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

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              <pb o="57" file="0077" n="77" rhead="LIBER I."/>
            GM, ideſt, vt, AD, ad, GH, ergo permutando, BA, ad, AD,
              <lb/>
              <note position="right" xlink:label="note-0077-01" xlink:href="note-0077-01a" xml:space="preserve">6. Sextr
                <lb/>
              Elem.</note>
            erit vt, IG, ad, GH, & </s>
            <s xml:id="echoid-s1498" xml:space="preserve">anguli, BAD, IGH, ſunt æquales, er-
              <lb/>
            go, BAD, IGH, erunt triangula ſimilia, ergo anguli, ADB, G
              <lb/>
            HI, æquales erunt, ſunt autem ęquales etiam, ADF, GHO, er-
              <lb/>
            go reliqui, BDF, IHO, erunt æquales, eſt verò, BD, ad, DA,
              <lb/>
            vt, IH, ad, HG, &</s>
            <s xml:id="echoid-s1499" xml:space="preserve">, AD, ad, DF, vt, GH, ad, HO, ergo ex
              <lb/>
            æquali, BD, ad, DF, eſt vt, IH, ad, HO, ergo triangula, BD
              <lb/>
            F, IHO, pariter ſimilia erunt, & </s>
            <s xml:id="echoid-s1500" xml:space="preserve">anguli, DFB, HOI, inter ſe,
              <lb/>
            necnon, DBF, HIO, inter ſe ęquales, ergo anguli, ABF, GIO,
              <lb/>
            ADF, GHO, erunt etiam ęquales, & </s>
            <s xml:id="echoid-s1501" xml:space="preserve">figurę, ABFD, GIOH,
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            æquiangulę, & </s>
            <s xml:id="echoid-s1502" xml:space="preserve">cum, BA, ad, DF, FB, binæ ſint in eadem ratio-
              <lb/>
            ne cum, IG, GH, HO, OI, patet, quod etiam circa ęquales an-
              <lb/>
            gulos ſunt latera proportionalia, ergo ipſæ figuræ, BADF, IG
              <lb/>
            HO, ſimiles erunt. </s>
            <s xml:id="echoid-s1503" xml:space="preserve">Eodem autem modo oſtendemus ſimiles eſſe, B
              <lb/>
            CEF, IMNO, patet autem ipſas, BF, IO, eſſe earum latera ho-
              <lb/>
            mologa, quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1504" xml:space="preserve"/>
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        <div xml:id="echoid-div161" type="section" level="1" n="108">
          <head xml:id="echoid-head119" xml:space="preserve">LEMMA IV.</head>
          <p>
            <s xml:id="echoid-s1505" xml:space="preserve">SI in ſimilibus ſolidis planis contentis iuxta def.</s>
            <s xml:id="echoid-s1506" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1507" xml:space="preserve">vndec. </s>
            <s xml:id="echoid-s1508" xml:space="preserve">Elem.
              <lb/>
            </s>
            <s xml:id="echoid-s1509" xml:space="preserve">quatuor quęlibet puncta ſumantur in vnoquoq; </s>
            <s xml:id="echoid-s1510" xml:space="preserve">eorundem (non
              <lb/>
            tamen in eodem plano conſtituta) ad quę anguli ſolidi æquales ter-
              <lb/>
            minantur, illaq; </s>
            <s xml:id="echoid-s1511" xml:space="preserve">iungatur rectis lineis, fient ſimiles pyramides trian-
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              <note position="right" xlink:label="note-0077-02" xlink:href="note-0077-02a" xml:space="preserve">Defin, 1.
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              @ti El.</note>
            gulatæ comprehenſæ ſub triangulis, ijſdem rectis lineis iungentibus
              <lb/>
            contentis.</s>
            <s xml:id="echoid-s1512" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1513" xml:space="preserve">Sint ſimilia ſolida, AHCD, FO
              <lb/>
              <figure xlink:label="fig-0077-01" xlink:href="fig-0077-01a" number="39">
                <image file="0077-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0077-01"/>
              </figure>
            GL, iuxta def.</s>
            <s xml:id="echoid-s1514" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1515" xml:space="preserve">vndec. </s>
            <s xml:id="echoid-s1516" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s1517" xml:space="preserve">& </s>
            <s xml:id="echoid-s1518" xml:space="preserve">in
              <lb/>
            ijs accepta quatuor quęcumq; </s>
            <s xml:id="echoid-s1519" xml:space="preserve">pun-
              <lb/>
            cta, nempè, A, H, C, D, in vno,
              <lb/>
            &</s>
            <s xml:id="echoid-s1520" xml:space="preserve">, F, O, G, L, in alio ſolido, quæ
              <lb/>
            non ſint in eodem plano, ſed ad an-
              <lb/>
            gulos ęquales conſtituta, iungantur-
              <lb/>
            querectis lineis, AH, AC, CD, C
              <lb/>
              <figure xlink:label="fig-0077-02" xlink:href="fig-0077-02a" number="40">
                <image file="0077-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0077-02"/>
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            H, HD; </s>
            <s xml:id="echoid-s1521" xml:space="preserve">FO, FG, FL, OG, G
              <lb/>
            L, LO, ſiue hęc iungentia ſint ipſo-
              <lb/>
            rum ſimilium ſolidorum latera. </s>
            <s xml:id="echoid-s1522" xml:space="preserve">Di-
              <lb/>
            copyramides, AHCD, FOGL,
              <lb/>
            ſimiles eſſe. </s>
            <s xml:id="echoid-s1523" xml:space="preserve">Vel ergo plana has py-
              <lb/>
            ramides continentia ſunt in ambitu
              <lb/>
            ſolidorum, vt ex.</s>
            <s xml:id="echoid-s1524" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1525" xml:space="preserve">CHD, GOL, & </s>
            <s xml:id="echoid-s1526" xml:space="preserve">tunc erunt ſimilia, ex ipſa de-
              <lb/>
            finitione, vel non ſunt in ambitu, tunc autem probandum eſt nihi-
              <lb/>
            lominus eſſe ſimilia, vt non ſint in ambitu ipſa triangula, ACH, </s>
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