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

List of thumbnails

< >
1
1 		2
2
3
3 		4
4
5
5 		6
6
7
7 		8
8
9
9 		10
10
< >
page |< < (45) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div138" type="section" level="1" n="95">
          <p>
            <s xml:id="echoid-s1172" xml:space="preserve">
              <pb o="45" file="0065" n="65" rhead="LIBERI."/>
            DB, ideſt vt, HO, ad, ON, at, vt ſupra, oſtendemus, HO, ad,
              <lb/>
            ON, eſſe vt, HG, ad, NR, ergo, PL, ad, BF, erit vt, HG,
              <lb/>
            ad, NR, erat autem, EL, ad VG, vt, PL, ad, HG, ergo, EL,
              <lb/>
            ad, VG, erit vt, BF, ad, NR, quia verò, BF, ad, NR, eſt vt,
              <lb/>
            DF, ad, OR, (nam, BF, NR, ſunt ſimiliter diuiſæ in punctis,
              <lb/>
            D, O,) ideſt vt, FL, ad, RG, ergo, EL, ad, VG, erit vt, FL,
              <lb/>
            ad, RG, ergo reliqua, EF, ad, VR, erit vt tota, EL, ad, VG,
              <lb/>
            ideſt vt, BF, ad, NR. </s>
            <s xml:id="echoid-s1173" xml:space="preserve">Idem oſtendemus de quibuslibet ductis ip-
              <lb/>
            ſis, EF, VG, parallelis, quę diuidant, BF, NR, ſimiliter ad ean-
              <lb/>
            dem partem, nempè eas, quæ inter ipſas, BF, NR, & </s>
            <s xml:id="echoid-s1174" xml:space="preserve">circuitum
              <lb/>
            figurarum, AE, MV, eodem ordine ſumptæ continentur, eſſe vt
              <lb/>
            ipias, BF, NR, ergo, BF, NR, ſunt incidentes ſimilium figura-
              <lb/>
              <note position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">B. Def. 10.</note>
            rum, MV, AE, & </s>
            <s xml:id="echoid-s1175" xml:space="preserve">ductarum tangentium, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s1176" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div140" type="section" level="1" n="96">
          <head xml:id="echoid-head107" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1177" xml:space="preserve">INnoteſcit exhoe conſequenter duarum ſimilium figurarum, & </s>
            <s xml:id="echoid-s1178" xml:space="preserve">ea-
              <lb/>
            rundem oppoſitarum tangentium, quæ ſuntregulæ homologarum,
              <lb/>
            tum incidentes ſimiliter diuidi ab homologis earundem figurarum, pro-
              <lb/>
            ductis, ſi opus ſit, tum quaſcumque alias, quæ cum homologis angulos
              <lb/>
            continent æquales, vt exempli gratia ipſæ, NR, BF. </s>
            <s xml:id="echoid-s1179" xml:space="preserve">Et vlterius ip-
              <lb/>
            ſas homologas eſſe tum vt quaſuis incidentes, tum vt eiſdem parallelas,
              <lb/>
            ideſt ex. </s>
            <s xml:id="echoid-s1180" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1181" xml:space="preserve">CI, ad, TS, mdum erit vt, PE, ad, HG, ſiue vt, BF, ad,
              <lb/>
            NR, ſed etiam vt, BF, ad quamcumque aliam parallolam ipſi, NR,
              <lb/>
            ductam inter parattelas, MN, VR, nam illa erit æqualis ipſi, NR.
              <lb/>
            </s>
            <s xml:id="echoid-s1182" xml:space="preserve">Patet igitur duarum ſimilium figurarum homologas nedum eſſe vt ea-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s1183" xml:space="preserve">oppoſitarum earundem tangentium, quæ ſunt regulæ homolo-
              <lb/>
            garum, incidentes, ſed etiam vt quaſuis alias inter eaſdem tangentes
              <lb/>
            ductas ipſis incidentibus æquidiſtantes, ſiue ad homologas ſimilium figu-
              <lb/>
            rarum æqualiter inclinatas.</s>
            <s xml:id="echoid-s1184" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div141" type="section" level="1" n="97">
          <head xml:id="echoid-head108" xml:space="preserve">THEOREMA XXII. PROPOS. XXV.</head>
          <p>
            <s xml:id="echoid-s1185" xml:space="preserve">SI quæcunque ſimiles figuræ planæ à rectis lineis deſcti-
              <lb/>
            bantur, quæ ſint earundem homologæ, & </s>
            <s xml:id="echoid-s1186" xml:space="preserve">inter ſe æqua-
              <lb/>
            les; </s>
            <s xml:id="echoid-s1187" xml:space="preserve">ſuperponantur autem ad inuicem ipſæ figuræ, ita vt ea-
              <lb/>
            ſdem deſcribentes rectæ lineæ ſibi congruant, figuræq; </s>
            <s xml:id="echoid-s1188" xml:space="preserve">ſint
              <lb/>
            fimiliter poſitæ, illæ quoque erunt ad inuicem congruentes.</s>
            <s xml:id="echoid-s1189" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1190" xml:space="preserve">Sint ſimiles figuræ planæ, ABXC, EFPG, quæcunq; </s>
            <s xml:id="echoid-s1191" xml:space="preserve">deſcri-
              <lb/>
            ptæ ab earundern homologis, & </s>
            <s xml:id="echoid-s1192" xml:space="preserve">æqualibus rectis lineis, BC, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum