Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s15181" xml:space="preserve">
              <pb o="324" file="354" n="354" rhead="GEOMETR. PRACT."/>
            pars eſt recta DR, totius ſemidiametri DA, quippe cum in deſcriptione Quadra-
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            tricis arcus D Q, totius arcus DB, tot particulas complectatur, quot partes re-
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              <figure xlink:label="fig-354-01" xlink:href="fig-354-01a" number="243">
                <image file="354-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/354-01"/>
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            cta DR, totius DA, continet: </s>
            <s xml:id="echoid-s15182" xml:space="preserve">quando quidem
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            rectæ A Q, R O, ſeſe interſecant in O, puncto
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            Quadratricis. </s>
            <s xml:id="echoid-s15183" xml:space="preserve">Neque hæc ſimilitudo impedi-
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            tur, etiamſi tam arcus DQ, toti arcui DB, quã
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            recta D R, totilateri D A, ſit incommenſura-
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            bilis, cum perpetuò Quadratrix eadem vni-
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            formitate progrediatur per omnia ſua puncta.
              <lb/>
            </s>
            <s xml:id="echoid-s15184" xml:space="preserve">Si enim recta DR, non eſt talis pars, ſiue com-
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            menſurabilis, ſiue incommenſurabilis totius
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            lateris D A, qualis pars eſt arcus D Q, totius
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            arcus DB; </s>
            <s xml:id="echoid-s15185" xml:space="preserve">ſi cogitetur pars lateris D A, minor
              <lb/>
            quam DR, vel maior, ſecabit parallela ex eius
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            puncto exrremo ducta rectam A Q, vel ſupra O, velinfra, in puncto, per quod
              <lb/>
            Quadratrix deſcribenda eſt: </s>
            <s xml:id="echoid-s15186" xml:space="preserve">ac proinde ea nõ tranſibit per O, quod eſt abſurdũ,
              <lb/>
            & </s>
            <s xml:id="echoid-s15187" xml:space="preserve">contra hypotheſim. </s>
            <s xml:id="echoid-s15188" xml:space="preserve">Quia inquam eadẽ pars eſt arcus D Q, totius arcus DB,
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              <note symbol="a" position="left" xlink:label="note-354-01" xlink:href="note-354-01a" xml:space="preserve">19. quinti.</note>
            quæ pars eſt recta DR, totius lateris DA; </s>
            <s xml:id="echoid-s15189" xml:space="preserve"> erit quoque reliquus arcus QB, ea- dem pars totius arcus D B, quæ pars eſt reliqua recta R A, totius lateris D A,
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            quod eadem ſit proportio totius D B, ad D Q, quæ totius D A, ad DR: </s>
            <s xml:id="echoid-s15190" xml:space="preserve">Et per-
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            mutando eadem totius DB, ad totam D A, quæ ablati arcus D Q, ad ablatam
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            rectam D R. </s>
            <s xml:id="echoid-s15191" xml:space="preserve">Quocirca erit, vt totus arcus D B, ad arcum Q B, ita totum latus
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            D A, ad rectam R A, hoc eſt, ad rectam perpendicularem ex O, ad AB, demiſ-
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            ſam, quæ ipſi R A, æqualis eſt.</s>
            <s xml:id="echoid-s15192" xml:space="preserve"/>
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          <note symbol="b" position="left" xml:space="preserve">34. primi.</note>
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        <div xml:id="echoid-div926" type="section" level="1" n="323">
          <head xml:id="echoid-head350" xml:space="preserve">II.</head>
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            <s xml:id="echoid-s15193" xml:space="preserve">SI Quadrantis, & </s>
            <s xml:id="echoid-s15194" xml:space="preserve">Quadratricis idem centrum ſit; </s>
            <s xml:id="echoid-s15195" xml:space="preserve">erunt arcus Qua-
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            drantis, ſemidiameter, & </s>
            <s xml:id="echoid-s15196" xml:space="preserve">baſis quadratricis continué proportionales.</s>
            <s xml:id="echoid-s15197" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15198" xml:space="preserve">
              <emph style="sc">Hæc</emph>
            eſt eximia, atque inſignis proprietas Quadratricis. </s>
            <s xml:id="echoid-s15199" xml:space="preserve">Sit Quadrans,
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            & </s>
            <s xml:id="echoid-s15200" xml:space="preserve">Quadratrix ex eo deſcripta, vt ſupra. </s>
            <s xml:id="echoid-s15201" xml:space="preserve">Dico arcum BD, ſemidiametrum AD,
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            & </s>
            <s xml:id="echoid-s15202" xml:space="preserve">Quadratricis baſem A E, continuè eſſe proportionales, hoc eſt, eſſe B D,
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            ad AD, vt AD, ad AE. </s>
            <s xml:id="echoid-s15203" xml:space="preserve">Sin minus, ſit vt BD, ad AD, ita AD, ad AF, maiorem ipſa
              <lb/>
              <figure xlink:label="fig-354-02" xlink:href="fig-354-02a" number="244">
                <image file="354-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/354-02"/>
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            AE, minoremue: </s>
            <s xml:id="echoid-s15204" xml:space="preserve">ſitque primum AF, maior, quam AE. </s>
            <s xml:id="echoid-s15205" xml:space="preserve">Deſcripto ex centro A,
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            Quadrante FG, per F, ſecante Quadratricem in H, ducatur per H, </s>
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