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

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              <s>
                <pb xlink:href="063/01/024.jpg"/>
              grad. 45. ſemiſſis nimirum anguli AOF: Si ad huius logarit­
                <lb/>
              mum addatur logaritmus lateris BF, erit aggregatum logarit­
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              mus lateris FG, ſeu BF partium 7653668. </s>
              <s>Quot nimirum
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              partium erat quoq, chorda AB, hoc eſt illi æqualis BF. </s>
              <s>Quòd
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              ſi
                <expan abbr="itaq;">itaque</expan>
              ducatur ex G termino motûs linea perpendicularis ad
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              BF, ſecabit eandem in puncto F: ac proinde motus ex B in G
                <lb/>
              eſt æqualis duratione motui ex B in F per prim. </s>
              <s>Theorema
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              huius.
                <expan abbr="additóq;">additóque</expan>
              motu communi ex A in B, lapſus per duas chor­
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              das AB. BF æquatur lapſui per chordam AF: qui per prop. 15.
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              erat æqualis duratione lapſui per chordam LF ſeu AG. </s>
            </p>
            <figure id="id.063.01.024.1.jpg" xlink:href="063/01/024/1.jpg" number="6"/>
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              <s>
                <emph type="center"/>
                <emph type="italics"/>
              ALITER.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Ducatur ex F perpendicularis ad BF: dico hanc productam
                <lb/>
              ſecare BG. in G. quod ſi non; ſecet ſi fieri poteſt, in alio pun.
                <lb/>
              cto VG: X vel Z. </s>
              <s>Et quia angulus externus NOL eſt grad:
                <lb/>
              45. erit angulus OLF internus grad: 22. prim: 30. & angu­
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              lus OLA grad. 67. prim: 30: propterea quod LOA ex hy­
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              potheſi ſit grad: 45:
                <expan abbr="Ablatoq;">Ablatoque</expan>
              OLF ex OLA, reſiduus FLA,
                <lb/>
              hoc eſt illi æqualis FGB grad: 45, ob parallelas nimirum &
                <lb/>
              æquales FLGA. </s>
              <s>Cùm
                <expan abbr="itaq;">itaque</expan>
              in triangulo FBG rectus ſit an­
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              gulus ZFB, & angulus FBG per lemma huius grad. 45: erit
                <lb/>
                <expan abbr="quoq;">quoque</expan>
              angulus FZB grad 45, ac proinde æqualis angulo FG
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              B, externus interno: quod eſt abſurdum. </s>
              <s>
                <expan abbr="Atq;">Atque</expan>
              ea­
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              dem ratione probabitur linea AG non ſecari à perpendiculari
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              XF. </s>
              <s>Aſſumatur rurſum arcus AC grad 67; & CF grad 23. pro­
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              ducatur autem AC in P ſumptâ AP æquali chordæ perallelæ F
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              M. </s>
              <s>Quòd ſi
                <expan abbr="itaq;">itaque</expan>
              in F excitetur linea perpendicularis ad FC:
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              dico protractam ſecare AP in P. </s>
              <s>Quòd ſi non; ſecet, ſi fieri
                <lb/>
              poteſt, in alio puncto V. G: I. </s>
              <s>Et quia angulus FCI per lemma
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              huius, eſtgrad 45 erit
                <expan abbr="quoq;">quoque</expan>
              angulus FIC grad 35 Exæquatur
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              autem angulus FMA angulo FPA ob lineas parallelas, & </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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