Clavius, Christoph, Geometria practica
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          <p>
            <s xml:id="echoid-s16145" xml:space="preserve">
              <pb o="344" file="372" n="372" rhead="GEOMETR. PRACT."/>
            non ſunt; </s>
            <s xml:id="echoid-s16146" xml:space="preserve">neque ipſi C, D, erunt ambo quadrati, vel cubi, vt demonſtratum
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            eſt. </s>
            <s xml:id="echoid-s16147" xml:space="preserve">quod cum hypotheſi pugnat.</s>
            <s xml:id="echoid-s16148" xml:space="preserve"/>
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        <div xml:id="echoid-div988" type="section" level="1" n="353">
          <head xml:id="echoid-head380" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s16149" xml:space="preserve">
              <emph style="sc">Hinc</emph>
            fit, ſi tam Numerator, quam Denominator alicuius minutiæ fuerit
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            quadratus aut cubus: </s>
            <s xml:id="echoid-s16150" xml:space="preserve">tam Numeratorem quoque, quam Denominatoreme-
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            iuſdem minutiæ ad minimos reductę terminos, eſſe quadratum, vel cubum; </s>
            <s xml:id="echoid-s16151" xml:space="preserve">cum
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            minimi termini ſint numeri inter ſe primi, habeantque eandem proportionem,
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            quam Numerator, ac Denominator prioris minutiæ: </s>
            <s xml:id="echoid-s16152" xml:space="preserve">quippe cum minutiæ ſint
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            æquales. </s>
            <s xml:id="echoid-s16153" xml:space="preserve">Item ſi vterque numerus minutiæ cuiuſpiam in minimis terminis non
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            ſit quadratus, aut cubus, neque vtrum que numerum alterius minutiæ æquiua-
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            lentis eſſe quadratum, aut cubum.</s>
            <s xml:id="echoid-s16154" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div989" type="section" level="1" n="354">
          <head xml:id="echoid-head381" xml:space="preserve">THEOR. 7. PROPOS. 12.</head>
          <p>
            <s xml:id="echoid-s16155" xml:space="preserve">IN omni quadrilatera figura rectilinea, tria latera, vt libet, aſſumpta, ma-
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            iora ſunt reliquo latere.</s>
            <s xml:id="echoid-s16156" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16157" xml:space="preserve">
              <emph style="sc">Sit</emph>
            quadrilaterum ABCD. </s>
            <s xml:id="echoid-s16158" xml:space="preserve">Dico quælibet tria latera, nimirum DA, AB,
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            BC, ſimul ſumpta eſſe maiora reliquo latere DC.
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            </s>
            <s xml:id="echoid-s16159" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-372-01" xlink:href="note-372-01a" xml:space="preserve">20. primi.</note>
              <figure xlink:label="fig-372-01" xlink:href="fig-372-01a" number="260">
                <image file="372-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/372-01"/>
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            Ducta enim diametro BD; </s>
            <s xml:id="echoid-s16160" xml:space="preserve"> eruntrectæ BD, BC, maiores quam DC; </s>
            <s xml:id="echoid-s16161" xml:space="preserve">Sed eadem ratione AB, AD,
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            maiores ſunt quam BD. </s>
            <s xml:id="echoid-s16162" xml:space="preserve">Maiores erunt ergo tres
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            AD, AB, BC, quam duæ B D, B C; </s>
            <s xml:id="echoid-s16163" xml:space="preserve">ac proinde
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            multo maiores, quam D C. </s>
            <s xml:id="echoid-s16164" xml:space="preserve">Idemque demon-
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            ſtrabitur ſimili modo de quibuſcunque alijs tri-
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            bus lateribus, vt conſtat. </s>
            <s xml:id="echoid-s16165" xml:space="preserve">In omni ergo quadrilatera figura rectilinea, tria latera,
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            vt libet, aſſumpta. </s>
            <s xml:id="echoid-s16166" xml:space="preserve">maiora ſunt reliquo latere. </s>
            <s xml:id="echoid-s16167" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s16168" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div991" type="section" level="1" n="355">
          <head xml:id="echoid-head382" xml:space="preserve">PROBL. 6. PROPOS. 13.</head>
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            <s xml:id="echoid-s16169" xml:space="preserve">DATIS tribus punctis, per quæ circulis deſcribendus ſit, inuenire alia
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            puncta, per quæ idem circulus tranſire debeat.</s>
            <s xml:id="echoid-s16170" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16171" xml:space="preserve">
              <emph style="sc">Solent</emph>
            interdum tria data puncta tam parum inter ſe diſtare, aut fere in
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            recta linea iacere, vt non facilè eorum centrum inueniri poſsit, propterea quod
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            rectæ ſecantes lineas illa puncta connectentes bifariam, & </s>
            <s xml:id="echoid-s16172" xml:space="preserve">ad angulos rectos,
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            nimis obliquè ſe in centro interſecant. </s>
            <s xml:id="echoid-s16173" xml:space="preserve">Vtigitur magis ex quiſitè centrum re-
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            periatur, inueſtiganda erunt alia duo puncta, vel plura, per quæ idem circulus
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            incedere debeat, hoc modo. </s>
            <s xml:id="echoid-s16174" xml:space="preserve">Sint data tria puncta A, B, C. </s>
            <s xml:id="echoid-s16175" xml:space="preserve">Iunctis rectis A B,
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            A C, BC, conſtituatur ſuper baſem BC, triangulum BCD, t@iangulo ABC, æqui-
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            laterum, ita vt angulus D, vergat in eampartem, verſus quam circumferentia
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            deſcribenda tranſire debet, lateraque æqualia non ab eodem puncto exeant,
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            hoceſt, latus C D, lateri B A, & </s>
            <s xml:id="echoid-s16176" xml:space="preserve">latus B D, lateri C A, ſit æquale. </s>
            <s xml:id="echoid-s16177" xml:space="preserve">Quod quidem
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            fiet, ſiex C, arcus delineetur ad interuallum BA, quem alius arcus ex B, ad inter-
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              <note symbol="b" position="left" xlink:label="note-372-02" xlink:href="note-372-02a" xml:space="preserve">8 primi.</note>
            uallum CA, delineatus ſecet in D. </s>
            <s xml:id="echoid-s16178" xml:space="preserve"> Erit enim angulus D, angulo A, æqualis: </s>
            <s xml:id="echoid-s16179" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-372-03" xlink:href="note-372-03a" xml:space="preserve">ſchol. 21.
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              tertij.</note>
            ac proinde circulus per tria puncta A, B, C, deſcriptus tranſibit quoq; </s>
            <s xml:id="echoid-s16180" xml:space="preserve">per </s>
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