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

Table of Notes

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        <div xml:id="echoid-div180" type="section" level="1" n="118">
          <head xml:id="echoid-head129" xml:space="preserve">DEFINITIO.</head>
          <p>
            <s xml:id="echoid-s1803" xml:space="preserve">SImiles coni, & </s>
            <s xml:id="echoid-s1804" xml:space="preserve">cylindriſunt, quorum & </s>
            <s xml:id="echoid-s1805" xml:space="preserve">axes, & </s>
            <s xml:id="echoid-s1806" xml:space="preserve">baſium diame-
              <lb/>
            tri eandem inter ſe proportionem habent. </s>
            <s xml:id="echoid-s1807" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s1808" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1809" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1810" xml:space="preserve">Elem.
              <lb/>
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            <s xml:id="echoid-s1811" xml:space="preserve">defin. </s>
            <s xml:id="echoid-s1812" xml:space="preserve">24.</s>
            <s xml:id="echoid-s1813" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1814" xml:space="preserve">Verum, quia ſupradicta definitonon
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            eſt niſi cylindrorum, & </s>
            <s xml:id="echoid-s1815" xml:space="preserve">conorum re-
              <lb/>
            ctorum, ideo aliam, quę affertur à Com-
              <lb/>
            mandino tum de rectis, tum etiam de
              <lb/>
            ſcalenis illi ſubiungo, quam ſufficiet o-
              <lb/>
            ſtendere cum mea ſuptadicta concor-
              <lb/>
            dare, nam hęcCommandinieam, quam
              <lb/>
            Euclides attulit, inuoluit.</s>
            <s xml:id="echoid-s1816" xml:space="preserve"/>
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        <div xml:id="echoid-div182" type="section" level="1" n="119">
          <head xml:id="echoid-head130" xml:space="preserve">DEFINITIO.</head>
          <p>
            <s xml:id="echoid-s1817" xml:space="preserve">SImiles coni, & </s>
            <s xml:id="echoid-s1818" xml:space="preserve">cylindri, ſiue recti, ſiue ſcaleni ſunt, quando per
              <lb/>
            axes ductis planis ad rectos angulos baſibus, communes ſectio-
              <lb/>
            nes eorum, & </s>
            <s xml:id="echoid-s1819" xml:space="preserve">baſium cum axibus æquales angulos continentes, ean-
              <lb/>
            dem inter ſe, quam axes, proportionem habent: </s>
            <s xml:id="echoid-s1820" xml:space="preserve">Commandinus lo-
              <lb/>
            co definitionis ſupra citatæ.</s>
            <s xml:id="echoid-s1821" xml:space="preserve"/>
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            <s xml:id="echoid-s1822" xml:space="preserve">Sint coni, BEC, GMN, & </s>
            <s xml:id="echoid-s1823" xml:space="preserve">cylindri, AC, FN, ſimiles iuxta
              <lb/>
              <note position="right" xlink:label="note-0091-01" xlink:href="note-0091-01a" xml:space="preserve">Defin. 11.</note>
            proximam definitionem. </s>
            <s xml:id="echoid-s1824" xml:space="preserve">Dico eoſdem eſſe ſimiles iuxta meam ſu-
              <lb/>
            pradictam. </s>
            <s xml:id="echoid-s1825" xml:space="preserve">Vt autem in ſimul pro conis, & </s>
            <s xml:id="echoid-s1826" xml:space="preserve">cylindris fiat demon-
              <lb/>
            ſtratio, ſupponanturconi, & </s>
            <s xml:id="echoid-s1827" xml:space="preserve">cylindri iam dicti eſſe in eiſdem baſi-
              <lb/>
            bus, & </s>
            <s xml:id="echoid-s1828" xml:space="preserve">circa eoſdem axes; </s>
            <s xml:id="echoid-s1829" xml:space="preserve">ducantur ergo in ipſis plana per axes, qui
              <lb/>
            ſint, EO, MR, quoniam ergo latera cylindrorum ſunt ſuis axibus
              <lb/>
            parallela, ideò dicta plana tranſibunt per latera cylindrorum, ſiue
              <lb/>
              <note position="right" xlink:label="note-0091-02" xlink:href="note-0091-02a" xml:space="preserve">Ex. def. 3.
                <lb/>
              & 4. Cor.</note>
            cylindricorum, AC, FN, & </s>
            <s xml:id="echoid-s1830" xml:space="preserve">per latera conorum, ſiue conicorum,
              <lb/>
            EBC, MGN, quia per eorum vertices intra ipſos ducuntur, ſint
              <lb/>
            autem dicta plana ea, quę ſint ad rectos angulos baſibus, quorum & </s>
            <s xml:id="echoid-s1831" xml:space="preserve">
              <lb/>
            baſium communes ſectiones, quæ ſint, BC, GN, cum axibus æ-
              <lb/>
            quales angulos continentes eandem interſe, quam axes proportio-
              <lb/>
            nem habeant, vt fert definitio, fient igitur in cylindricis parallelo-
              <lb/>
            gramma, vt, AC, FN, & </s>
            <s xml:id="echoid-s1832" xml:space="preserve">in conicis triangula, vt, BEC, GMN,
              <lb/>
              <note position="right" xlink:label="note-0091-03" xlink:href="note-0091-03a" xml:space="preserve">Ex Cor. 5.
                <lb/>
              & ex 16.
                <lb/>
              huius.</note>
            & </s>
            <s xml:id="echoid-s1833" xml:space="preserve">quia anguli, BOE, GRM, ſunt ęquales, ideò etiam ipſi, BCD,
              <lb/>
            GNH, ſunt æquales, & </s>
            <s xml:id="echoid-s1834" xml:space="preserve">eſt, BC, ad, CD, vt, GN, ad, NH,
              <lb/>
            ideò parallelogramma, AC, FN, & </s>
            <s xml:id="echoid-s1835" xml:space="preserve">triangula, BEC, GMN, e-
              <lb/>
            runt ſimilia iuxta definitionem Euclidis, & </s>
            <s xml:id="echoid-s1836" xml:space="preserve">ideò etiam iuxta meam,
              <lb/>
            & </s>
            <s xml:id="echoid-s1837" xml:space="preserve">quia ipſæ, AD, BC, FH, GN, tangunt figuras, AC, FN,
              <lb/>
              <note position="right" xlink:label="note-0091-04" xlink:href="note-0091-04a" xml:space="preserve">27. huius.</note>
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