xlink:href="009/01/165/1.jpg" number="93"/>
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              rectos angulos ſuper B G, & à
                <expan abbr="pũcto">puncto</expan>
              A, recta A H,
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              ſuper D F: itemque à puncto E, recta C E, ſuper
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              E R; ipſarum verò rectarum linearum E R, &
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              A H, ſectio ſit in K, ſed C F., & D F, ſit in Z, & quo­
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              niam A K, id ſpatium eſt, quod motu proprio re­
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              mi manubrium permeauit, curuilineo enim re­
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              ſpondeat A R, recta autem B G, id ſpatium eſt,
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              quod nauigium confecit: ipſæ igitur rectæ lineæ
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              H K, & B G, æquales erunt. </s>
              <s id="s.002815">Atqui in duobus æqui­
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              angulis triangulis E B C, & B A K, vel per 26.
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              propoſitionem primi Euclidis, vel 4. 6. æquales
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              eſſe concludes A K, & E C, rectas lineas: quapro­
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              pter æqualis erit E C, rectæ B G, per communem
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              ſententiam: eidem autem B G, æqualis eſt E Z,
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              in parallelogrammo, per 34. propoſitionem ip­
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              ſius primi libri: æqualis igitur erit recta E Z, re­
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              ctæ E C, pars toti, quod eſt impoſſibile. </s>
              <s id="s.002816">Et pro­
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              pterea immota manebit palmula C, quod erat à
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              nobis oſtendendum.</s>
            </p>
            <p type="head">
              <s id="s.002817">
                <emph type="italics"/>
              PROPOSITIO TERTIA.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="s.002818">Si remi manubrium motu proprio duplum confecerit ſpa­
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              tium, quàm nauigium, tantum prouehetur ea remiga­
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              tione nauigium, quantum palmula retroceſſerit.</s>
            </p>
            <p type="main">
              <s id="s.002819">Remus enim incipiente motu poſitionem habeat A C, deſinente
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              verò rectitudinis ſitum F G. ſcalmus igitur B, propter nauigij
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              motum, ſpatium conficiet B D. </s>
              <s id="s.002820">Excitetur à puncto B, in
                <expan abbr="vtramq;">vtramque</expan>
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              partem perpendicularis E Z, in quam veniant a punctis A, & C,
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              ad rectos angulos rectæ lineæ A E, & C Z: ſpatium autem A E, à manubrio </s>
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