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

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            <s xml:id="echoid-s12967" xml:space="preserve">
              <pb o="505" file="0525" n="525" rhead="LIBER VII."/>
            LDGF, æquari ipſi, HZ {00/ }, &</s>
            <s xml:id="echoid-s12968" xml:space="preserve">, 3687, ſolido, ΣΓ2, pariter ex prima
              <lb/>
            huius colligemus. </s>
            <s xml:id="echoid-s12969" xml:space="preserve">In ſec. </s>
            <s xml:id="echoid-s12970" xml:space="preserve">D. </s>
            <s xml:id="echoid-s12971" xml:space="preserve">quod figura, LED, ad, OED, ſit vt,
              <lb/>
            LE, ad, EO, ſeu quod figura, QAMY, ad, TIMY, ſit vt, QY, ad, Y
              <lb/>
            T, ideſt vt, LE, ad, EO, vel quod figura, LFE, ad, OFE, ſfit vt, LE,
              <lb/>
            ad, EO, patet, ex prop. </s>
            <s xml:id="echoid-s12972" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12973" xml:space="preserve">huius: </s>
            <s xml:id="echoid-s12974" xml:space="preserve">Quod verò ſolidum, LDFE, ad
              <lb/>
            ſolidum, ODFE, ſit vt figura, LEF, ad figuram, OEF, ideſi vt, LE,
              <lb/>
            ad, EO, manifeſtum eſt pariter ex 3. </s>
            <s xml:id="echoid-s12975" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s12976" xml:space="preserve">In ſec. </s>
            <s xml:id="echoid-s12977" xml:space="preserve">F. </s>
            <s xml:id="echoid-s12978" xml:space="preserve">ſolidum, O
              <lb/>
            DFE, ad ſolidum, 3674, eſſe vt figura, EDF, ad figuram, 467,
              <lb/>
            pateb@t ex 3. </s>
            <s xml:id="echoid-s12979" xml:space="preserve">huius, ſunt enim dicta ſolida figuræ proportionali-
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            ter analogæ vt conſideranti manifeſtum erit. </s>
            <s xml:id="echoid-s12980" xml:space="preserve">Cætera huius prop.
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            </s>
            <s xml:id="echoid-s12981" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s12982" xml:space="preserve">& </s>
            <s xml:id="echoid-s12983" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s12984" xml:space="preserve">18. </s>
            <s xml:id="echoid-s12985" xml:space="preserve">abſq; </s>
            <s xml:id="echoid-s12986" xml:space="preserve">methodo Indiuiſibilium ſubſiſtunt,
              <lb/>
            vt examinantifacilè apparebit.</s>
            <s xml:id="echoid-s12987" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1165" type="section" level="1" n="697">
          <head xml:id="echoid-head730" xml:space="preserve">THEOREMA VI. PROPOS. VI.</head>
          <p>
            <s xml:id="echoid-s12988" xml:space="preserve">QVæcunq; </s>
            <s xml:id="echoid-s12989" xml:space="preserve">de parallelogrammis oſtenduntur in Prop.
              <lb/>
            </s>
            <s xml:id="echoid-s12990" xml:space="preserve">5. </s>
            <s xml:id="echoid-s12991" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12992" xml:space="preserve">7. </s>
            <s xml:id="echoid-s12993" xml:space="preserve">& </s>
            <s xml:id="echoid-s12994" xml:space="preserve">8. </s>
            <s xml:id="echoid-s12995" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s12996" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12997" xml:space="preserve">eadem etiam de triangulis, con-
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            ditiones ibi ſuppoſitas circa ſuas baſes, & </s>
            <s xml:id="echoid-s12998" xml:space="preserve">altitudines, ſeu
              <lb/>
            latera æqualiter baſibus inclinata, habentibus, verifi-
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            cantur.</s>
            <s xml:id="echoid-s12999" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13000" xml:space="preserve">Hæe Propoſitio maniſeſta eſt, cum enim expoſito quocunq;
              <lb/>
            </s>
            <s xml:id="echoid-s13001" xml:space="preserve">triangulo, & </s>
            <s xml:id="echoid-s13002" xml:space="preserve">aſſumptis duobus quibuſuis lateribus angulum quē-
              <lb/>
            libet continentibus parallelogrammum compleri poſſit in illo an-
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            gulo, cuius triangulum erit dimidium, ideò quæcunq; </s>
            <s xml:id="echoid-s13003" xml:space="preserve">triangula
              <lb/>
              <note position="right" xlink:label="note-0525-01" xlink:href="note-0525-01a" xml:space="preserve">34. Primi
                <lb/>
              Elem.</note>
            erunt, vt eorum completa paral clogramma, habentibus autem
              <lb/>
            triangulis circa baſes, & </s>
            <s xml:id="echoid-s13004" xml:space="preserve">altitudines, ſeu latera æqualiter baſibus
              <lb/>
            inclinata, præfatas conditiones, eam pariter habent completa
              <lb/>
            parallelogramma, & </s>
            <s xml:id="echoid-s13005" xml:space="preserve">de illis verificantur ea, quæ in dictis propo-
              <lb/>
              <note position="right" xlink:label="note-0525-02" xlink:href="note-0525-02a" xml:space="preserve">4. huius,
                <lb/>
              cum An-
                <lb/>
              not.</note>
            ſitionibus fuerunt propoſita, ergo eadem de eorum medietatibus,
              <lb/>
            hoc eſt de dictis triangulis verificabuntur. </s>
            <s xml:id="echoid-s13006" xml:space="preserve">Triangula ergo, quæ
              <lb/>
            ſunt in eadem altitudine inter ſe ſunt, vt baſes; </s>
            <s xml:id="echoid-s13007" xml:space="preserve">Et quæ ſunt in
              <lb/>
            ea dem, vel æqualibus baſibus, vt altitudines, vel vt latera, quæ
              <lb/>
            æqualiter baſi, ſeu baſibus, inclinantur. </s>
            <s xml:id="echoid-s13008" xml:space="preserve">Habent inter ſe rationem
              <lb/>
            compoſitam ex ratione baſium, & </s>
            <s xml:id="echoid-s13009" xml:space="preserve">altitudinum, vel laterum ęqua-
              <lb/>
            liter baſibus inclinatorum. </s>
            <s xml:id="echoid-s13010" xml:space="preserve">Habentia baſes altitudinibus, vel la-
              <lb/>
            teribus baſibus æqual ter incl natis, reciprocas, ſunt æqualia; </s>
            <s xml:id="echoid-s13011" xml:space="preserve">Et
              <lb/>
            quæ ſunt æqualia baſes habent altitudinibus, vel lateribus æqua-
              <lb/>
            liter baſibus inclinatis, reciprocas. </s>
            <s xml:id="echoid-s13012" xml:space="preserve">Et tandem ſimil a triangula
              <lb/>
            ſunt in dupla ratione laterum homologorum; </s>
            <s xml:id="echoid-s13013" xml:space="preserve">Quæ omnia etiam
              <lb/>
            Lib. </s>
            <s xml:id="echoid-s13014" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13015" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13016" xml:space="preserve">19. </s>
            <s xml:id="echoid-s13017" xml:space="preserve">Coroll. </s>
            <s xml:id="echoid-s13018" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13019" xml:space="preserve">ex methodo Indiuiſibilium collige </s>
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