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

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          <p>
            <s xml:id="echoid-s1192" xml:space="preserve">
              <pb o="46" file="0066" n="66" rhead="GEOMETRIÆ"/>
            quæ ita inuicem ſuperponantur, vt, BC, FG, ſibi congruant, & </s>
            <s xml:id="echoid-s1193" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">D. Defin.
                <lb/>
              10.</note>
            ipſæ ſint ſimiliter poſitæ. </s>
            <s xml:id="echoid-s1194" xml:space="preserve">Dico etiam ipſas figuras ad inuicem fore
              <lb/>
            congruentes. </s>
            <s xml:id="echoid-s1195" xml:space="preserve">Sint oppoſitæ tangentes ductæ pro figura, ABXC,
              <lb/>
            ipſæ, AD, XQ, regula, BC, & </s>
            <s xml:id="echoid-s1196" xml:space="preserve">pro figura, EFPG, regula, F
              <lb/>
              <note position="left" xlink:label="note-0066-02" xlink:href="note-0066-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            G, ipſæ, EM, PN, quarum figurarum, ac oppoſitarum tangen-
              <lb/>
            tium ſint quoque incidentes ipſę, DQ, MN, productis verò, BC,
              <lb/>
              <note position="left" xlink:label="note-0066-03" xlink:href="note-0066-03a" xml:space="preserve">B. Def. 10.</note>
            FG, verſus, DQ, MN, illis incidant in punctis, O, R, & </s>
            <s xml:id="echoid-s1197" xml:space="preserve">ſuper-
              <lb/>
            ponatur figura, ABXC, figuræ, EFPG, ita vt, BC, congruat
              <lb/>
            ipſi, FG, & </s>
            <s xml:id="echoid-s1198" xml:space="preserve">ſint ſimiliter poſitę: </s>
            <s xml:id="echoid-s1199" xml:space="preserve">Erunt ergo ipſæ incidentes, DQ,
              <lb/>
              <note position="left" xlink:label="note-0066-04" xlink:href="note-0066-04a" xml:space="preserve">D. Defin.
                <lb/>
              10.</note>
            MN, ad eandem partem figurarum iam ſuperpoſitarum, & </s>
            <s xml:id="echoid-s1200" xml:space="preserve">inuicem
              <lb/>
            parallelæ, vel congruentes, ſed in noſtro caſu erunt congruentes,
              <lb/>
            cum enim vt, BC, ad, FG, ita ſit, DQ, ad, MN, ipſæ verò, B
              <lb/>
            C, FG, ſint ęquales, etiam, DQ, MN, ęquales erunt, ſicut etiam,
              <lb/>
              <note position="left" xlink:label="note-0066-05" xlink:href="note-0066-05a" xml:space="preserve">A. Def. 10.</note>
            CO, GR, (quæ ſunt inter ſe vt, DQ, MN,) ergo cum punctus,
              <lb/>
            B, poſitus ſit in, F, erit, O, in, R, & </s>
            <s xml:id="echoid-s1201" xml:space="preserve">DQ, extenſa ſuper, MN,
              <lb/>
              <figure xlink:label="fig-0066-01" xlink:href="fig-0066-01a" number="33">
                <image file="0066-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0066-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s1202" xml:space="preserve">cum etiam, DO, MR, ſint ęquales
              <lb/>
            punctus, D, erit in, M, ſic autem oſten-
              <lb/>
            demus quoque punctum, Q, cadere in,
              <lb/>
            N, & </s>
            <s xml:id="echoid-s1203" xml:space="preserve">conſequenter, XQ, cadere ſuper,
              <lb/>
            PN, &</s>
            <s xml:id="echoid-s1204" xml:space="preserve">, AD, ſuper, EM, ſi ergo figu-
              <lb/>
            ra, ABXC, cadens ſuper, EFPG, non
              <lb/>
            congruit illi, eſto quod ceciderit, ſi poſ-
              <lb/>
            ſibile eſt vt, FVIG, ita vt ambitus ex-
              <lb/>
            tra ambitum cadat, ſumpto autem quo-
              <lb/>
            cunque puncto, I, qui ſit in ambitu fi-
              <lb/>
            guræ, VFPGI, ſed cadens non in am-
              <lb/>
            bitu figuræ, EFPG, per ipſum duca-
              <lb/>
            tur, TZ, parallela, EM, ſecans, MN,
              <lb/>
            in, Z, ambitum figuræ, VPI, in, V, I, & </s>
            <s xml:id="echoid-s1205" xml:space="preserve">ambitum figuræ, EF
              <lb/>
            PG, in, T, S, erunt autem homologę, VI, TS, & </s>
            <s xml:id="echoid-s1206" xml:space="preserve">inter ſe ęqua-
              <lb/>
              <note position="left" xlink:label="note-0066-06" xlink:href="note-0066-06a" xml:space="preserve">C. Defin.
                <lb/>
              10.</note>
            les cum ſint, vt incidentes, DQ, MN, quæ ſunt ęquales, necnon
              <lb/>
            æquales reliquæ vſq; </s>
            <s xml:id="echoid-s1207" xml:space="preserve">ad incidentes, nempè, SZ, IZ, quod eſt ab-
              <lb/>
              <note position="left" xlink:label="note-0066-07" xlink:href="note-0066-07a" xml:space="preserve">A. Defin.
                <lb/>
              10.</note>
            ſurdum, punctus enim, I, non eſt in S, non ergo cadet ambitus fi-
              <lb/>
            guræ, ABXC, ſuperpoſitę, ipſi, EFPG, vt dictum eſt, extra am-
              <lb/>
            bitum eiuſdem figurę, EFPG, igitur cadet ſuper illius ambitum, & </s>
            <s xml:id="echoid-s1208" xml:space="preserve">
              <lb/>
            ipſę figurę erunt ſibi inuicem congruentes, quod oſtendendum erat.</s>
            <s xml:id="echoid-s1209" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div143" type="section" level="1" n="98">
          <head xml:id="echoid-head109" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1210" xml:space="preserve">EX hoc inſuper colligitur figuras quaſcumq; </s>
            <s xml:id="echoid-s1211" xml:space="preserve">planas ſimiles ab æqua-
              <lb/>
            libus rectis lineis, tanquam ab bomologis, deſcriptas interfé æqua-
              <lb/>
            les eſſe, cum ita ad inuicem ſuperponi poſſint, vt ſibi congruant, </s>
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