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

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        <div xml:id="echoid-div120" type="section" level="1" n="71">
          <p>
            <s xml:id="echoid-s1448" xml:space="preserve">
              <pb o="41" file="0065" n="65" rhead=""/>
            eſt, inſcriptam, vel minorem eſſe ea, cuius tranſuerſum minus eſt; </s>
            <s xml:id="echoid-s1449" xml:space="preserve">& </s>
            <s xml:id="echoid-s1450" xml:space="preserve">è con-
              <lb/>
            tra eam eſſe circumſcriptam, ſiue maiorem, cuius tranſuerſum minus eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s1451" xml:space="preserve">Nam in 9. </s>
            <s xml:id="echoid-s1452" xml:space="preserve">figura, in qua ſectiones ſunt Hyperbolæ ſimul adſcriptæ cum eo-
              <lb/>
            dem recto latere, oſtenſum fuit Hyperbolen DBE, cuius tranſuerſum BI ma-
              <lb/>
            ius eſt, totam cadere intra Hyperbolen ABC, cuius tranſuerſum BL minus
              <lb/>
            eſt, & </s>
            <s xml:id="echoid-s1453" xml:space="preserve">ideo DBE erit inſcripta, ſiue minor; </s>
            <s xml:id="echoid-s1454" xml:space="preserve">& </s>
            <s xml:id="echoid-s1455" xml:space="preserve">è contra ipſa ABC, cuius tranſ-
              <lb/>
            uerſum eſt minus, erit circumſcripta, ſiue maior.</s>
            <s xml:id="echoid-s1456" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div121" type="section" level="1" n="72">
          <head xml:id="echoid-head77" xml:space="preserve">COROLL. IV.</head>
          <p>
            <s xml:id="echoid-s1457" xml:space="preserve">PAtet etiam in Ellipſibus tantùm, vel in Ellipſibus, & </s>
            <s xml:id="echoid-s1458" xml:space="preserve">circulis per cundem
              <lb/>
            verticé ſimul adſcriptis cũ eodem recto latere, eam eſſe inſcriptam, ſiue
              <lb/>
            minorem, cuius tranſuerſum latus minus eſt, & </s>
            <s xml:id="echoid-s1459" xml:space="preserve">è contra eam circumſcriptam,
              <lb/>
            vel maiorem eſſe, cuius tranſuerſum maius eſt: </s>
            <s xml:id="echoid-s1460" xml:space="preserve">quoniam in 10. </s>
            <s xml:id="echoid-s1461" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1462" xml:space="preserve">& </s>
            <s xml:id="echoid-s1463" xml:space="preserve">12. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">figu-
              <lb/>
            ra oſtenſum fuit Ellipſim, vel circulum DBE, cuius tranſuerſum BI minus
              <lb/>
            eſt, totam cadere intra Ellipſim, vel circulum ABC, cuius latus tranſuerſum
              <lb/>
            BL maius eſt; </s>
            <s xml:id="echoid-s1465" xml:space="preserve">quare ipſa DBE erit inſcripta, ſiue minor: </s>
            <s xml:id="echoid-s1466" xml:space="preserve">& </s>
            <s xml:id="echoid-s1467" xml:space="preserve">è contra Ellipſis,
              <lb/>
            vel circulus ABC erit circumſcriptus, ſiue maior, &</s>
            <s xml:id="echoid-s1468" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1469" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div122" type="section" level="1" n="73">
          <head xml:id="echoid-head78" xml:space="preserve">COROLL. V.</head>
          <p>
            <s xml:id="echoid-s1470" xml:space="preserve">MAnifeſtum eſt etiam ſimiles coni-ſectiones per vertices ſimul adſcri-
              <lb/>
            ptas habere regulas parallelas, & </s>
            <s xml:id="echoid-s1471" xml:space="preserve">eam ſectionem eſſe inſcriptam, vel
              <lb/>
            minorem, cuius latera minora ſunt; </s>
            <s xml:id="echoid-s1472" xml:space="preserve">& </s>
            <s xml:id="echoid-s1473" xml:space="preserve">è contra eam eſſe circumſcriptam, vel
              <lb/>
            maiorem, cuius latera ſunt maiora. </s>
            <s xml:id="echoid-s1474" xml:space="preserve">Si enim in 6. </s>
            <s xml:id="echoid-s1475" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1476" xml:space="preserve">& </s>
            <s xml:id="echoid-s1477" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">figura coni-ſectio-
              <lb/>
            nes ABC, DBE eiuſdem nominis, ac per verticem B ſimul adſcriptæ, fuerint
              <lb/>
            ſimiles, erit tranſuerſum LB ad rectum BH vt tranſuerſum IB ad rectum BG,
              <lb/>
            & </s>
            <s xml:id="echoid-s1479" xml:space="preserve">permutando, & </s>
            <s xml:id="echoid-s1480" xml:space="preserve">diuidendo, LI ad IB, vt HG ad GB, vndæ regulæ LH,
              <lb/>
            IG erunt parallelæ, ſed in hoc Theoremate demonſtratum eſt ſectioné ABE
              <lb/>
            minorum laterum, totam cadere intra ſectionem ABC maiorum laterum,
              <lb/>
            ergo ipſa DBE erit inſcripta; </s>
            <s xml:id="echoid-s1481" xml:space="preserve">& </s>
            <s xml:id="echoid-s1482" xml:space="preserve">è contra demonſtrauimus ABC maiorum
              <lb/>
            laterum totam cadere extra DBE minorum laterum, ac propterea erit ei cir-
              <lb/>
            cumſcripta.</s>
            <s xml:id="echoid-s1483" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div123" type="section" level="1" n="74">
          <head xml:id="echoid-head79" xml:space="preserve">COROLL. VI.</head>
          <p>
            <s xml:id="echoid-s1484" xml:space="preserve">EX ipſa demum huius Theorematis demonſtratione elicitur, quod in co-
              <lb/>
            ni-ſectionibus per vertices ſimul adſcriptis, quadrata ſemi- applicata-
              <lb/>
            rum ex eodem diametri puncto inter ſe ſunt vt earundem latitudines. </s>
            <s xml:id="echoid-s1485" xml:space="preserve">Oſten-
              <lb/>
            dimus enim in qualibet præcedentis ſchematis figura, quadratum ſemi-ap-
              <lb/>
            plicatæ MF, in ſectione ABC, ad quadratum ſemi-applicatæ NF, in ſectio-
              <lb/>
            ne DBE, eſſe vt latitudo propria FP, ad propriam latitudinem FO.</s>
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