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

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          <pb o="56" file="0076" n="76" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s1458" xml:space="preserve">Hocautem ex Propoſ.</s>
            <s xml:id="echoid-s1459" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1460" xml:space="preserve">huius facilè comprehendemus, ſunt.</s>
            <s xml:id="echoid-s1461" xml:space="preserve">n.
              <lb/>
            </s>
            <s xml:id="echoid-s1462" xml:space="preserve">(ijſdem vtibi conſtructis) duo oppoſita plana parallela tangentia fi-
              <lb/>
            guras, AV, Κ Λ, ipſa, BD, HV; </s>
            <s xml:id="echoid-s1463" xml:space="preserve">LQ, & </s>
            <s xml:id="echoid-s1464" xml:space="preserve">Λ, quibus incidunt pla-
              <lb/>
            na figurarum ſimilium, AV, Κ Λ, ęquè ad eandem partem inclina-
              <lb/>
            ta, quæ ſint nobis tanquam prima, ijſdem autem incidunt etiam ſe-
              <lb/>
            cunda plana prima diuidentia, nempè plana, AGH, KYT, anguli
              <lb/>
            autem, HGV, & </s>
            <s xml:id="echoid-s1465" xml:space="preserve">Υ Λ, ſunt æquales, qui nempè continentur com-
              <lb/>
            munibus ſectionibus primorum, & </s>
            <s xml:id="echoid-s1466" xml:space="preserve">ſecundorum planorum cum pla-
              <lb/>
            nis, HV, & </s>
            <s xml:id="echoid-s1467" xml:space="preserve">Λ, quæ ſunt duo parallelorum planorum, ſimiliter an-
              <lb/>
            guli, AGV, Κ Υ Λ, (contenti communibus ſectionibus primorum,
              <lb/>
            & </s>
            <s xml:id="echoid-s1468" xml:space="preserve">ſecundorum planorum, & </s>
            <s xml:id="echoid-s1469" xml:space="preserve">communibus ſectionib. </s>
            <s xml:id="echoid-s1470" xml:space="preserve">primorum pla-
              <lb/>
            norum, & </s>
            <s xml:id="echoid-s1471" xml:space="preserve">ipſorum, HV, & </s>
            <s xml:id="echoid-s1472" xml:space="preserve">Λ,) ſunt æquales, ſunt.</s>
            <s xml:id="echoid-s1473" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1474" xml:space="preserve">fimilium fi-
              <lb/>
            gurarum, AV, Κ Λ, ergo etiam anguli, AGH, KY &</s>
            <s xml:id="echoid-s1475" xml:space="preserve">, æquales
              <lb/>
            erunt, vt in Propoſ.</s>
            <s xml:id="echoid-s1476" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1477" xml:space="preserve">iam oſtenſum eſt. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">Cum autem figurę, AV,
              <lb/>
            Κ Λ, ſint ſimiles, &</s>
            <s xml:id="echoid-s1479" xml:space="preserve">, AG, KY, latera homologa, erit, AG, ad,
              <lb/>
            GV, vt, KY, ad, Υ Λ, oſtendemus autem eadem ratione, VG, ad,
              <lb/>
            GH, eſſe vt, Λ Υ, ad, Y &</s>
            <s xml:id="echoid-s1480" xml:space="preserve">, ergo ex ęquali, AG, ad, GH, erit vt,
              <lb/>
            KY, ad, Y &</s>
            <s xml:id="echoid-s1481" xml:space="preserve">. Eodem modo probabimus angulos, DVN, Q Λ ℟,
              <lb/>
            ęquales eſſe (ſiue plana, AH, DN; </s>
            <s xml:id="echoid-s1482" xml:space="preserve">K &</s>
            <s xml:id="echoid-s1483" xml:space="preserve">, Q ℟, ſint parallela, ſiue
              <lb/>
            non, hoc.</s>
            <s xml:id="echoid-s1484" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1485" xml:space="preserve">nihil refert) & </s>
            <s xml:id="echoid-s1486" xml:space="preserve">circa eos latera eſſe proportionalia, quod
              <lb/>
            oſtendere opus erat.</s>
            <s xml:id="echoid-s1487" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div159" type="section" level="1" n="107">
          <head xml:id="echoid-head118" xml:space="preserve">LEMMA III.</head>
          <p>
            <s xml:id="echoid-s1488" xml:space="preserve">SI in ſimilibus rectilineis figuris, iuxta Euclidem, ducantur rectæ
              <lb/>
            lineæ quęcumque, earundem latera homologa ſimiliter ad ean-
              <lb/>
            dem partem diuidentes, ipſę diuident eaſdem in ſimiles figuras, ſimi-
              <lb/>
            les autem erunt, quę ad eandem partem diuidentium linearum con-
              <lb/>
            ſtituentur, & </s>
            <s xml:id="echoid-s1489" xml:space="preserve">ipſæ ſecantes earundem erunt homologa latera.</s>
            <s xml:id="echoid-s1490" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1491" xml:space="preserve">Sint ſimiles rectilineæ figuræ iuxta Euclidem,
              <lb/>
              <figure xlink:label="fig-0076-01" xlink:href="fig-0076-01a" number="38">
                <image file="0076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0076-01"/>
              </figure>
            ACED, GMNH, quibus incidant rectæ, B
              <lb/>
            F, IO, ſecantes latera homologa, AC, GM;
              <lb/>
            </s>
            <s xml:id="echoid-s1492" xml:space="preserve">necnon, DE, HN, ſimiliter ad eandem pa-
              <lb/>
            tem, vt, AC, GM, in punctis, B, I, &</s>
            <s xml:id="echoid-s1493" xml:space="preserve">, DE,
              <lb/>
            HN, in punctis, F, O. </s>
            <s xml:id="echoid-s1494" xml:space="preserve">Dico figuras ab eiſdem
              <lb/>
            conſtitutas ad eandem partem, nempè, BAD
              <lb/>
            F, IGHO; </s>
            <s xml:id="echoid-s1495" xml:space="preserve">BCEF, IMNO, inter ſe ſimi-
              <lb/>
            les eſſe. </s>
            <s xml:id="echoid-s1496" xml:space="preserve">Ducantur à punctis, B, I, ad angulos
              <lb/>
            oppoſitos rectæ lineæ, BD, BE, IH, IN, vt
              <lb/>
            ſi figuræ ſint quadrilateræ, vel multilateræ, in
              <lb/>
            triangula diſceparentur. </s>
            <s xml:id="echoid-s1497" xml:space="preserve">Quoniam ergo, AC,
              <lb/>
            GM, ſimiliter diuiduntur in, B, I, erit, BA, ad, IG, vt, AC, </s>
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