Clavius, Christoph, Geometria practica

Table of Notes

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            puncta D, G, recta D G. </s>
            <s xml:id="echoid-s13978" xml:space="preserve"> Quoniam igitur circulus A B C, æqualis eſt
              <note symbol="a" position="right" xlink:label="note-325-01" xlink:href="note-325-01a" xml:space="preserve">1. de Dimẽs.
                <lb/>
              circuli Ar-
                <lb/>
              chim.</note>
            DBG: </s>
            <s xml:id="echoid-s13979" xml:space="preserve"> Eſt autem triangulum DBG, rectangulo D B E F, æquale; </s>
            <s xml:id="echoid-s13980" xml:space="preserve">quod
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              <note symbol="b" position="right" xlink:label="note-325-02" xlink:href="note-325-02a" xml:space="preserve">ſchol. 41.
                <lb/>
              primi.</note>
            trianguli dupla ſit baſis rectanguli; </s>
            <s xml:id="echoid-s13981" xml:space="preserve">(Id quod etiam ex demonſtratione antece-
              <lb/>
            dentis propoſ. </s>
            <s xml:id="echoid-s13982" xml:space="preserve">liquet, vbi oſtendimus, triangulum DEF, æquale eſſe rectangu-
              <lb/>
            lo DEHI:) </s>
            <s xml:id="echoid-s13983" xml:space="preserve">erit quoque circulus ABC, rectangulo DBEF, æqualis. </s>
            <s xml:id="echoid-s13984" xml:space="preserve">Area ergo
              <lb/>
            cuiuslibet circuli æqualis eſt rectangulo, &</s>
            <s xml:id="echoid-s13985" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13986" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s13987" xml:space="preserve"/>
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          <head xml:id="echoid-head322" xml:space="preserve">THEOR. 5. PROPOS. 5.</head>
          <note position="right" xml:space="preserve">Propriet{as}
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          quædam tri-
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          anguli rectan-
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          guli.</note>
          <p>
            <s xml:id="echoid-s13988" xml:space="preserve">IN omnitriangulo rectangulo, ſi ab vno acutorum angulorum vtcun-
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            que ad latus oppoſitum linea recta ducatur, erit maior proportio hu-
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            ius lateris ad eius ſegmentum, quod prope angulum rectum exiſtit,
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            quam anguli acuti prædicti, ad eius partem dicto ſegmento lateris op-
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            poſitum.</s>
            <s xml:id="echoid-s13989" xml:space="preserve"/>
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          <p>
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              <emph style="sc">Sit</emph>
            triangulum rectangulum ABC, cuius angulus C, ſitrectus; </s>
            <s xml:id="echoid-s13991" xml:space="preserve">ducaturque
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            ab acuto angulo A, ad latus oppoſitum BC, recta AD, vt-
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            cunque; </s>
            <s xml:id="echoid-s13992" xml:space="preserve">Dico maiorem eſſe proportionem rectæ B C, ad
              <lb/>
            rectam CD, quam anguli BAC, ad angulum CAD. </s>
            <s xml:id="echoid-s13993" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-325-04" xlink:href="note-325-04a" xml:space="preserve">19. primi.</note>
            niam enim recta AD, maior quidem eſt, quam A C; </s>
            <s xml:id="echoid-s13994" xml:space="preserve">minor
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            verò, quam AB; </s>
            <s xml:id="echoid-s13995" xml:space="preserve">ſi centro A, interuallo autem A D, circu-
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            lus deſcribatur, ſecabit is rectam A C, protractam infra
              <lb/>
            punctum C, vtin E, at verò rectam AB, ſupra punctum B,
              <lb/>
            vtin F. </s>
            <s xml:id="echoid-s13996" xml:space="preserve">Et quia maior eſt proportio trianguli BAD, ad ſectorem FAD, quã tri-
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            anguli DAC, ad ſectorem DAE, (propterea quod ibi eſt proportio maioris in-
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            æqualitatis, hic autem minoris inæqualitatis) erit quoque permutando
              <note symbol="d" position="right" xlink:label="note-325-05" xlink:href="note-325-05a" xml:space="preserve">27. quinti.</note>
            proportio trianguli BAD, ad triangulum D A C, quam ſectoris FAD, ad ſectorẽ
              <lb/>
            D A E. </s>
            <s xml:id="echoid-s13997" xml:space="preserve"> Componendo igitur maior quoque erit proportio trianguli B A C,
              <note symbol="e" position="right" xlink:label="note-325-06" xlink:href="note-325-06a" xml:space="preserve">28. quinti.</note>
            triangulum D A C, hoc eſt, rectæ BC, ad rectam CD, (habent enim triangula
              <note symbol="f" position="right" xlink:label="note-325-07" xlink:href="note-325-07a" xml:space="preserve">1. ſexti.</note>
            AC, DAC, eandem proportionem, quam baſes BC, CD.) </s>
            <s xml:id="echoid-s13998" xml:space="preserve">quam ſectoris F A E,
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            ad ſectorẽ DAE, hoc eſt, quam anguli BAC, ad angulum CAD; </s>
            <s xml:id="echoid-s13999" xml:space="preserve"> quod
              <note symbol="g" position="right" xlink:label="note-325-08" xlink:href="note-325-08a" xml:space="preserve">coroll. 33.
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              ſexti.</note>
            habeant proportionem ſectores, quam anguli. </s>
            <s xml:id="echoid-s14000" xml:space="preserve">Quo circa in omnitriangulo re-
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            ctangulo, &</s>
            <s xml:id="echoid-s14001" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14002" xml:space="preserve">quod demonſtrandum erat.</s>
            <s xml:id="echoid-s14003" xml:space="preserve"/>
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              <emph style="sc">Hæc</emph>
            propoſitio vera quoque eſt in triangulo non rectangulo, dummodo
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            angulus C, maior ſit angulo A D C, vt patet; </s>
            <s xml:id="echoid-s14005" xml:space="preserve"> quod tunc etiam A D, maior
              <note symbol="h" position="right" xlink:label="note-325-09" xlink:href="note-325-09a" xml:space="preserve">19. primi.</note>
            quam AC, minor vero, quam AB, &</s>
            <s xml:id="echoid-s14006" xml:space="preserve">c.</s>
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Impressum