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

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        <body>
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            <p type="main">
              <s>
                <pb xlink:href="063/01/071.jpg"/>
              angulo interno
                <emph type="italics"/>
              hei,
                <emph.end type="italics"/>
              æqualis autem angulo
                <emph type="italics"/>
              ifh;
                <emph.end type="italics"/>
              propterea
                <lb/>
              quòd
                <expan abbr="uterq;">uterque</expan>
              aſſumpto angulo communi
                <emph type="italics"/>
              ihf
                <emph.end type="italics"/>
              facit rectum:
                <lb/>
              & angulo
                <emph type="italics"/>
              ifh
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              eſt æqualis angulus
                <emph type="italics"/>
              kfm;
                <emph.end type="italics"/>
              erit
                <expan abbr="quoq;">quoque</expan>
              æqualis an­
                <lb/>
              gulo
                <emph type="italics"/>
              ahi,
                <emph.end type="italics"/>
              ac proinde maior angulo interno
                <emph type="italics"/>
              hei,
                <emph.end type="italics"/>
              angulo inci­
                <lb/>
              dentiæ. </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Obijcies. </s>
              <s>Si vectis continet gr auitatem mobilis, totus totam, pars ve­
                <lb/>
              rò partem proportionalem per 2 Axioma; et impulſus centri grauitatis
                <lb/>
              totus mouet, cùm huius interuallum ab hypomochlio eidem eſt æquale per
                <lb/>
              7 theorema 2 partis; neceßè in figurâ 3 theor: 2 huius, cùm tota ſemidia­
                <lb/>
              meter figuræ motûs ſit extra hypomochlium, & non niſi in puncto tan­
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              gat planum AZ; aut nullam, aut inſenſibilem inferre plagam: non igi­
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              tur rectè aſſumebatur ratio plagæ ad reliquum impulſum, quam habet
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              quadratum ED ad quadratum EA: ſiquidem totum impulſum metitur
                <lb/>
              quadratum eiuſdem ED.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Reſpondeo noſtram aſſertionem veram eſſe, cùm ſemidia­
                <lb/>
              meter figuræ motûs eâ ratione ſecatur ab hypomochlio, ut re­
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              liquus impulſus ab illatâ plaga non prohibeatur à ſuo mo­
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              tu: at verò hic impulſus cogitur ab hypomochlio ad
                <expan abbr="motũ">motum</expan>
              incli­
                <lb/>
              natum
                <emph type="italics"/>
              di,
                <emph.end type="italics"/>
              per tangentem circuli centro
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              a
                <emph.end type="italics"/>
              deſcripti. </s>
              <s>Erit
                <expan abbr="itaq;">itaque</expan>
                <lb/>
              impulſus reliquus in eâratione ad totum impulſum, quam ha­
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              bet motus in eiuſmodi plano inclinato ad motum verticalem. </s>
              <lb/>
              <s>Ducatur enim
                <emph type="italics"/>
              el
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              parallela ipſi
                <emph type="italics"/>
              di:
                <emph.end type="italics"/>
                <expan abbr="eritq;">eritque</expan>
              motus verticalis in
                <lb/>
                <emph type="italics"/>
              ea
                <emph.end type="italics"/>
              ad motum inclinatum in
                <emph type="italics"/>
              el,
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              ut quadratum
                <emph type="italics"/>
              ea
                <emph.end type="italics"/>
              ad quadratum
                <lb/>
                <emph type="italics"/>
              el,
                <emph.end type="italics"/>
              hoc eſt ut quadratum
                <emph type="italics"/>
              da
                <emph.end type="italics"/>
              ad quadratum
                <emph type="italics"/>
              de:
                <emph.end type="italics"/>
              quòd ſimilia
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              ſunt triangula
                <emph type="italics"/>
              ael. aed.
                <emph.end type="italics"/>
              Et quia quadratum
                <emph type="italics"/>
              ad
                <emph.end type="italics"/>
              hoc eſt totus
                <lb/>
              impulſus æquatur duobus quadratis
                <emph type="italics"/>
              de. ae;
                <emph.end type="italics"/>
              eſt autem quadra­
                <lb/>
              tum
                <emph type="italics"/>
              de
                <emph.end type="italics"/>
              impulſus movens, erit quadratum
                <emph type="italics"/>
              ae
                <emph.end type="italics"/>
              impulſus qui­
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              eſcens, hoc eſt plaga; quam infert eidem plano
                <emph type="italics"/>
              az.
                <emph.end type="italics"/>
              Magis er­
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              go univerſalis eſt hæc ratio, quàm à ſemidiametro figuræ </s>
            </p>
          </chap>
        </body>
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