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

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            <p type="main">
              <s>
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              les FM, PA. </s>
              <s>Cùm
                <expan abbr="itaq;">itaque</expan>
              angulus OMF ſit grad. 33. prim. 30.
                <lb/>
              ſemiſſis nimirum anguli externi NOM grad. 67: & angulus
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              OMA grad: 78. prim: 30; quòd æquales ſint arcus AM. FC:
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              ablato angulo OMF ex OMA, erit angulus reliquus FMA,
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              hoc eſt illi æqualis FPA grad: 45. </s>
              <s>Cùm
                <expan abbr="itaq;">itaque</expan>
              angulus FIC ſit
                <lb/>
                <expan abbr="quoq;">quoque</expan>
              oſtenſus grad. 45, erit angulus FIC externus æqualis
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              angulo interno FPI: quod eſt abſurdum. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA III.
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              </s>
            </p>
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              <s>
                <emph type="center"/>
                <emph type="italics"/>
              Lapſus grauium in ſegmento
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              Circuli minore, quàm grad: 90. eſt velocior per duas chordas, quàm per
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              unam chordam.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Moueatur graue ex B in F per arcum grad: 45. </s>
              <s>Dico veloci­
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              ùs moueri per duas chordas BC. CF, quàm per unam chordam
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              BF. </s>
              <s>Supponatur BC æqualis CF: & ducatur FQ parallela BC:
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              in productâ verò BC ſumatur BT æqualis
                <expan abbr="Fq.">Fque</expan>
              erit
                <expan abbr="itaq;">itaque</expan>
              BT
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              partium 11111400, & BC partium 3901806. </s>
              <s>Quâ ablatâ ex
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              BT manet CT partium 7209594. </s>
              <s>Adde Logaritmum huius
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              logaritmo anguli CTH grad. 67. prim. 30; qui per lemma eſt
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              complementum anguli FCT grad: 22. prim. 30.
                <expan abbr="eritq;">eritque</expan>
              aggre­
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              gatum logaritmus lateris CH partium 6659688. </s>
              <s>Eſt autem
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              CH maius latere BC, ſeu CF partium 3901806. </s>
              <s>Cùm
                <expan abbr="itaq;">itaque</expan>
              ,
                <lb/>
              motus ex C in H ſit æqualis duratione motui ex C in T, per pri:
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              theorema huius; erit mot
                <emph type="sup"/>
              9
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              in CF minor duratione motu in CH:
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              additoque communi motu in BC, motus in BC, CF minor du­
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              ratione motu in BT ſeu
                <expan abbr="Fq.">Fque</expan>
              hoc eſt per prop. 15. illi æquali
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              motu in BF. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA IV.
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              </s>
            </p>
          </chap>
        </body>
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