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

Page concordance

< >
Scan Original
31 11
32 12
33 13
34 14
35 15
36 16
37 17
38 18
39 19
40 20
41 21
42 22
43 23
44 24
45 25
46 26
47 27
48 28
49 29
50 30
51 31
52 32
53 33
54 34
55 35
56 36
57 37
58 38
59 39
60 40
< >
page |< < (84) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div203" type="section" level="1" n="131">
          <p>
            <s xml:id="echoid-s2074" xml:space="preserve">
              <pb o="84" file="0104" n="104" rhead="GEOMETRI Æ"/>
            nitè ſecat baſis productum planum in recta, 2, Z, perpendiculari
              <lb/>
            triangulo per axem, ACF, & </s>
            <s xml:id="echoid-s2075" xml:space="preserve">ſint adhuc per puncta, N, S, ipſi, C
              <lb/>
            F, ductæ parallelæ, TL, HR, igitur quadratum, ℟ S, erit ęquale
              <lb/>
              <note position="left" xlink:label="note-0104-01" xlink:href="note-0104-01a" xml:space="preserve">14. Secunn.
                <lb/>
              Elem.</note>
              <figure xlink:label="fig-0104-01" xlink:href="fig-0104-01a" number="58">
                <image file="0104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0104-01"/>
              </figure>
            rectangulo, TSL, & </s>
            <s xml:id="echoid-s2076" xml:space="preserve">quadra-
              <lb/>
            tum, MN, æquale rectangulo,
              <lb/>
              <note position="left" xlink:label="note-0104-02" xlink:href="note-0104-02a" xml:space="preserve">Ex Sexta
                <lb/>
              lib. 2. feq.
                <lb/>
              velex 23.
                <lb/>
              Sext. El.</note>
            HNR, at rectangulum, TSL,
              <lb/>
            ad, HNR, habet rationem com-
              <lb/>
            poſitam ex ea, quam habet, T
              <lb/>
            S, ad, HN, .</s>
            <s xml:id="echoid-s2077" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">SB, ad, BN,
              <lb/>
            quia trianguli, BTS, BHN,
              <lb/>
            ſunt æquianguli, & </s>
            <s xml:id="echoid-s2079" xml:space="preserve">ex ea, quam
              <lb/>
            habet, SL, ad, NR, .</s>
            <s xml:id="echoid-s2080" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2081" xml:space="preserve">SV,
              <lb/>
            ad, VN, quia pariter trianguli,
              <lb/>
            SVL, NVR, ſunt æquiangu-
              <lb/>
            li, duę autem rationes, SB, ad,
              <lb/>
            BN, &</s>
            <s xml:id="echoid-s2082" xml:space="preserve">, SV, ad, VN, componunt rationem rectanguli, BSV,
              <lb/>
              <note position="left" xlink:label="note-0104-03" xlink:href="note-0104-03a" xml:space="preserve">Ex Sexta
                <lb/>
              lib. 2. feq.
                <lb/>
              vel ex 23.
                <lb/>
              Sexti El.</note>
            ad rectangulum, BNV, ergo rectangulum, TSL, ad, HNR, .</s>
            <s xml:id="echoid-s2083" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s2084" xml:space="preserve">quadratum, ℟ S, ad quadratum, MN, vel quadratum, ℟ D, ad
              <lb/>
            quadratum, MO, erit vt rectangulum, VSB, ad rectangulum, V
              <lb/>
            NB, quod oſtendere opu erat; </s>
            <s xml:id="echoid-s2085" xml:space="preserve">hæc autem ab Apollonio vocatur
              <lb/>
            Ellipſis.</s>
            <s xml:id="echoid-s2086" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div205" type="section" level="1" n="132">
          <head xml:id="echoid-head143" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2087" xml:space="preserve">_H_Aec circa ſectiones conicas appoſui, tum vt quod menti meæ ſuc-
              <lb/>
            currit in lucem proferrem, tum vt eluceſcat, quam facilè paſſio-
              <lb/>
            nes, quæ ab. </s>
            <s xml:id="echoid-s2088" xml:space="preserve">Apollonio in Elementis conicis circa earundem diametros,
              <lb/>
            vel axes quoſcumque demonſtrantur, circa eos, qui axes, vel diametri
              <lb/>
            princibales, ſiue ex generatione vocantur modo ſupradicto oſtendantur.
              <lb/>
            </s>
            <s xml:id="echoid-s2089" xml:space="preserve">His tamen contenti ex Apollonio recipiemus pro dictarum ſectionum
              <lb/>
            axibus, vel diametris quibuſcumq; </s>
            <s xml:id="echoid-s2090" xml:space="preserve">quod ipſe colligit ad finem Trop. </s>
            <s xml:id="echoid-s2091" xml:space="preserve">51. </s>
            <s xml:id="echoid-s2092" xml:space="preserve">
              <lb/>
            primi Conicorum, ſcilicet.</s>
            <s xml:id="echoid-s2093" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2094" xml:space="preserve">In Parabola vnamquamque rectarum linearum, quę diametro ex
              <lb/>
            generatione ducuntur æquidiſtantes, diametrum eſſe: </s>
            <s xml:id="echoid-s2095" xml:space="preserve">In hyperbola
              <lb/>
            verò, & </s>
            <s xml:id="echoid-s2096" xml:space="preserve">ellipſi, & </s>
            <s xml:id="echoid-s2097" xml:space="preserve">oppoſitis ſectionibus vnamquamque earum, quę
              <lb/>
            per centrum ducuntur, & </s>
            <s xml:id="echoid-s2098" xml:space="preserve">in parabola quidem applicatas ad vnam-
              <lb/>
            quamq; </s>
            <s xml:id="echoid-s2099" xml:space="preserve">diametrum, ęquidiſtantes contingentibus, poſte rectangula
              <lb/>
            ipſi adiacentia: </s>
            <s xml:id="echoid-s2100" xml:space="preserve">In hyperbola, & </s>
            <s xml:id="echoid-s2101" xml:space="preserve">oppoſitis poſſe rectangula adiacen-
              <lb/>
            tia ipſi, quę excedunt eadem figura: </s>
            <s xml:id="echoid-s2102" xml:space="preserve">In ellipſi autem, quę eadem de-
              <lb/>
            ficiunt: </s>
            <s xml:id="echoid-s2103" xml:space="preserve">Poſt@@mò quęcumque circa ſectiones adhibitis principalibus
              <lb/>
            diametris demonſtrata ſunt, & </s>
            <s xml:id="echoid-s2104" xml:space="preserve">alijs diametris aſſumptis eadem con-
              <lb/>
            tingere.</s>
            <s xml:id="echoid-s2105" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum