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

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        <div xml:id="echoid-div531" type="section" level="1" n="316">
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              <pb o="215" file="0235" n="235" rhead="LIBER III."/>
            quorum latera ſint prædictis diametris parallela, quæ ideò ſunt æquian-
              <lb/>
            gula, vniuerſaliter igitur prædicta ſunt iter ſe, vt parallelogramna re-
              <lb/>
            ctangula, vel æquiangula illis circumſcripta; </s>
            <s xml:id="echoid-s5224" xml:space="preserve">Vnde etiam habetur pa-
              <lb/>
            rallelogramma rectangula illis circumſcripta eſſe, vt parallelogramma
              <lb/>
            æquiangula pariter illis circumſcripta.</s>
            <s xml:id="echoid-s5225" xml:space="preserve"/>
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        <div xml:id="echoid-div532" type="section" level="1" n="317">
          <head xml:id="echoid-head334" xml:space="preserve">COROLL II. A. SECTIO I.</head>
          <note position="right" xml:space="preserve">A.</note>
          <p style="it">
            <s xml:id="echoid-s5226" xml:space="preserve">_H_INC vlterius colligitur, quod quæcunque de binis parallelo-
              <lb/>
            grammis oſtenſa ſunt in Theorem. </s>
            <s xml:id="echoid-s5227" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5228" xml:space="preserve">6. </s>
            <s xml:id="echoid-s5229" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5230" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5231" xml:space="preserve">lib 2. </s>
            <s xml:id="echoid-s5232" xml:space="preserve">præſuppoſitis
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            conditionibus illic conſideratis circa eorum baſes, & </s>
            <s xml:id="echoid-s5233" xml:space="preserve">altitudines, vel
              <lb/>
            circa eorum latera, eadem & </s>
            <s xml:id="echoid-s5234" xml:space="preserve">de ellipſibus verificabuntur eaſdem con-
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            ditiones in proprijs axibus, vel diametris habentibus; </s>
            <s xml:id="echoid-s5235" xml:space="preserve">nam his poſitis
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            parallelogrammaillis circumſcripta, & </s>
            <s xml:id="echoid-s5236" xml:space="preserve">æquiangula habent in ſuis la-
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            teribus, vel in baſi, & </s>
            <s xml:id="echoid-s5237" xml:space="preserve">altitudine eaſdem conditiones, vnde ſicuti di-
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            ctæ concluſiones ſequuntur pro parallelogrammis circumſcriptis, ita
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            etiam verificantur pro inſcriptis ellipſibus, ad quas dicta parallelo-
              <lb/>
            gramma habent eaſdem rationes, vt probatum eſt, quæ igitur hic non
              <lb/>
              <note position="right" xlink:label="note-0235-02" xlink:href="note-0235-02a" xml:space="preserve">_11. Huius._</note>
            ſunt pro ellipſibus ad inuicem comparatis oſtenſa, per ſupracitata
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            Theoremata ſupplentur, pro circulis autem hoc tantum habemus, quod
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            ſint, vt eorum axium, vel (ſimanis dicere) diametrorum quadrata,
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            non aliaque circa eoſdem variatio contingit.</s>
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        <div xml:id="echoid-div534" type="section" level="1" n="318">
          <head xml:id="echoid-head335" xml:space="preserve">B. SECTIO II.</head>
          <note position="right" xml:space="preserve">B.</note>
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            <s xml:id="echoid-s5239" xml:space="preserve">_C_olliguntur ergo hæc de binis ellipſibus .</s>
            <s xml:id="echoid-s5240" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5241" xml:space="preserve">quod quæ ſunt circa ean.
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            </s>
            <s xml:id="echoid-s5242" xml:space="preserve">dem diametrum, ſunt vt reliquæ ſecundæ diametri.</s>
            <s xml:id="echoid-s5243" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div535" type="section" level="1" n="319">
          <head xml:id="echoid-head336" xml:space="preserve">C. SECTIO III.</head>
          <note position="right" xml:space="preserve">C.</note>
          <p style="it">
            <s xml:id="echoid-s5244" xml:space="preserve">_Q_V æcunq; </s>
            <s xml:id="echoid-s5245" xml:space="preserve">ellipſes habent rationem ex axibus, vel diametris con-
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            iugatis, æqualiter ad inuicem inclinatis compoſitam.</s>
            <s xml:id="echoid-s5246" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div536" type="section" level="1" n="320">
          <head xml:id="echoid-head337" xml:space="preserve">D. SECTIO IV.</head>
          <note position="right" xml:space="preserve">D.</note>
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            <s xml:id="echoid-s5247" xml:space="preserve">_E_Llipſes habentes axes, vel diametros coniugatas, quæ æqualiter
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            ſunt inclinatæ, reciprocè reſpondentes, ſunt æquales; </s>
            <s xml:id="echoid-s5248" xml:space="preserve">& </s>
            <s xml:id="echoid-s5249" xml:space="preserve">quæ
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            ſunt æquales, & </s>
            <s xml:id="echoid-s5250" xml:space="preserve">habent axes, vel diametros ad inuicem æqualiter in-
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            clinatas, eaſdem habent reciprocè reſpondentes.</s>
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