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

Table of contents

< >
[321.] E. SECTIO V.
Page: 236 (216)
[322.] F. SECTIO VI.
Page: 236 (216)
[323.] THEOREMA XI. PROPOS. XII.
Page: 236 (216)
[324.] THEOREMA XII. PROPOS. XIII.
Page: 237 (217)
[325.] COROLLARIVM.
Page: 239 (219)
[326.] THEOREMA XIII. PROPOS. XIV.
Page: 239 (219)
[327.] COROLLARIVM.
Page: 242 (222)
[328.] THEOREMA XIV. PROPOS. XV.
Page: 242 (222)
[329.] ALITER.
Page: 244 (224)
[330.] THEOREMA XV. PROPOS. XVI.
Page: 244 (224)
[331.] THEOREMA XVI. PROPOS. XVII.
Page: 247 (227)
[332.] COROLLARIVM I.
Page: 248 (228)
[333.] COROLLARIVM II.
Page: 249 (229)
[334.] THEOREMA XVII. PROPOS. XVIII.
Page: 249 (229)
[335.] COROLLARIVM.
Page: 251 (231)
[336.] THEOREMA XVIII. PROPOS. XIX.
Page: 251 (231)
[337.] COROLLARIVM.
Page: 252 (232)
[338.] THEOREMA XIX. PROPOS. XX.
Page: 252 (232)
[339.] COROLLARIVM.
Page: 254 (234)
[340.] THEOREMA XX. PROPOS. XXI.
Page: 254 (234)
[341.] COROLLARIVM.
Page: 256 (236)
[342.] THEOREMA XXI. PROPOS. XXII.
Page: 257 (237)
[343.] THEOREMA XXII. PROPOS. XXIII.
Page: 261 (241)
[344.] THEOREMA XXIII. PROPOS. XXIV.
Page: 262 (242)
[345.] THEOREMA XXIV. PROPOS. XXV.
Page: 264 (244)
[346.] THEOREMA XXV. PROPOS. XXVI.
Page: 265 (245)
[347.] THEOREMA XXVI. PROPOS. XXVII.
Page: 267 (247)
[348.] THEOREMA XXVII. PROPOS. XXVIII.
Page: 268 (248)
[349.] THEOREMA XXVIII. PROPOS. XXIX.
Page: 269 (249)
[350.] THEOREMA XXIX. PROPOS. XXX.
Page: 271 (251)
< >
page |< < (302) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div720" type="section" level="1" n="424">
          <p>
            <s xml:id="echoid-s7300" xml:space="preserve">
              <pb o="302" file="0322" n="322" rhead="GEOMETRIÆ"/>
            tionculam, ASB, .</s>
            <s xml:id="echoid-s7301" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7302" xml:space="preserve">exratione, BH, ad, CE, quæ duæ rationes
              <lb/>
              <note position="left" xlink:label="note-0322-01" xlink:href="note-0322-01a" xml:space="preserve">Ex Co-
                <lb/>
              tol.antec.</note>
            componunt rationem parallelepipedi ſub altitudine, BH, baſi re-
              <lb/>
            ctangulo, HOB, vel quadrato, OH, ad parallelepipedum ſub
              <lb/>
            altitudine, CE, baſi rectangulo, HCB, ergo triangulum, HNB,
              <lb/>
            ad portionculam, ASB, eſt vt parallelepipedum ſub altitudine,
              <lb/>
            BH, baſi quadrato, HO, ad parallelepipedum ſub altitudine, C
              <lb/>
            E, baſi rectangulo, HCB, eſt autem, vt dicebatur, triangulum,
              <lb/>
            HNB, ad triangulum, HAB, vt rectangulum, HOB, vel qua-
              <lb/>
            dratum, HO, ad rectangulum, HCB, ideſt ſumpta, HB, com-
              <lb/>
            munialtitudine, vt parallelepipedum ſub altitudine, HB, baſi qua-
              <lb/>
            drato, HO, ad parallelepipedum ſub altitudine, HB baſi rectan-
              <lb/>
            gulo, HCB, ergo, colligendo, triangulum, HNB, ad portion-
              <lb/>
            culam, ASB, cum triangulo, ABH, ſilicet ad trilineum, HAS
              <lb/>
            B, erit vt parallelepipedum ſub altitudine, HB, baſi quadrato, H
              <lb/>
            O, ad parallelepipedum ſub altitudine compoſita ex, HB, CE,
              <lb/>
            baſi rectangulo, HCB; </s>
            <s xml:id="echoid-s7303" xml:space="preserve">vel vt iſtorum quadrupla ſilicet vt paralle-
              <lb/>
            lepipedum ſub eadem altitudine, HB, baſi quadruplo quadrati, H
              <lb/>
            O, ideſt quadrato, HB, ſilicet vt cubus, HB, ad parallelepipedum
              <lb/>
            ſub eadem altitudine compoſita ex, HB, CE, baſi quadruplo re-
              <lb/>
              <note position="left" xlink:label="note-0322-02" xlink:href="note-0322-02a" xml:space="preserve">1.huius.</note>
            ctanguli, HCB. </s>
            <s xml:id="echoid-s7304" xml:space="preserve">Quia verò parabola, HNB, eſt ſexquitertia trian-
              <lb/>
            guli, HNB, ideò erit ad ipſum, vt ſolidum ſexquitertium cubi, H
              <lb/>
            B, ad cubum, HB, eſt autem triangulum, HNB, ad trilineum,
              <lb/>
            HASB, vt cubus, HB, ad parallelepipedum ſub altitudine com-
              <lb/>
            poſita ex, HB, CE, & </s>
            <s xml:id="echoid-s7305" xml:space="preserve">ſub baſi quadruplo rectanguli, HCB, ergo
              <lb/>
              <figure xlink:label="fig-0322-01" xlink:href="fig-0322-01a" number="216">
                <image file="0322-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0322-01"/>
              </figure>
            ex æquali parabola, HNB,
              <lb/>
            ad trilineum, HASB, erit vt
              <lb/>
            ſolidum ſexquitertium cubi, H
              <lb/>
            B, ad parallelepipedum ſub al-
              <lb/>
            titudine compoſita ex, HB, C
              <lb/>
            E, baſi quadruplo rectanguli,
              <lb/>
            HCB; </s>
            <s xml:id="echoid-s7306" xml:space="preserve">vel vt iſtorum ſubſex-
              <lb/>
            quitertia ſilicet vt cubus, HB,
              <lb/>
            ab parallelepipedum ſub ea-
              <lb/>
            dem altitudine compoſita ex,
              <lb/>
            HB, CE, baſi triplo rectan-
              <lb/>
            guli, HCB, eſt enim quadruplum rectanguli, HCB, ſexquiter-
              <lb/>
            tium tripli eiuſdem rectanguli; </s>
            <s xml:id="echoid-s7307" xml:space="preserve">hoc autem conſequens parallelepi-
              <lb/>
              <note position="left" xlink:label="note-0322-03" xlink:href="note-0322-03a" xml:space="preserve">38.1.2.</note>
            pedum poteſt diuidi in parallelepipedum ſub altitudine, CE, baſi
              <lb/>
            triplo rectanguli, HCB, vel baſi rectangulo ſub, BC, & </s>
            <s xml:id="echoid-s7308" xml:space="preserve">tripla,
              <lb/>
            CH, & </s>
            <s xml:id="echoid-s7309" xml:space="preserve">in parallelepipedum ſub altitudine, HB, baſi etiam rectan-
              <lb/>
            gulo ſub, BCH, ter ſumpto, quoniam verò tripla, HC, &</s>
            <s xml:id="echoid-s7310" xml:space="preserve">, CB,
              <lb/>
            CE, ſunt deinceps proportionales, ideò parallelepipedum, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum