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

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          <head xml:id="echoid-head14" xml:space="preserve">PRÆFATIO</head>
          <p style="it">
            <s xml:id="echoid-s56" xml:space="preserve">_N_Eminem profectò mathamaticarum demon-
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            ſtrationum dulceainem, vel primoribus la-
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            bris vix attigiſſe puto, qui (non ſccus ac,
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            mellis in arbore latentis deguſtata paululũ
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            fuauitate, innumera licet ferientibus certa-
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            tim aculeis apium caterua deglutientẽ Vr-
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            ſum agrè arcere poſſunt) ſummarum, qua illas commitantur dif-
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            ficult atum copia crebris velut ictibus obliſtenterepulſus, ad ſatie-
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            catem vſq; </s>
            <s xml:id="echoid-s57" xml:space="preserve">eadem vbiq; </s>
            <s xml:id="echoid-s58" xml:space="preserve">perfundi totis viribus non contendat.
              <lb/>
            </s>
            <s xml:id="echoid-s59" xml:space="preserve">Talia tibi amice Lector, qui melleos hoſce fructus depaſcere con-
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            ſueſti, cuiſdam in Geometriarei admiranda caſu in me orta ſpe-
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            culationis occaſione, parta, huiuſce dulcedinis amore flagranti,
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            libanda propone. </s>
            <s xml:id="echoid-s60" xml:space="preserve">Cum ergo ſolidorum, quæ ex reuolutione circa
              <lb/>
            axim oriuntur, genefim aliquando meditarer, rationemq; </s>
            <s xml:id="echoid-s61" xml:space="preserve">gignẽ. </s>
            <s xml:id="echoid-s62" xml:space="preserve">
              <lb/>
            tium planarum figurarum cum genitis ſolidis compararem, maxi-
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            mè ſanè admirabar quod à propriorum parẽtum conditione adeò
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            natæ figuræ degenerarent, vt aliam omninò ab eiſdem rationem
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            ſequi viderentur. </s>
            <s xml:id="echoid-s63" xml:space="preserve">Cylindrus enim exempli gratia, in eadem ba-
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            ſi, & </s>
            <s xml:id="echoid-s64" xml:space="preserve">circa eundem axim, cum cono conſtitutus, eſt eiuſdem tri-
              <lb/>
              <note symbol="a" position="right" xlink:label="note-0013-01" xlink:href="note-0013-01a" xml:space="preserve">_10. Duod._
                <lb/>
              _Elem._</note>
            vlus, cum tamen ex parallelogrammo trianguli dictum conum
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              <note symbol="b" position="right" xlink:label="note-0013-02" xlink:href="note-0013-02a" xml:space="preserve">_41. Pri._
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              _Elem._</note>
            generantis duplo per reuolutionem oriatur. </s>
            <s xml:id="echoid-s65" xml:space="preserve">Similiter ſi in eadẽ
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            baſi, & </s>
            <s xml:id="echoid-s66" xml:space="preserve">circa eundem axim, bæmiſphærium, vel hamuphæroides,
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            necnon conoides parabolicum, atq; </s>
            <s xml:id="echoid-s67" xml:space="preserve">cylindcus, extiterint, hic erit
              <lb/>
            hæmiſphery, vel hæmiſphæroidis ſexquialter, conoidis verò du-
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              <note symbol="c" position="right" xlink:label="note-0013-03" xlink:href="note-0013-03a" xml:space="preserve">_Coro. I_
                <lb/>
              _34.l 3._</note>
            plus, cum tamen gignens par allelogrammum dictum cylindrum
              <lb/>
              <note symbol="d" position="right" xlink:label="note-0013-04" xlink:href="note-0013-04a" xml:space="preserve">_Cor, I._
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              _51.l.4._</note>
            ad inſcriptum gignentem circulum, ſeu ellipſim, proximèrationẽ
              <lb/>
              <note symbol="e" position="right" xlink:label="note-0013-05" xlink:href="note-0013-05a" xml:space="preserve">_A ch._
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              _de Dim._
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              _Cuc._</note>
            habeat, quam quatuordecim, ad vndecim ad parabolã verò ſit in
              <lb/>
            ratione ſexquialteræ. </s>
            <s xml:id="echoid-s68" xml:space="preserve">Quinimmò & </s>
            <s xml:id="echoid-s69" xml:space="preserve">in planis figuris per reuolu.
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            </s>
            <s xml:id="echoid-s70" xml:space="preserve">
              <note symbol="f" position="right" xlink:label="note-0013-06" xlink:href="note-0013-06a" xml:space="preserve">_Piop. I._
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              _l. 4._</note>
            tionẽ rectarum linearum circa punctum genitis, quales ſunt cir-
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            culi, eandem varietatem licet experiri. </s>
            <s xml:id="echoid-s71" xml:space="preserve">Sicnim plures circuli
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            concentrici intelligantur expoſiti radios habentes ex. </s>
            <s xml:id="echoid-s72" xml:space="preserve">g. </s>
            <s xml:id="echoid-s73" xml:space="preserve">in pro-
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            portione numcrorum ab vnitate deinceps expoſitorum, ipſi circuli
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            non eandem radiorum proportionem conſeruabunt, ſedeam, </s>
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