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

Table of figures

< >
[Figure 131]
Page: 217
[Figure 132]
Page: 218
[Figure 133]
Page: 220
[Figure 134]
Page: 221
[Figure 135]
Page: 222
[Figure 136]
Page: 223
[Figure 137]
Page: 224
[Figure 138]
Page: 225
[Figure 139]
Page: 226
[Figure 140]
Page: 229
[Figure 141]
Page: 229
[Figure 142]
Page: 230
[Figure 143]
Page: 230
[Figure 144]
Page: 232
[Figure 145]
Page: 233
[Figure 146]
Page: 234
[Figure 147]
Page: 236
[Figure 148]
Page: 237
[Figure 149]
Page: 238
[Figure 150]
Page: 240
[Figure 151]
Page: 243
[Figure 152]
Page: 245
[Figure 153]
Page: 246
[Figure 154]
Page: 247
[Figure 155]
Page: 250
[Figure 156]
Page: 250
[Figure 157]
Page: 252
[Figure 158]
Page: 253
[Figure 159]
Page: 255
[Figure 160]
Page: 258
< >
page |< < (112) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div273" type="section" level="1" n="174">
          <pb o="112" file="0132" n="132" rhead="GEOMETRIÆ"/>
          <p style="it">
            <s xml:id="echoid-s2655" xml:space="preserve">Non inutile autem mibi videtur eſſe animaduerter e pro huius confir-
              <lb/>
            matione, hoc pro vero ſuppoſito, quam plurima, quæ ab Euclide, Ar-
              <lb/>
            chimede, & </s>
            <s xml:id="echoid-s2656" xml:space="preserve">alijs oſtenſa ſunt, à me pariter fuiſſe demonſtrata, meaſq;
              <lb/>
            </s>
            <s xml:id="echoid-s2657" xml:space="preserve">concluſiones ad vnguem cum illorum concluſionibus concordare, quod
              <lb/>
            euidens ſignum eſſe poteſt, me in principijs vera aſſumpſiſſe, licet ſciam,
              <lb/>
            & </s>
            <s xml:id="echoid-s2658" xml:space="preserve">ex falſis principijs ſophiſticè vera aliquando deduci poſſe, quod ta-
              <lb/>
            men in tot, & </s>
            <s xml:id="echoid-s2659" xml:space="preserve">tot concluſionibus, methodo geometrica demonſtratis mihi
              <lb/>
            accidiſſe abſurdum putarem: </s>
            <s xml:id="echoid-s2660" xml:space="preserve">Hoc tamen addo, non tanquam præfatæ ve-
              <lb/>
            ritatis legitimum fundamentum, ſed vt non negligendum, immò ſummè
              <lb/>
            expendendum illius argumentum, quod ſequentia percurrenti continuò
              <lb/>
            magis, ac magis eluceſcet.</s>
            <s xml:id="echoid-s2661" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div274" type="section" level="1" n="175">
          <head xml:id="echoid-head190" xml:space="preserve">THEOREMA II. PROPOS. II.</head>
          <p>
            <s xml:id="echoid-s2662" xml:space="preserve">AEqualium planarum figurarum omnes lineæ ſunt ęqua-
              <lb/>
            les, & </s>
            <s xml:id="echoid-s2663" xml:space="preserve">æqualium ſolidarum omnia plana ſunt æqua-
              <lb/>
            lia, regula quauis affumpta.</s>
            <s xml:id="echoid-s2664" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2665" xml:space="preserve">Sint duę æquales planę figuræ, ADC, AEB, in figura, ADC,
              <lb/>
            ſit regula, AC, vtcunque, & </s>
            <s xml:id="echoid-s2666" xml:space="preserve">in figura, AEB, regula vtcunque ſit,
              <lb/>
            AB. </s>
            <s xml:id="echoid-s2667" xml:space="preserve">Dico omnes lineas figuræ, ADC, regula, AC, ęquales eſſe
              <lb/>
            omnibus lineis figurę, AEB, regula, AB; </s>
            <s xml:id="echoid-s2668" xml:space="preserve">intelligatur ſiguram, A
              <lb/>
            EB, ita ſuperponi figuræ, ADC, vt regulæ ſint ad inuicem ſuper-
              <lb/>
            poſitę, velut eſt, AB, in, AC, vel ſaltem ęquidiſtent, vel ergo tota
              <lb/>
            figura congruit toti, vel pars parti, congruat pars parti, ergo con-
              <lb/>
              <note position="left" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">Poſtul. 1.
                <lb/>
              huius.</note>
              <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a" number="72">
                <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0132-01"/>
              </figure>
            gruentium harum partium omnes lineæ erunt
              <lb/>
            pariter congruentes, ſcilicet omnes lineę, AD
              <lb/>
            B, partis figurę, AEB, erunt congruentes om-
              <lb/>
            nibus lineis, ADB, partis figuræ, ADC, ſu
              <lb/>
            perponantur adhuc reſiduæ harum figurarum
              <lb/>
            partes, hac lege tamen, vt omnes earundem li-
              <lb/>
            neæ regulis, AB, AC, fiue regulę communi,
              <lb/>
            AB, vel, AC, ſemper ſituentur æquidiſtantes,
              <lb/>
            & </s>
            <s xml:id="echoid-s2669" xml:space="preserve">hoc ſemper fiat, donec omnes refiduę partes ad inuicem ſuperpo-
              <lb/>
            ſitæ fuerint, quia ergo integræ figuræ ſunt æquales erunt dictæ par-
              <lb/>
            tes ſuperpoſitæ inuicem congruentes, ergo & </s>
            <s xml:id="echoid-s2670" xml:space="preserve">earum omnes lineæ
              <lb/>
            erunt pariter congruentes, magnitudines autem congruentes ſunt
              <lb/>
            ad inuicem æquales, ergo omnes lineæ partium figuræ, AEB, ſi-
              <lb/>
            mul ſumptarum.</s>
            <s xml:id="echoid-s2671" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2672" xml:space="preserve">omnes lineæ figuræ, AEB, ſumptæ regula, A
              <lb/>
            B, erunt ęquales omnibus lineis partium figurę, ADC, quibus prę-
              <lb/>
            dictæ partes congruerunt, ſimul ſumptarum.</s>
            <s xml:id="echoid-s2673" xml:space="preserve">. omnibus lineis </s>
          </p>
        </div>
      </text>
    </echo>
Impressum