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

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          <pb o="52" file="0072" n="72" rhead="GEOMETRIÆ"/>
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        <div xml:id="echoid-div150" type="section" level="1" n="101">
          <head xml:id="echoid-head112" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1338" xml:space="preserve">_Q_Via verò oppoſitæ tangentes, AH, DF, MN, RQ, ductæ ſunt
              <lb/>
            vtcumque, angulos tamen æquales ad eandem partem cum homo-
              <lb/>
            logis lateribus continentes, ideò quaſcumq; </s>
            <s xml:id="echoid-s1339" xml:space="preserve">duxerimus oppoſitas
              <lb/>
            tangentes in figuris rectilineis ſimilibus iuxta Euclidem, dummodo fa-
              <lb/>
            ciant angulos æquales ad eandem partem cum lateribus homologis, ea-
              <lb/>
            ſdem eſſe regulas homologarum ſimilium figurarum poterit probari.</s>
            <s xml:id="echoid-s1340" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div151" type="section" level="1" n="102">
          <head xml:id="echoid-head113" xml:space="preserve">THEOREMA XXV. PROPOS. XXVIII.</head>
          <p>
            <s xml:id="echoid-s1341" xml:space="preserve">POſita infraſcripta definitione ſimilium portionum ſectio-
              <lb/>
            num coni, illi adiuncti, quod infra dicetur, ſequitur
              <lb/>
            pro ipſis etiam mea definitio generalis ſimilium planarum fi-
              <lb/>
            gurarum. </s>
            <s xml:id="echoid-s1342" xml:space="preserve">Hoc autem dico pro ſpatijs ſub ipſis ſectionibus,
              <lb/>
            & </s>
            <s xml:id="echoid-s1343" xml:space="preserve">rectis lineis contentis, non autem pro ipſis tanquam lineis,
              <lb/>
            licet crediderim Apolloniũ ipſarum ſimilium ſectionum tan-
              <lb/>
            quam linearum, non autem figurarum, quę fiunt ab ipſis, ſi-
              <lb/>
            militudinem attendiſſe, ego verò ipſam recipio tanquam ip-
              <lb/>
            ſarum figurarum ſimilitudini congruam, dum illi adiungitur,
              <lb/>
            quod in ipſa Propoſ. </s>
            <s xml:id="echoid-s1344" xml:space="preserve">explicatur.</s>
            <s xml:id="echoid-s1345" xml:space="preserve"/>
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        <div xml:id="echoid-div152" type="section" level="1" n="103">
          <head xml:id="echoid-head114" xml:space="preserve">DEFINITIO.</head>
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            <s xml:id="echoid-s1346" xml:space="preserve">SImiles portiones ſectionum coni ſunt, in quarum ſingulis ductis
              <lb/>
            lineis baſi parallelis numero æqualibus, ſunt ipſæ parallelæ, & </s>
            <s xml:id="echoid-s1347" xml:space="preserve">
              <lb/>
            baſes ad abſciſſas diametrorum partes ſumptas à verticibus, in ijſdem
              <lb/>
            rationibus, tumabſciſſæ ipſæ ad abſciſſas: </s>
            <s xml:id="echoid-s1348" xml:space="preserve">Apollonius lib.</s>
            <s xml:id="echoid-s1349" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1350" xml:space="preserve">Coni-
              <lb/>
            corum, vt refert Eutocius.</s>
            <s xml:id="echoid-s1351" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1352" xml:space="preserve">Sint ſimiles portiones ſectionum coni, DAF, QRK, in baſibus,
              <lb/>
            DF, QK, quarum diametri ſint ipſæ, AE, RG, ſecentur autem
              <lb/>
            ſimiliter ipſæ diametri in punctis, N, O; </s>
            <s xml:id="echoid-s1353" xml:space="preserve">V, X; </s>
            <s xml:id="echoid-s1354" xml:space="preserve">& </s>
            <s xml:id="echoid-s1355" xml:space="preserve">ſit, D F, ad, E
              <lb/>
            A, vt, Q K, ad, G R, &</s>
            <s xml:id="echoid-s1356" xml:space="preserve">, C H, ad, O A, vt, T L, ad, X R, &</s>
            <s xml:id="echoid-s1357" xml:space="preserve">, P
              <lb/>
            M, ad, N A, vt, S P, ad, V R; </s>
            <s xml:id="echoid-s1358" xml:space="preserve">has igitur Apollonius in ſupradicta
              <lb/>
            definitione ſimiles vocat, mihi autem hoc opus eſt illi adiungere.</s>
            <s xml:id="echoid-s1359" xml:space="preserve">ſ.
              <lb/>
            </s>
            <s xml:id="echoid-s1360" xml:space="preserve">quod anguli baſibus, & </s>
            <s xml:id="echoid-s1361" xml:space="preserve">diametris, ad eandem partem contenti ſint
              <lb/>
            æquales, vt angulus, A E D, ipſi, R G Q, ſi.</s>
            <s xml:id="echoid-s1362" xml:space="preserve">u. </s>
            <s xml:id="echoid-s1363" xml:space="preserve">hoc non ponatur
              <lb/>
            poſſet contingere eſſe baſes, D F, Q K, æquales, & </s>
            <s xml:id="echoid-s1364" xml:space="preserve">ipſas, A E, R
              <lb/>
            G, in quo caſu tot figuras ſimiles, & </s>
            <s xml:id="echoid-s1365" xml:space="preserve">æquales, ex. </s>
            <s xml:id="echoid-s1366" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1367" xml:space="preserve">ipſi, A D </s>
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