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

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              <pb o="407" file="0427" n="427" rhead="LIBER V."/>
            nientia, eaſdemq; </s>
            <s xml:id="echoid-s10587" xml:space="preserve">oppoſitas ſectiones diuidentia’ alterutro
              <lb/>
            axium, vel diametrorum, ſumpto pro regula. </s>
            <s xml:id="echoid-s10588" xml:space="preserve">Omnia qua-
              <lb/>
            drata deſcripti parallelogrammi ad omnia quadrata figurę
              <lb/>
            duobus oppoſitis lateribus parallelogrammi regulæ æqui-
              <lb/>
            diſtantibus, & </s>
            <s xml:id="echoid-s10589" xml:space="preserve">reliquorum laterum portionibus inter ſe-
              <lb/>
            ctiones coniugatas, & </s>
            <s xml:id="echoid-s10590" xml:space="preserve">prædicta latera concluſis, & </s>
            <s xml:id="echoid-s10591" xml:space="preserve">ipſis
              <lb/>
            coniugatis ſectionibus, comprehenſæ, demptis ab ijſdem
              <lb/>
            omnibus quadratis oppoſitarum hyperbolarum, quarum
              <lb/>
            latus tranſuerſum non fuit ſumptum pro regula, erunt vt
              <lb/>
            cubus dimidij lateris parallelogrammi regulæ non æqui-
              <lb/>
            diſtantis, ad duo parallelepipeda, quorum vnum contine-
              <lb/>
            tur ſub dimidio exceſſus dicti lateris ſuper baſim hyperbo-
              <lb/>
            læ, quam idem latus abſcindit, & </s>
            <s xml:id="echoid-s10592" xml:space="preserve">ſub quadrato dimidij
              <lb/>
            eiuſdem lateris, aliud verò ſub dimidio baſis dictæ hyper-
              <lb/>
            bolæ, & </s>
            <s xml:id="echoid-s10593" xml:space="preserve">ſub @. </s>
            <s xml:id="echoid-s10594" xml:space="preserve">quadrati eiuſdem, cum quadrato dimidij
              <lb/>
            lateristranſuerſi, quod non eſt regula, ab his tamen dem-
              <lb/>
            pto paralleledipedo ſub dimidio lateris tranſuerſi, quod
              <lb/>
            non eſt regu a, & </s>
            <s xml:id="echoid-s10595" xml:space="preserve">ſub quadrato axis, vel diametri alteru-
              <lb/>
            trius hyperbolarum, quarum eſt latus tranſuerſum, vna cũ
              <lb/>
            {1/3}. </s>
            <s xml:id="echoid-s10596" xml:space="preserve">cubi eiuſdem axis, vel diametri.</s>
            <s xml:id="echoid-s10597" xml:space="preserve"/>
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            <s xml:id="echoid-s10598" xml:space="preserve">Sintigitur expoſitæ ſectiones coniugatæ, AEC, MON, PIQ,
              <lb/>
            BFH, quarum communes aſymptoti indefinitè cum ſectionibus
              <lb/>
            fint producti, qui ſint, TSV, RSX, ſint autem earum axes, vel dia-
              <lb/>
            metri coniugatæ, EO, FI, quarum alterutra ſit ſumpta pro regu-
              <lb/>
            la, vt, FI, ſit vlterius deſcriptum parallelogrammum, TV, latera
              <lb/>
            habens æquidiſtantia ipſis, EO, FI, & </s>
            <s xml:id="echoid-s10599" xml:space="preserve">in aſymptotis, TV, XR, cõ-
              <lb/>
            uenientia in punctis, T, R, V, X, ipſaſq; </s>
            <s xml:id="echoid-s10600" xml:space="preserve">ſectiones diuidentia, ita
              <lb/>
            vt, quæ inter ſectiones manent, fiuntq; </s>
            <s xml:id="echoid-s10601" xml:space="preserve">hyperbolarum baſes ſint,
              <lb/>
            PQ, NM, HB, AC, quorum æquidiſtantia erunt æqualia. </s>
            <s xml:id="echoid-s10602" xml:space="preserve">Dico
              <lb/>
            ergo omnia quadrata parallelogrammi, TV, ad omnia quadrata
              <lb/>
            figuræ inte, TX, RV, TB, HR, VQ, PX, & </s>
            <s xml:id="echoid-s10603" xml:space="preserve">ſectiones, BFH, PIQ,
              <lb/>
            cõcluſæ, demptis ab ijſdë omnibus quadratis oppoſitarum hyper-
              <lb/>
            bolarum, AEC, MON, eſſe vt cubus dimidij, XV, ad parallelepi-
              <lb/>
            pedum ſub, QV, & </s>
            <s xml:id="echoid-s10604" xml:space="preserve">quadrato dimidij lateris, XV, vna cum paral-
              <lb/>
            lelepipedo ſub dimidio, PQ, & </s>
            <s xml:id="echoid-s10605" xml:space="preserve">ſub compoſito ex {1/3}. </s>
            <s xml:id="echoid-s10606" xml:space="preserve">quadrati eiuſ-
              <lb/>
            dem dimidij, PQ, & </s>
            <s xml:id="echoid-s10607" xml:space="preserve">quadrato, SO, ab his tamen dempto paralle-
              <lb/>
            lepipedo ſub, SO, & </s>
            <s xml:id="echoid-s10608" xml:space="preserve">quadrato reliquæ ad medietatem, XV, </s>
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