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

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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="063/01/067.jpg"/>
              centrum eſt perpendicularis ad
                <emph type="italics"/>
              eg
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              parallelum ipſi
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              bd,
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              erunt an­
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              guli
                <emph type="italics"/>
              ace. acg
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              inter ſe æquales. </s>
              <s>Sunt autem triangula
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              ica. lcn
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                <lb/>
              ex conſtructione ſimilia; & angulus
                <emph type="italics"/>
              ica
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              æqualis angulo
                <emph type="italics"/>
              lcn:
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                <lb/>
              quibus ablatis ex
                <emph type="italics"/>
              ace. acg
                <emph.end type="italics"/>
              anguli reliqui
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              ecf. mcn,
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              incidentiæ
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              & reflexionis inter ſe ſunt æquales. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              THEOREMA IX.
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              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              Motus Trianguli Iſogoni ſi ne〈que〉 ad planum, ne〈que〉 ad baſim ſit per­
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              pendicularis, ad angulos inæquales reflectit.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>In 3 figurâ triangulum
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              abc
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              occurrat plano habens latus
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              ac
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                <lb/>
              eidem parallelum:
                <expan abbr="ſitq;">ſitque</expan>
              Iinea hypomochlij
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              cd,
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              & linea ad eam
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              perpendicularis
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              ef:
                <emph.end type="italics"/>
                <expan abbr="eritq;">eritque</expan>
              grauitas mouens centri Quadratum
                <lb/>
                <emph type="italics"/>
              ef:
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              plaga autem huius complementum quadratum
                <emph type="italics"/>
              go.
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              quod
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              quidem habetur, ſi lineâ
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              gf
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              ſectâ bifarium in
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              p,
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              eo centro de­
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              ſcribatur ſemicirculus
                <emph type="italics"/>
              gof,
                <emph.end type="italics"/>
                <expan abbr="ſumaturq;">ſumaturque</expan>
              chorda
                <emph type="italics"/>
              fo
                <emph.end type="italics"/>
              æqualis
                <emph type="italics"/>
              fe:
                <emph.end type="italics"/>
              nam
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              chorda reliqua
                <emph type="italics"/>
              og
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              dabit illud quadratum. propterea quòd gra­
                <lb/>
              uitas tota ſit quadratum
                <emph type="italics"/>
              fg.
                <emph.end type="italics"/>
              fiat
                <expan abbr="itaq;">itaque</expan>
              ut
                <emph type="italics"/>
              fo
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              og,
                <emph.end type="italics"/>
              ita
                <emph type="italics"/>
              fi
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              fb;
                <emph.end type="italics"/>
                <lb/>
              erit motus reflexus in lineâ
                <emph type="italics"/>
              fh
                <emph.end type="italics"/>
              diametro parallelogrammi
                <emph type="italics"/>
              fb hi:
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                <lb/>
              angulus autem reflexionis
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              ifh:
                <emph.end type="italics"/>
              quem dico angulo
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              acd
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              eſſe in­
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              æqualem. </s>
              <s>Quia angulus
                <emph type="italics"/>
              age
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              externus cſt maior angulo in­
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              terno
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              ecg,
                <emph.end type="italics"/>
              æqualis autem angulo
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              ofg;
                <emph.end type="italics"/>
              propterea quòd
                <expan abbr="uterq;">uterque</expan>
                <lb/>
              aſſumpto angulo communi
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              ogf
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              facit rectum: eſt verò huic
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              angulo æqualis angulus reflexionis
                <emph type="italics"/>
              hfi;
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              quòd ſimilia ſint trian­
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              gula
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              gef: hfi:
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              erit ergo æqualis
                <expan abbr="quoq;">quoque</expan>
              angulo externo
                <emph type="italics"/>
              age:
                <emph.end type="italics"/>
              ac
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              proinde maior interno
                <emph type="italics"/>
              acd
                <emph.end type="italics"/>
              angulo incidentiæ. </s>
              <s>In 4 demum
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              figurâ centrum
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              e
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              cadat intra lineam hypomochlij. cùm igitur
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              centrum gravitatis contineatur in hypomochlio, erit plaga per­
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              fecta:
                <expan abbr="atq;">atque</expan>
              huius lineæ
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              ea. ef. ec:
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              ac proinde per 1 theor: hu­
                <lb/>
              ius motus reflexus in lineâ
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              eb.
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              Quia ergo angulus reflexionis </s>
            </p>
          </chap>
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