Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div1171" type="section" level="1" n="700">
          <pb o="508" file="0528" n="528" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div1173" type="section" level="1" n="701">
          <head xml:id="echoid-head734" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13071" xml:space="preserve">PErant. </s>
            <s xml:id="echoid-s13072" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s13073" xml:space="preserve">ſatisfit prop. </s>
            <s xml:id="echoid-s13074" xml:space="preserve">22. </s>
            <s xml:id="echoid-s13075" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13076" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13077" xml:space="preserve">ex ea enim pariter habe-
              <lb/>
            tur omnes cylindricos eandem rationem habere ad conicos
              <lb/>
            in eadem baſi, & </s>
            <s xml:id="echoid-s13078" xml:space="preserve">altitudine cum ipſis exiſtentes, cum eorum eſſe
              <lb/>
            triplos fuerit demonſtratum, & </s>
            <s xml:id="echoid-s13079" xml:space="preserve">eadem, quæ ex ipſa deduceban-
              <lb/>
            tur, hic pariter colliguntur, proprietates inquam illæ, quas cylin-
              <lb/>
            dricis competere dictum eſt in Annot. </s>
            <s xml:id="echoid-s13080" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s13081" xml:space="preserve">5. </s>
            <s xml:id="echoid-s13082" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s13083" xml:space="preserve">Sic ergo
              <lb/>
            ratum, ac firmum eſt, Conicos in eadem, vel æqualibus baſibus
              <lb/>
            exiſtentes, eſſe inter ſe vt altitudines. </s>
            <s xml:id="echoid-s13084" xml:space="preserve">Habereq; </s>
            <s xml:id="echoid-s13085" xml:space="preserve">rationem compo-
              <lb/>
            ſitam ex ratione baſium, & </s>
            <s xml:id="echoid-s13086" xml:space="preserve">altitudinum. </s>
            <s xml:id="echoid-s13087" xml:space="preserve">Eos verò, quorum ba-
              <lb/>
            ſes altitudinibus reciprocantur, æquales eſſe, & </s>
            <s xml:id="echoid-s13088" xml:space="preserve">æqualium baſe-
              <lb/>
            altitudinibus reciprocari. </s>
            <s xml:id="echoid-s13089" xml:space="preserve">Ac tandem ſimiles conicos eſſe in tri-
              <lb/>
            pla ratione linearum, vel laterum homologorum eorundem ba-
              <lb/>
            ſium, ſeu ſimilium triangulorum per verticem traſeuntium, quæ
              <lb/>
            in ipſius prop. </s>
            <s xml:id="echoid-s13090" xml:space="preserve">22. </s>
            <s xml:id="echoid-s13091" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s13092" xml:space="preserve">Sectionibus, in gratiam Conicorum pari-
              <lb/>
            ter colligebantur. </s>
            <s xml:id="echoid-s13093" xml:space="preserve">Per hanc etiam ſatisſit prop. </s>
            <s xml:id="echoid-s13094" xml:space="preserve">24. </s>
            <s xml:id="echoid-s13095" xml:space="preserve">eiuſdem lib.
              <lb/>
            </s>
            <s xml:id="echoid-s13096" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13097" xml:space="preserve">cum per eam ibi demonſtrati intendatur cylindricum quemcũq; </s>
            <s xml:id="echoid-s13098" xml:space="preserve">
              <lb/>
            triplum eſſe conici in eadem baſi, & </s>
            <s xml:id="echoid-s13099" xml:space="preserve">altitudine cum eo exiſtentis,
              <lb/>
            vt in Sec. </s>
            <s xml:id="echoid-s13100" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13101" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s13102" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13103" xml:space="preserve">gen. </s>
            <s xml:id="echoid-s13104" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s13105" xml:space="preserve">34. </s>
            <s xml:id="echoid-s13106" xml:space="preserve">poſtea declaratur. </s>
            <s xml:id="echoid-s13107" xml:space="preserve">Aduerte au-
              <lb/>
            tem, quod pag. </s>
            <s xml:id="echoid-s13108" xml:space="preserve">79. </s>
            <s xml:id="echoid-s13109" xml:space="preserve">lin. </s>
            <s xml:id="echoid-s13110" xml:space="preserve">15. </s>
            <s xml:id="echoid-s13111" xml:space="preserve">hæc verba, _& </s>
            <s xml:id="echoid-s13112" xml:space="preserve">cum omnibus quadratis_
              <lb/>
            _duorum triangulorun CBM, EMF_, ponenda ſunt poſt hæc verba,
              <lb/>
            _dupla erunt omnium quadratorum, AF_.</s>
            <s xml:id="echoid-s13113" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1174" type="section" level="1" n="702">
          <head xml:id="echoid-head735" xml:space="preserve">THEOREMA IX. PROPOS. IX.</head>
          <p>
            <s xml:id="echoid-s13114" xml:space="preserve">COnicorum fruſta æquè alta, & </s>
            <s xml:id="echoid-s13115" xml:space="preserve">in baſibus æquè alto-
              <lb/>
            rum conicorum, à quibus abſcinduntur, conſtituta;</s>
            <s xml:id="echoid-s13116" xml:space="preserve">
              <lb/>
            inter ſe ſunt vt baſes.</s>
            <s xml:id="echoid-s13117" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13118" xml:space="preserve">Videatur ſchema prop. </s>
            <s xml:id="echoid-s13119" xml:space="preserve">7. </s>
            <s xml:id="echoid-s13120" xml:space="preserve">huius, in quo ſint conicorum æquè
              <lb/>
            altorum, AkLM, BSQTR, fruſta, GIOLKM, XVTS, in eiſdem
              <lb/>
            cum illis baſibus, kLM, SQTR, & </s>
            <s xml:id="echoid-s13121" xml:space="preserve">in æqualibus altitudinibus, C
              <lb/>
            E, DF, exiſtentia, igitur abſciſſis verſus puncta, C, D, altitudinum
              <lb/>
            partibus æqualibus, & </s>
            <s xml:id="echoid-s13122" xml:space="preserve">per earum terminos ductis planis baſibus
              <lb/>
            parallelis, oſtendemus ab ijſdem productas in fruſtis figuras eſſe
              <lb/>
              <note position="left" xlink:label="note-0528-01" xlink:href="note-0528-01a" xml:space="preserve">3. huius.</note>
            inter ſe vt ipſæ baſes eodem modo, quo ibi factum eſt, vnde pate-
              <lb/>
            bit dicta ſruſta eſſe figuras proportionaliter analogas, quapropter
              <lb/>
            ipſa eſſe inter ſe vt baſes pariter concludemus, quod erat demon-
              <lb/>
            ſtrandum.</s>
            <s xml:id="echoid-s13123" xml:space="preserve"/>
          </p>
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