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

Page concordance

< >
Scan Original
31 11
32 12
33 13
34 14
35 15
36 16
37 17
38 18
39 19
40 20
41 21
42 22
43 23
44 24
45 25
46 26
47 27
48 28
49 29
50 30
51 31
52 32
53 33
54 34
55 35
56 36
57 37
58 38
59 39
60 40
< >
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