Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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            <s xml:id="echoid-s8108" xml:space="preserve">
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            rum altero maius: </s>
            <s xml:id="echoid-s8109" xml:space="preserve">quare omnino inter ſe ſunt æqualia. </s>
            <s xml:id="echoid-s8110" xml:space="preserve">Quod erat demon-
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            ſtrandum.</s>
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        <div xml:id="echoid-div841" type="section" level="1" n="334">
          <head xml:id="echoid-head343" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s8112" xml:space="preserve">NOn paucas alias ſolidorum Acuminatorum, eorumque trunco-
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            rum proprietates (quales nimirum attigimus de planis, & </s>
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            menſalibus Acuminatis in Scholio propoſ. </s>
            <s xml:id="echoid-s8114" xml:space="preserve">37. </s>
            <s xml:id="echoid-s8115" xml:space="preserve">huius) facilè
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            huc eſſet, ſi locus requireret, ex ſuperioribus afferre: </s>
            <s xml:id="echoid-s8116" xml:space="preserve">ve-
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            rùm ad opportuniorem occaſionem hæc omnia, aliaque fuſius forſan per-
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            tractabimus, ſi Deo nobis valetudinem cum vita, vel ſaltem mitio-
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            rem ægritudinem præſtare placuerit. </s>
            <s xml:id="echoid-s8117" xml:space="preserve">Modò ad inuentionem MAXI-
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            MARVM, MINIMARVMQVE ſolidarum portionum acce-
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            damus, nonnullis adhuc præoſtenſis.</s>
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          </p>
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        <div xml:id="echoid-div842" type="section" level="1" n="335">
          <head xml:id="echoid-head344" xml:space="preserve">LEMMA XIV. PROP. LXXV.</head>
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            <s xml:id="echoid-s8119" xml:space="preserve">Datæ portioni anguli rectilinei, circa diuerſam diametrum
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            datam, æqualem portionem conſtituere.</s>
            <s xml:id="echoid-s8120" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8121" xml:space="preserve">ESto ex angulo rectilineo abſciſſa portio A B C, cuius baſis A C, dia-
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            meter verò B D; </s>
            <s xml:id="echoid-s8122" xml:space="preserve">ſitque data alia diameter B E, circa quam oporteat
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            portionem ipſi A B C æqualem conſtituere.</s>
            <s xml:id="echoid-s8123" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8124" xml:space="preserve">Latus A B ſecetur bifariam in F, & </s>
            <s xml:id="echoid-s8125" xml:space="preserve">per F agatur F G parallela ad B C
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            cum B E occurrens in G, per G verò ducatur A G H ipſam B C ſecans
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            in H, atque inter C B, B H ſumatur media proportionalis B I agaturque
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            per I recta IL baſim A C ſecans in M, & </s>
            <s xml:id="echoid-s8126" xml:space="preserve">datam diametrum B E in N, & </s>
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            B A productam, in L. </s>
            <s xml:id="echoid-s8128" xml:space="preserve">Dico ipſam I L abſcindere L B I portionem quæ-
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            ſitam.</s>
            <s xml:id="echoid-s8129" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s8130" xml:space="preserve">Triangulum enim A B C ad triangulum A B H eſt vt baſis C B ad B H,
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            vel vt quadratum mediæ proportionalis I B ad quadratum tertiæ B H, vel
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            vt triangulum L B I ad idem triangulum A B H. </s>
            <s xml:id="echoid-s8131" xml:space="preserve">(ob ſimilitudinem) quare
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            triangula A B C, L B I ſunt æqualia.</s>
            <s xml:id="echoid-s8132" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s8133" xml:space="preserve">Et cum rectæ L I, A H ſimul æquidiſtent, ſecenturque ab eadem B N ex
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            vertice B trianguli L B I ducta, erit L N ad N I, vt A G ad G H, vel vt
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            A F ad F B (ob parallelas F G, B H) ſed eſt A F ipſi F B æqualis (per con-
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            ſtructionem) ergo, & </s>
            <s xml:id="echoid-s8134" xml:space="preserve">L N ipſi N I æqualis erit. </s>
            <s xml:id="echoid-s8135" xml:space="preserve">Itaque ad datam diame-
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            trum B N, in angulo A B C ordinatim applicata eſt L I abſcindens trian-
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            gulum, vel portionem L B I alteri datæ portioni A B C æqualem. </s>
            <s xml:id="echoid-s8136" xml:space="preserve">Quod
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            faciendum erat.</s>
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