Clavius, Christoph, Geometria practica
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              <pb o="356" file="384" n="384" rhead="GEOMETR. PRACT."/>
            catur in numerũ partium ipſius AD, ipſi AE, æqualium, nimirum in 4.) </s>
            <s xml:id="echoid-s16637" xml:space="preserve">ac pro-
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            inde ſi AB, diuiſa eſſe intelligatur in 3. </s>
            <s xml:id="echoid-s16638" xml:space="preserve">partes, tota AD, continebit tales partes
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            36. </s>
            <s xml:id="echoid-s16639" xml:space="preserve">Quo circa ſi in inſtrumento partiũ lib. </s>
            <s xml:id="echoid-s16640" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16641" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s16642" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16643" xml:space="preserve">conſtructo interuallum AD,
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            ſtatuatur inter partes 36. </s>
            <s xml:id="echoid-s16644" xml:space="preserve">36. </s>
            <s xml:id="echoid-s16645" xml:space="preserve">Deinde interuallũ inter 35. </s>
            <s xml:id="echoid-s16646" xml:space="preserve">35. </s>
            <s xml:id="echoid-s16647" xml:space="preserve">(nimirum tota AD,
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            vna parte minus) tranferatur ex D, ad I, erit AI, tertia pars ipſius AB, hoc eſt,
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            pars trigeſima ſexta totius AD. </s>
            <s xml:id="echoid-s16648" xml:space="preserve">Cum ergo AB, contineat tres trigeſimas ſextas
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            partes totius AD, erit AG, ipſius AB, pars tertia. </s>
            <s xml:id="echoid-s16649" xml:space="preserve">quod eſt propoſitum.</s>
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        <div xml:id="echoid-div1030" type="section" level="1" n="369">
          <head xml:id="echoid-head396" xml:space="preserve">PROBL. 16. PROPOS. 25.</head>
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            <s xml:id="echoid-s16651" xml:space="preserve">ANGVLVM datum rectilineum in tres æquales partes partiri.</s>
            <s xml:id="echoid-s16652" xml:space="preserve"/>
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              <emph style="sc">Problema</emph>
            hoc veteres Geometras diu, multumque exagitauit, neque
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            ab vllo ad hanc vſque diem Geometrice eſt ſolutum. </s>
            <s xml:id="echoid-s16654" xml:space="preserve">Pappus Alexandrinus
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            inter alios illud ſoluere conatus eſt per deſcriptionem hyperboles. </s>
            <s xml:id="echoid-s16655" xml:space="preserve">Nos idem
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              <figure xlink:label="fig-384-01" xlink:href="fig-384-01a" number="276">
                <image file="384-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/384-01"/>
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            abſoluemus per lineam Conchoideos, quam lib. </s>
            <s xml:id="echoid-s16656" xml:space="preserve">6. </s>
            <s xml:id="echoid-s16657" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s16658" xml:space="preserve">15. </s>
            <s xml:id="echoid-s16659" xml:space="preserve">huius ex Nico-
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            mede deſcripſimus, hoc modo. </s>
            <s xml:id="echoid-s16660" xml:space="preserve">Sit datus angulus acutus ABC: </s>
            <s xml:id="echoid-s16661" xml:space="preserve">Demiſſa au-
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            tem ex quouis puncto A, ad BC, perpendiculari AD, fumatur ipſius AB, dupla
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            DC; </s>
            <s xml:id="echoid-s16662" xml:space="preserve">Et polo B, interuallo autem DC, deſcribatur linea Conchoideos CE, ſe-
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            cans rectam AE, ipſi BC, ductam parallelam in E, ducatur que recta BE. </s>
            <s xml:id="echoid-s16663" xml:space="preserve">Di-
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            co angulum CBE, eſſe tertiam partem dati anguli ABC; </s>
            <s xml:id="echoid-s16664" xml:space="preserve">hoc eſt, angulum ABE,
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            duplum eſſe anguli CBE, adeò vt diuiſo angulo ABE, bifariam, totus angulus
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            ABC, ſectus ſit in tres partes æquales. </s>
            <s xml:id="echoid-s16665" xml:space="preserve">Quoniam enim ex deſo
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            riptione Con-
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            choideos, recta GE, ipſi DC, æqualis eſt; </s>
            <s xml:id="echoid-s16666" xml:space="preserve">ac proinde ipſius AB, dupla: </s>
            <s xml:id="echoid-s16667" xml:space="preserve">ſi ſecetur
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            bifariamin F, erit vtra que ſemiſsis ipſi AB, æqualis. </s>
            <s xml:id="echoid-s16668" xml:space="preserve"> Quia verò circulus ex
              <note symbol="a" position="left" xlink:label="note-384-01" xlink:href="note-384-01a" xml:space="preserve">ſchol. 31.
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              tertii.</note>
            circa GE, deſcriptus tranſit per angulum rectum GAE, erit quoque ducta FA,
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            vtrique ſemiſsi FE, FG, ideo que & </s>
            <s xml:id="echoid-s16669" xml:space="preserve">ipſi AB, æqualis. </s>
            <s xml:id="echoid-s16670" xml:space="preserve"> Igitur tam anguli
              <note symbol="b" position="left" xlink:label="note-384-02" xlink:href="note-384-02a" xml:space="preserve">5. primi.</note>
            FEA, quam AFB, ABF, æquales erunt. </s>
            <s xml:id="echoid-s16671" xml:space="preserve"> Eſt autem externus AFB, duobus
              <note symbol="c" position="left" xlink:label="note-384-03" xlink:href="note-384-03a" xml:space="preserve">32. primi.</note>
            ternis FAE, FEA. </s>
            <s xml:id="echoid-s16672" xml:space="preserve">æqualis: </s>
            <s xml:id="echoid-s16673" xml:space="preserve">ideoque ipſius FEA, duplus. </s>
            <s xml:id="echoid-s16674" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s16675" xml:space="preserve">ABF, eiuſ-
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              <note symbol="d" position="left" xlink:label="note-384-04" xlink:href="note-384-04a" xml:space="preserve">29. primi.</note>
            dem FEA, hoc eſt, alterni CBE, duplus erit.</s>
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              <emph style="sc">Si</emph>
            angulus datus rectus eſt, diuidetur in tres æquales angulos, vt in ſcholio
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            propoſ. </s>
            <s xml:id="echoid-s16678" xml:space="preserve">32. </s>
            <s xml:id="echoid-s16679" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16680" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16681" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s16682" xml:space="preserve">tradidimus.</s>
            <s xml:id="echoid-s16683" xml:space="preserve"/>
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            <s xml:id="echoid-s16684" xml:space="preserve">
              <emph style="sc">Si</emph>
            verò eſt obtuſus, ſecabimus eum bifariam, & </s>
            <s xml:id="echoid-s16685" xml:space="preserve">ſemiſſem alterutram intres
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            partes æquales, vt docuimus hoc loco. </s>
            <s xml:id="echoid-s16686" xml:space="preserve">Nam duæ partes tertiæ illius ſemiſsis ef-
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            ficient propoſiti anguli obtuſi tertiam partem, vt perſpicuum eſt.</s>
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