Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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[101.] LEMMA IV. PROP. XXXIX.
[102.] THEOR. XX. PROP. XXXX.
[103.] COROLL.
[104.] THEOR. XXI. PROP. XXXXI.
[105.] COROLL.
[106.] THEOR. XXII. PROP. XXXXII.
[107.] ALITER.
[108.] COROLL. I.
[109.] COROLL. II.
[110.] LEMMA V. PROP. XXXXIII.
[111.] THEOR. XXIII. PROP. XXXXIV.
[112.] COROLL.
[113.] Quod ſuperiùs promiſimus oſtendetur ſic.
[114.] THEOR. XXIV. PROP. XXXXV.
[115.] COROLL.
[116.] LEMMA VI. PROP. XXXXVI.
[117.] THEOR. XXV. PROP. XXXXVII.
[118.] ALITER.
[119.] COROLL. I.
[120.] COROLL. II.
[121.] THEOR. XXVI. PROP. XXXXVIII.
[122.] MONITVM.
[123.] THEOR. XXVII. PROP. XXXXIX.
[124.] THEOR. XXVIII. PROP. L.
[125.] COROLL.
[126.] PROBL. XVII. PROP. LI.
[127.] PROBL. XVIII. PROP. LII.
[128.] ALITER.
[129.] ALITER breuiùs.
[130.] PROBL. XIX. PROP. LIII.
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          <head xml:id="echoid-head119" xml:space="preserve">THEOR. XXIV. PROP. XXXXV.</head>
          <p>
            <s xml:id="echoid-s2672" xml:space="preserve">Similes Hyperbolæ per diuerſos vertices ſimul adſcriptæ, & </s>
            <s xml:id="echoid-s2673" xml:space="preserve">
              <lb/>
            quarum eadem ſit regula, ſunt inter ſe nunquam coeuntes, & </s>
            <s xml:id="echoid-s2674" xml:space="preserve">in in-
              <lb/>
            finitum productæ ad ſe propiùs accedentes, ſed ad interuallum
              <lb/>
            nunquam perueniunt æquale cuidam dato interuallo.</s>
            <s xml:id="echoid-s2675" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2676" xml:space="preserve">SInt duæ Hyperbolæ ABC, DEF per diuerſos vertices B, E ſimul adſcri-
              <lb/>
            ptæ, quarum eadem ſit regula GH (ſic enim
              <unsure/>
            ſimiles erunt,
              <note symbol="a" position="right" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">6. ſecúd.
                <lb/>
              defin.</note>
            ductis contingentibus BI, EL; </s>
            <s xml:id="echoid-s2677" xml:space="preserve">eſt tranſuerſum GB ad rectum BI, vt tranſuer-
              <lb/>
            ſum GE ad rectum EL.) </s>
            <s xml:id="echoid-s2678" xml:space="preserve">Dico primùm, has in infinitum productas, nun-
              <lb/>
            quam ſimul conuenire.</s>
            <s xml:id="echoid-s2679" xml:space="preserve"/>
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            <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0103-01"/>
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          <p>
            <s xml:id="echoid-s2680" xml:space="preserve">Protracta enim contingente LE, ſectionem ABC ſecane in M, N, quæ
              <lb/>
            erit ipſi ordinata, cum ſectiones ponantur ſimul adſcriptæ; </s>
            <s xml:id="echoid-s2681" xml:space="preserve">patet ſectionem
              <lb/>
            DEF totam cadere infra contingentem MN. </s>
            <s xml:id="echoid-s2682" xml:space="preserve">Iam ſumpto in ſectione DEF
              <lb/>
            quolibet puncto D, per ipſum ordinatim applicetur ADOH alteram ſectio-
              <lb/>
            nem ſecans in A, regulam verò in H: </s>
            <s xml:id="echoid-s2683" xml:space="preserve">erit quadratum AO, ad quadratum
              <lb/>
            DO, vt rectangulum BOH ad rectangulum EOH (ob ęqualitatem) vel
              <note symbol="b" position="right" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">Coroll.
                <lb/>
              1. huius.</note>
            altitudo BO ad altitudinem EO, ſed eſt BO maior EO, quare quadratum
              <lb/>
            AO maius erit quadrato DO, ex quo punctum D cadit intra Hyperbolen
              <lb/>
            ABC; </s>
            <s xml:id="echoid-s2684" xml:space="preserve">& </s>
            <s xml:id="echoid-s2685" xml:space="preserve">ſic de quibuſcunque alijs punctis Hyperbolę DEF: </s>
            <s xml:id="echoid-s2686" xml:space="preserve">quare huiuſmo-
              <lb/>
            di ſectiones inter ſe nunquam conueniunt. </s>
            <s xml:id="echoid-s2687" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s2688" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2689" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2690" xml:space="preserve">Iam ſi datæ Hyperbolæ, per verticem E, adſcribatur Hyperbole P E Q
              <lb/>
            cuius latera ER, ES æqualia ſint lateribus BG, BI, vtrunque vtrique, ipſæ
              <lb/>
            Hyperbolæ ABC, PEQ, congruentes erunt, eritque, (ob
              <note symbol="c" position="right" xlink:label="note-0103-03" xlink:href="note-0103-03a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            RE ad ES, vt GB ad BI, vel vt GE ad EL, quare Hyperbolæ DEF, </s>
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