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

Table of contents

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[421.] THEOREMA X. PROPOS. XI.
Page: 318 (298)
[422.] COROLLARIV M.
Page: 320 (300)
[423.] THEOREMA XI. PROPOS. XII.
Page: 320 (300)
[424.] THEOREMA XII. PROPOS. XIII.
Page: 321 (301)
[425.] THEOREMA XIII. PROPOS. XIV.
Page: 323 (303)
[426.] THEOREMA XIV. PROPOS. XV.
Page: 324 (304)
[427.] THEOREMA XV. PROPOS. XVI.
Page: 325 (305)
[428.] THEOREMA XVI. PROPOS. XVII.
Page: 325 (305)
[429.] COROLLARIVM.
Page: 327 (307)
[430.] THEOREMA XVII. PROPOS. XVIII.
Page: 327 (307)
[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
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            drato, ZS, (quæ habetur, productis, ZC, OI, donec ſibi
              <lb/>
            occurrant, vt in, S,) ad parallelepipedum bis ſub, LT, & </s>
            <s xml:id="echoid-s10523" xml:space="preserve">
              <lb/>
            quadrato, TO, cum cubo, TO, & </s>
            <s xml:id="echoid-s10524" xml:space="preserve">amplius @. </s>
            <s xml:id="echoid-s10525" xml:space="preserve">eiuſdem cubi.</s>
            <s xml:id="echoid-s10526" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10527" xml:space="preserve">Producatur, OL, indefinitè, cui occurrat, SG, ducta per, S, ipſi,
              <lb/>
            ZO, æquidiſtans, & </s>
            <s xml:id="echoid-s10528" xml:space="preserve">occurſus ſit in puncto, G, & </s>
            <s xml:id="echoid-s10529" xml:space="preserve">per, T, ipſa, MT,
              <lb/>
            æquidiſtans ducatur ipſi, AV, & </s>
            <s xml:id="echoid-s10530" xml:space="preserve">per, V, VM, æquidiſtans ipſi, V
              <lb/>
            T, quæ tangent ſectiones in punctis, VT, & </s>
            <s xml:id="echoid-s10531" xml:space="preserve">conuenient interſe
              <lb/>
            in aſymptoto, OS, vt in, M, vt ex pri. </s>
            <s xml:id="echoid-s10532" xml:space="preserve">Secundi Conicorum elici
              <lb/>
            poteſt: </s>
            <s xml:id="echoid-s10533" xml:space="preserve">Omnia ergo quadrata, FC, ad omnia quadrata figuræ,
              <lb/>
            FADCVE, vel omnia quadrata, RC, ad omnia quadrata figuræ,
              <lb/>
              <note position="right" xlink:label="note-0425-01" xlink:href="note-0425-01a" xml:space="preserve">21. huius.</note>
            DAVC, ſunt vt quadratum, DC, ad quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10534" xml:space="preserve">qua-
              <lb/>
            drati, kI, ſiue vt quadratum, CL, ad quadratum, OV, vel, TM,
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            cum {1/3}. </s>
            <s xml:id="echoid-s10535" xml:space="preserve">quadrati, LI, quia verò quadratum, CL, vel, SG, ad qua-
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            dratum, MT, eſt vt quadratum, GO, ad quadratum, OT, & </s>
            <s xml:id="echoid-s10536" xml:space="preserve">qua-
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            dratum, GS, ad quadratum, LI, eſt vt quadratum, GO, ad quadra-
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            tum, OL, ideo quadratum, SG, ad quadratum, TM, vel, OV, cum
              <lb/>
            {1/3}. </s>
            <s xml:id="echoid-s10537" xml:space="preserve">quadrati, LI, erit vt quadratum, GO, ad quadratum, OT, cum
              <lb/>
            {1/3}. </s>
            <s xml:id="echoid-s10538" xml:space="preserve">quadrati, OL, ſiue vt triplum quadrat, GO, ad quadratum, LO,
              <lb/>
            cum tribus quadratis, OT, vel ſumpta, ’LO, communi altitudine,
              <lb/>
            vt parallelepipedum ſub, LO, & </s>
            <s xml:id="echoid-s10539" xml:space="preserve">triplo quadrati, OG, ad paralle-
              <lb/>
            le ipedum ſub, LO, & </s>
            <s xml:id="echoid-s10540" xml:space="preserve">quadrato, OL, cum triplo quadrati, OT,
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            ſic igitur erunt omnia quadrata, RC, ad omnia quadrata figuræ,
              <lb/>
            DAVC, quod ſerua.</s>
            <s xml:id="echoid-s10541" xml:space="preserve"/>
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            <s xml:id="echoid-s10542" xml:space="preserve">Inſuper omnia quadrata, RC, ad omnia quadrata trianguli, K
              <lb/>
            OI, ſunt vt quadratum, DC, ad {1/3}. </s>
            <s xml:id="echoid-s10543" xml:space="preserve">quadrati, kI, vel vt quadratum,
              <lb/>
            CL, vel quadratum, GS, ad {1/3}. </s>
            <s xml:id="echoid-s10544" xml:space="preserve">quadrati, LI, vel vt quadratum, G
              <lb/>
            O, ad {1/3}. </s>
            <s xml:id="echoid-s10545" xml:space="preserve">quadrati, OL, vel vt trip um quadrati, GO, ad quadra-
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            tum, OL, Vel, ſump@@, OL, communi altitudine, vt parallelepipe-
              <lb/>
            dum ſub, LO, & </s>
            <s xml:id="echoid-s10546" xml:space="preserve">triplo quadrati, CG, ad parallelepipedum ſub L
              <lb/>
            O, & </s>
            <s xml:id="echoid-s10547" xml:space="preserve">quadrato, LO, .</s>
            <s xml:id="echoid-s10548" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10549" xml:space="preserve">ad cubum, LO. </s>
            <s xml:id="echoid-s10550" xml:space="preserve">Vlterius omnia quadra
              <lb/>
              <note position="right" xlink:label="note-0425-02" xlink:href="note-0425-02a" xml:space="preserve">9. huius.</note>
            ta trianguli, KOI, ad omnia quadrata hyperbolæ, HTN, ſunt vt
              <lb/>
            cubus, LO, ad parallelepipedum ter ſub, OT, & </s>
            <s xml:id="echoid-s10551" xml:space="preserve">quadrato, TL, cũ
              <lb/>
            cubo, TL, ergo, ex æquali, omnia quadrata, RC, ad omnia qua-
              <lb/>
            drata hyperbolæ, HTN, erunt vt parallelepipedum ſub, LO, & </s>
            <s xml:id="echoid-s10552" xml:space="preserve">
              <lb/>
            triplo quadrati, OG, ad parallelepipedum ter ſub, OT, & </s>
            <s xml:id="echoid-s10553" xml:space="preserve">qua-
              <lb/>
            drato, TL, cum cubo, TL, erant autem omnia quadrata, RC, ad
              <lb/>
            omnia quadrata figurę, DAVC, vt idem parallelepipedum ſub, L
              <lb/>
            O, & </s>
            <s xml:id="echoid-s10554" xml:space="preserve">triplo quadrati, OG, ad parallelepipedum ſub, LO, & </s>
            <s xml:id="echoid-s10555" xml:space="preserve">qua-
              <lb/>
            drato, OL, cuin triplo quadrati, OT, ergo omnia quadrata, RC,
              <lb/>
            ad omnia quadrata figuræ, DAVC, demptis omnibus </s>
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