Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="063/01/070.jpg"/>
                <emph type="italics"/>
              ab
                <emph.end type="italics"/>
              linea hypomochlij, &
                <emph type="italics"/>
              fg
                <emph.end type="italics"/>
              ad eam perpendicularis:
                <expan abbr="eritq;">eritque</expan>
              ex
                <lb/>
              iam demonſtratis
                <emph type="italics"/>
              fg
                <emph.end type="italics"/>
              grauitas mouens, &
                <emph type="italics"/>
              ag
                <emph.end type="italics"/>
              plaga eiuſdem
                <lb/>
              centri. </s>
              <s>Et quia plaga eſt in lineâ
                <emph type="italics"/>
              af;
                <emph.end type="italics"/>
              erit motus reflexus in
                <lb/>
              eadem lineâ
                <emph type="italics"/>
              af.
                <emph.end type="italics"/>
              quòd ſi ergo fiat ut
                <emph type="italics"/>
              ag
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              gf,
                <emph.end type="italics"/>
              ita
                <emph type="italics"/>
              ah
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              ak,
                <emph.end type="italics"/>
              erit
                <lb/>
              motus medius in
                <emph type="italics"/>
              ai,
                <emph.end type="italics"/>
              & angulus reflexûs
                <emph type="italics"/>
              iak:
                <emph.end type="italics"/>
              quem dico æqua­
                <lb/>
              lem angulo incidentiæ
                <emph type="italics"/>
              oab.
                <emph.end type="italics"/>
              Quia enim angulus
                <emph type="italics"/>
              oab
                <emph.end type="italics"/>
              eſt æ­
                <lb/>
              qualis angulo
                <emph type="italics"/>
              afg,
                <emph.end type="italics"/>
              propterea quòd
                <expan abbr="uterq;">uterque</expan>
              ſit complementum
                <lb/>
              anguli
                <emph type="italics"/>
              fag:
                <emph.end type="italics"/>
              angulo autem
                <emph type="italics"/>
              gfa
                <emph.end type="italics"/>
              æquatur angulus
                <emph type="italics"/>
              iak,
                <emph.end type="italics"/>
              quòd ſi­
                <lb/>
              milia ſint triangula
                <emph type="italics"/>
              agf. iak:
                <emph.end type="italics"/>
              erit
                <expan abbr="quoq;">quoque</expan>
              angulo
                <emph type="italics"/>
              oab
                <emph.end type="italics"/>
              idem
                <lb/>
              angulus
                <emph type="italics"/>
              iak
                <emph.end type="italics"/>
              æqualis. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA XIII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              Motus Pentagoni ſecans obliquè planum, ſi latus, quod tangit pla­
                <lb/>
              num eidem ſit parallelum, ad angulos inæquales reſle­
                <lb/>
              ctit.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Motus Pentagoni
                <emph type="italics"/>
              abcde
                <emph.end type="italics"/>
              incidat obliquè plano
                <emph type="italics"/>
              ſt
                <emph.end type="italics"/>
              habens la­
                <lb/>
              tus
                <emph type="italics"/>
              ae,
                <emph.end type="italics"/>
              quod tangit planum, eidem parallelum: dico hunc mo­
                <lb/>
              tum reflecti ad angulos inæquales. </s>
              <s>Excitetur linea hypomo­
                <lb/>
              chlij
                <emph type="italics"/>
              en,
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              fg
                <emph.end type="italics"/>
              ad eam perpendicularis:
                <expan abbr="eritq;">eritque</expan>
              grauitas tota
                <expan abbr="qua-dratũ">qua­
                  <lb/>
                dratum</expan>
                <emph type="italics"/>
              fh;
                <emph.end type="italics"/>
              grauitas autem mo vens quadratum
                <emph type="italics"/>
              fg.
                <emph.end type="italics"/>
              dividatur bi­
                <lb/>
              fariam linea
                <emph type="italics"/>
              hf
                <emph.end type="italics"/>
              in
                <emph type="italics"/>
              p;
                <emph.end type="italics"/>
                <expan abbr="eoq;">eoque</expan>
              centro circulus deſcribatur
                <emph type="italics"/>
              hif.
                <emph.end type="italics"/>
                <lb/>
              Quòd ſi ergo ſumatur chorda
                <emph type="italics"/>
              fi
                <emph.end type="italics"/>
              æqualis
                <emph type="italics"/>
              fg;
                <emph.end type="italics"/>
              erit chorda re­
                <lb/>
              liqua
                <emph type="italics"/>
              hi;
                <emph.end type="italics"/>
                <expan abbr="atq;">atque</expan>
              huius quadratum dabit plagam. </s>
              <s>Et quia plaga
                <lb/>
              fit per lineas
                <emph type="italics"/>
              fa. fh. fe:
                <emph.end type="italics"/>
              erit per 5 theor: huius motus reflexus
                <lb/>
              in lineâ
                <emph type="italics"/>
              fc,
                <emph.end type="italics"/>
              & motus centri in lineâ
                <emph type="italics"/>
              fm
                <emph.end type="italics"/>
              eidem plano parallelâ. </s>
              <lb/>
              <s>Si ergo fiat ut
                <emph type="italics"/>
              fi
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              ih,
                <emph.end type="italics"/>
              ita
                <emph type="italics"/>
              fm
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              fl;
                <emph.end type="italics"/>
              erit motus medius
                <emph type="italics"/>
              fk,
                <emph.end type="italics"/>
              &
                <lb/>
              angulus reflexionis
                <emph type="italics"/>
              kfm;
                <emph.end type="italics"/>
              quem dico inæqualem angulo in­
                <lb/>
              cidentiæ
                <emph type="italics"/>
              hen.
                <emph.end type="italics"/>
              Quia enim angulus
                <emph type="italics"/>
              ahi
                <emph.end type="italics"/>
              externus eſt maior </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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