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

Table of contents

< >
[511.] SECTIO POSTERIOR.
[512.] COROLLARIVM XI.
[513.] COROLL. XII. SECTIO PRIOR.
[514.] SECTIO POSTERIOR,
[515.] COROLL. XIII. SECTIO PRIOR.
[516.] SECTIO POSTERIOR.
[517.] COROLLARIVM XIV.
[518.] COROLLARIVM XV.
[519.] COROLLARIVM XVI.
[520.] COROLLARIVM XVII.
[521.] COROLL XVIII. SECTIO PRIOR.
[522.] SECTIO POSTERIOR.
[523.] COROLLARIVM XIX.
[524.] COROLLARIVM XX.
[525.] COROLLARIVM XXI.
[526.] COROLLARIVM XXII.
[527.] COROLLARIVM XXIII.
[528.] COROLLARIVM XXIV.
[529.] COROLLARIVM XXV.
[530.] COROLLARIVM XXVI.
[531.] COROLLARIVM XXVII.
[532.] SCHOLIV M.
[533.] Finis quarti Libri.
[534.] GEOMETRIÆ CAVALERII. LIBER QVINTVS. In quo de Hyperbola, Oppoſitis Sectionib us, ac ſolidis ab eiſdem genitis, babetur contemplatio. THEOREMA I. PROPOS. I.
[535.] THEOREMA II. PROPOS. II.
[536.] THEOREMA III. PROPOS. III.
[537.] THEOREMA IV. PROPOS. IV.
[538.] THEOREMA V. PROPOS. V.
[539.] PROBLEMA I. PROPOS. VI.
[540.] THEOREMA VI. PROPOS. VII.
< >
page |< < (493) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1145" type="section" level="1" n="686">
          <p>
            <s xml:id="echoid-s12594" xml:space="preserve">
              <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"/>
          </p>
        </div>
        <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>
        </div>
        <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"/>
          </p>
          <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"/>
              </figure>
            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>
          </p>
        </div>
      </text>
    </echo>