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

Table of contents

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[451.] THEOREMA XXVI. PROPOS. XXVIII.
Page: 340 (320)
[452.] COROLLARIVM.
Page: 341 (321)
[453.] THEOREMA XXVII. PROPOS. XXIX:
Page: 341 (321)
[454.] A. COROLL. SECTIO I.
Page: 341 (321)
[455.] B. SECTIO II.
Page: 342 (322)
[456.] C. SECTIO III.
Page: 342 (322)
[457.] D. SECTIO IV.
Page: 342 (322)
[458.] E. SECTIO V.
Page: 342 (322)
[459.] THEOREMA XXVIII. PROPOS. XXX.
Page: 343 (323)
[460.] A. COROLL. SECT IO I.
Page: 344 (324)
[461.] B. SECTIO II.
Page: 344 (324)
[462.] C. SECTIO III.
Page: 344 (324)
[463.] D. SECTIO IV.
Page: 344 (324)
[464.] E. SECTIO V.
Page: 345 (325)
[465.] THEOREMA XXIX. PROPOS. XXXI.
Page: 345 (325)
[466.] THEOREMA XXX. PROPOS. XXXII.
Page: 346 (326)
[467.] COROLLARIVM.
Page: 347 (327)
[468.] THEOREMA XXXI. PROPOS. XXXIII.
Page: 347 (327)
[469.] THEOREMA XXXII. PROPOS. XXXIV.
Page: 348 (328)
[470.] COROLLARIVM.
Page: 349 (329)
[471.] THEOREMA XXXIII. PROPOS. XXXV.
Page: 349 (329)
[472.] COROLLARIVM.
Page: 350 (330)
[473.] THEOREMA XXXIV. PROPOS. XXXVI.
Page: 351 (331)
[474.] THEOREMA XXXV. PROPOS. XXXVII.
Page: 352 (332)
[475.] THEOREMA XXXVI. PROP. XXXVIII.
Page: 353 (333)
[476.] THEOREMA XXXVII. PROP. XXXIX.
Page: 354 (334)
[477.] THEOREMA XXXVIII. PROP. XL.
Page: 354 (334)
[478.] COROLLARIVM.
Page: 354 (334)
[479.] THEOREMA XXXIX. PROPOS. XLI
Page: 355 (335)
[480.] THEOREMA XL. PROPOS. XLII.
Page: 356 (336)
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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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