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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              <pb o="493" file="0513" n="513" rhead="LIBER VII."/>
            tem rectæ, DF, vel nihil eſt ſaltem ad alteram partem, ſi enim ali-
              <lb/>
            qua illius portio eſſet ad alteram partem rectæ, DF, iam recta, D
              <lb/>
            F, ſecaret figuram, BAC, quod eſt abſurdum, ergorecta, DF, tan-
              <lb/>
            git curuam, BAC, igitur poſſibile eſt, &</s>
            <s xml:id="echoid-s12595" xml:space="preserve">c.</s>
            <s xml:id="echoid-s12596" xml:space="preserve"/>
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        <div xml:id="echoid-div1147" type="section" level="1" n="687">
          <head xml:id="echoid-head720" xml:space="preserve">COROLL ARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s12597" xml:space="preserve">_H_Inc manifeſtum eſt quomodo ducenda ſit recta linea datam cur-
              <lb/>
            uam totam in eodem plano cum ea exiſtentem contingens, quæ
              <lb/>
            quidem data recta linea ſit æquidiſtans.</s>
            <s xml:id="echoid-s12598" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1148" type="section" level="1" n="688">
          <head xml:id="echoid-head721" xml:space="preserve">LEMMA IV.</head>
          <p>
            <s xml:id="echoid-s12599" xml:space="preserve">SI propoſita quæcumque figura plana vni regulæ paral-
              <lb/>
            lelis quotcumque lineis ita ſecari poſſit, vt conceptæ
              <lb/>
            in figura rectæ lineæ integræ ſemper exiſtant: </s>
            <s xml:id="echoid-s12600" xml:space="preserve">Ipſa ex pa-
              <lb/>
            rallelogrammis rectilineis, aut curuilineis, ſeu ex figuris
              <lb/>
            in alteram partem deficientibus, regula eadem, compo-
              <lb/>
            netur.</s>
            <s xml:id="echoid-s12601" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12602" xml:space="preserve">Sit quæcumque figura plana, SPFR, talis tamen, vt ſecta quot-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s12603" xml:space="preserve">vni regulæ, vt, FE, parallelis, conceptæ in ipſa rectæ lineę
              <lb/>
            integræ ſint. </s>
            <s xml:id="echoid-s12604" xml:space="preserve">Dico ipſam, velex parallelogrammis rectilineis, aut
              <lb/>
              <figure xlink:label="fig-0513-01" xlink:href="fig-0513-01a" number="343">
                <image file="0513-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0513-01"/>
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            curuilineis, vel ex figuris in al-
              <lb/>
            teram partem deficientibus,
              <lb/>
            reg. </s>
            <s xml:id="echoid-s12605" xml:space="preserve">eadem, FE, componi.
              <lb/>
            </s>
            <s xml:id="echoid-s12606" xml:space="preserve">Sint enim ductæ, SA, FE, op-
              <lb/>
            poſitæ tangentes figuræ, SPF
              <lb/>
            R, regula eadem, FE, quibus
              <lb/>
            incidat quomodocumq; </s>
            <s xml:id="echoid-s12607" xml:space="preserve">recta
              <lb/>
            linea, AE, moueatur autem, F
              <lb/>
              <note position="right" xlink:label="note-0513-01" xlink:href="note-0513-01a" xml:space="preserve">1. lib. 1</note>
            E, verſus, SA, ſemperæquidi-
              <lb/>
            ſtanter eidem, SA, donec illi
              <lb/>
            congruat, interim verò punctum, E, ita in ipſa feratur, vt deſcri-
              <lb/>
            bat lineam, ENA, cum, AE, figuram, ANE, comprehenden@em,
              <lb/>
            quæ eidem, SPFR, ſit æqualiter analoga iuxta regulam, FE; </s>
            <s xml:id="echoid-s12608" xml:space="preserve">in
              <lb/>
            eadem integris exiſtentibus parallelis ipſi, FE, ad ambitum, ANE,
              <lb/>
            terminantibus: </s>
            <s xml:id="echoid-s12609" xml:space="preserve">rurſus feratur recta linea, AE, verſus ambitum, A
              <lb/>
            NE, ſemper ipſi, AE, æquidiſtanter donec totam pertranſierit fi-
              <lb/>
            guram, ANE, adnotentur autem contactus lineæ ſic </s>
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