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

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          <head xml:id="echoid-head567" xml:space="preserve">THEOREMA IX. PROPOS. X.</head>
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            <s xml:id="echoid-s9747" xml:space="preserve">SI à centro hyperbolæ duæ intra aſymptotos eiuſdem
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            ductæ fuerint rectæ lineæ indefinitè productæ, agan-
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            tur autem intra curuam hyperbolicam parallelæ tangenti-
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            bus in punctis concurius ductarum linearum, & </s>
            <s xml:id="echoid-s9748" xml:space="preserve">curuæ hy-
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            perbolicæ hinc inde ad eandem productæ, erunt iſtæ ba-
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            ſes hyperbolarum, quarum diametri, vel axes erunt por-
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            tiones ductarum à centro interceptæ inter ipſas, & </s>
            <s xml:id="echoid-s9749" xml:space="preserve">earun-
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            dem hyperbolarum vertices: </s>
            <s xml:id="echoid-s9750" xml:space="preserve">Dico autem omnia quadra-
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            ta vnius dictarum hyperbolarum, regula eiuſdem baſi, ad
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            omnia quadrata alterius regula quoq; </s>
            <s xml:id="echoid-s9751" xml:space="preserve">huius baſi, habere
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            rationem compoſitam ex ratione rectanguli ſub compoſita
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            ex ſexquialtera tranſuerſi lateris hyperbolæ primò dictæ,
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            & </s>
            <s xml:id="echoid-s9752" xml:space="preserve">axi, vel diametro eiuſdem, & </s>
            <s xml:id="echoid-s9753" xml:space="preserve">ſub compoſita extran-
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            ſuerſo latere, & </s>
            <s xml:id="echoid-s9754" xml:space="preserve">axi, vel diametro hyperbolæ ſecundò di-
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            ctæ, ad rectangulum ſub compoſita ex ſexquialtera tran-
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            ſuerſi lateris hyperbolæ ſecundò dictæ, & </s>
            <s xml:id="echoid-s9755" xml:space="preserve">axi, vel diame-
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            tro eiuſdem, & </s>
            <s xml:id="echoid-s9756" xml:space="preserve">ſub compoſita ex tranſuerſo latere, & </s>
            <s xml:id="echoid-s9757" xml:space="preserve">axi,
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            vel diametro hyperbolæ primò dictæ; </s>
            <s xml:id="echoid-s9758" xml:space="preserve">& </s>
            <s xml:id="echoid-s9759" xml:space="preserve">ex ratione paral-
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            lelepipedi ſub altitudine hyperbolæ primò dictæ, baſi ve-
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            rò, baſis eiuſdem quadrato ad parallelepipedum ſub alti-
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            tudine hyperbolæ ſecundò dictæ, baſiq; </s>
            <s xml:id="echoid-s9760" xml:space="preserve">pariter eiuſdem
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            baſis quadrato.</s>
            <s xml:id="echoid-s9761" xml:space="preserve"/>
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            <s xml:id="echoid-s9762" xml:space="preserve">Sit ergo hyperbolæ, ADC, vtcunq: </s>
            <s xml:id="echoid-s9763" xml:space="preserve">baſis, AC, centrum, E, per
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            quod intra eiuſdem aſymptotos, EY, EZ, ductæ ſint, FEDB, HE
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            VI, vtcunq; </s>
            <s xml:id="echoid-s9764" xml:space="preserve">indefinitè productæ, ſit tamen altera earum diameter
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            iam expoſite hyperbolæ, pro alia hyperbola autem conſtituenda,
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            ducta pariter ſit vtcunq: </s>
            <s xml:id="echoid-s9765" xml:space="preserve">intra curuam hyperbolicam, & </s>
            <s xml:id="echoid-s9766" xml:space="preserve">in eandẽ
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            hinc inde producta ipſa, OX, parallela tangenti curuam hyperbo-
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            licam in puncto, V, in quo ipſam, HI, ſecat. </s>
            <s xml:id="echoid-s9767" xml:space="preserve">Dico ergo omnia
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            quadrata hyperbolæ, ADC, regula, AC, ad omnia quadrata hy-
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            perbolæ, OVX, regula, OX, habere rationem compoſitam (ſum-
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            ptis, EF, FM, æqualibus ipſi, ED, &</s>
            <s xml:id="echoid-s9768" xml:space="preserve">, EH, HR, æqualibus ipſi,
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            EV,) ex ratione rectanguli ſub, MB, HI, ad rectangulum ſub, RI,
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            FB; </s>
            <s xml:id="echoid-s9769" xml:space="preserve">& </s>
            <s xml:id="echoid-s9770" xml:space="preserve">ex ratione parallelepipedi ſub altitudine hyperbolæ, </s>
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