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

Page concordance

< >
Scan Original
121 101
122 102
123 103
124 104
125 105
126 106
127 107
128 108
129 109
130 110
131 111
132 112
133 113
134 114
135 115
136 116
137 117
138 118
139 119
140 120
141 121
142 122
143 123
144 124
145 125
146 126
147 127
148 128
149 129
150 130
< >
page |< < (110) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div269" type="section" level="1" n="173">
          <p>
            <s xml:id="echoid-s2621" xml:space="preserve">
              <pb o="110" file="0130" n="130" rhead="GEOMETRIÆ"/>
            nium linearum figurę, GOQ, hac lege producta, complectetur eas,
              <lb/>
            quæ de ip. </s>
            <s xml:id="echoid-s2622" xml:space="preserve">a manent in figuris iam diſpoſitis, ergo omnes lineæ figu-
              <lb/>
            ræ, GOQ, ſic productæ complectentur omnes lineas figurarum ſic
              <lb/>
            diſpoſitarum, ergo erunt ad illas ſimul ſumptas, vt totum ad partem,
              <lb/>
            nam illæ in his reperientur, & </s>
            <s xml:id="echoid-s2623" xml:space="preserve">aliquid amplius, ergo erunt illis ma-
              <lb/>
            iores, omnes lineę autem figurarum ſic diſpoſitarum ſunt non mino-
              <lb/>
            res omnibus lineis figuræ, EAG, ex qua deſumptæ ſunt, ergo om-
              <lb/>
            nes lineę figurę, GOQ, ſic productæ ſunt, vt effectæ fuerint maio-
              <lb/>
            res omnibus lineis figurę, EAG; </s>
            <s xml:id="echoid-s2624" xml:space="preserve">eodem pacto oſtendemus nos poſ-
              <lb/>
            ſe vice verſa iſtas illis efficere maiores, ergo omnes lineæ figurarum,
              <lb/>
            EAG, GOQ, ſumptæ cum regulis vtcumque ſuppoſitis, cuiuſuis
              <lb/>
              <note position="left" xlink:label="note-0130-01" xlink:href="note-0130-01a" xml:space="preserve">Diffin. 4.
                <lb/>
              1.5. Elem.</note>
              <figure xlink:label="fig-0130-01" xlink:href="fig-0130-01a" number="71">
                <image file="0130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0130-01"/>
              </figure>
            ſint altitudinis ſumptę iux-
              <lb/>
            ta eaſdem regulas, ſunt
              <lb/>
            magnitudines inter ſe ra-
              <lb/>
            tionem habentes, quod ſi
              <lb/>
            ſubter rectam, HQ, ad-
              <lb/>
            huc eſſent portiones con-
              <lb/>
            ſideratarum à nobis figu-
              <lb/>
            rarum, EAG, GOQ, eo-
              <lb/>
            dem modo oſtenderemus omnes lineas earundem ſumptas, cum ijſ-
              <lb/>
            dem regulis eſſe magnitudines rationem inter ſe habentes, vnde inte-
              <lb/>
            grarum figurarum omnes lineę eſſent magnitudines inter ſe rationem
              <lb/>
            habentes, quod in fig. </s>
            <s xml:id="echoid-s2625" xml:space="preserve">planis oſtendere opus erat.</s>
            <s xml:id="echoid-s2626" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2627" xml:space="preserve">In ſiguris autem ſolidis conſimiliter procedemus; </s>
            <s xml:id="echoid-s2628" xml:space="preserve">nam ſi in ſupe-
              <lb/>
            riori figura intellexerimus, EAG, GOQ, eſſe figuras ſolidas, & </s>
            <s xml:id="echoid-s2629" xml:space="preserve">
              <lb/>
            pro rectis lineis æquidiſtantibus intellexerimus plana æquidiſtantia,
              <lb/>
            vt pro rectis, EG, GQ, plana, EG, GQ, quibus plana, LM, N
              <lb/>
            S, ſint æquidiſtanter ducta, ſumptis pro regulis planis, EG, GQ,
              <lb/>
            ijſque in directum ſibi conſtitutis.</s>
            <s xml:id="echoid-s2630" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">ita vt iaceant regulæ in eodem
              <lb/>
            plano, oſtendemus nos poſſe ita producere omnia plana ſolidæ figu-
              <lb/>
            ræ, GOQ, vt eadem complectantur omnia plana figuræ, EAG,
              <lb/>
            (ſi ſint eiuſdem altitudinis dictæ figuræ) integræ exiſtentis, vel (ſi
              <lb/>
            non ſint) diuiſæ in figuras ſolidas, ex. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s2633" xml:space="preserve">EBDG, BAD, ſic di-
              <lb/>
            ſpoſitas, vt baſes, ſiue regulę iaceant in eodem plano, & </s>
            <s xml:id="echoid-s2634" xml:space="preserve">ita, vt om-
              <lb/>
            nia plana dictarum ſigurarum ſolidarum, vel ſint intra oppoſita pla-
              <lb/>
            na dictas figuras tangentia, vel nihil eorum extra, vnde omnia pla-
              <lb/>
            na figuræ ſolidæ, GOQ, ſic producta fient totum, & </s>
            <s xml:id="echoid-s2635" xml:space="preserve">portiones ab
              <lb/>
            eiſdem captæ in figura ſolida, EAG, integra, vel diuiſa, vt dictum
              <lb/>
            eſt.</s>
            <s xml:id="echoid-s2636" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2637" xml:space="preserve">omnia plana figuræ, EAG, fient pars omnium planorum fi-
              <lb/>
            guræ, GOQ, ſic productorum, nam hæc in illis tota reperientur,
              <lb/>
            & </s>
            <s xml:id="echoid-s2638" xml:space="preserve">aliquid amplius, vnde omnia plana figuræ, GOQ, ſic producta
              <lb/>
            erunt, vt effecta ſint maiora omnibus planis figuræ, EAG; </s>
            <s xml:id="echoid-s2639" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum