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

Page concordance

< >
Scan Original
141 121
142 122
143 123
144 124
145 125
146 126
147 127
148 128
149 129
150 130
151 131
152 132
153 133
154 134
155 135
156 136
157 137
158 138
159 139
160 140
161 141
162 142
163 143
164 144
165 145
166 146
167 147
168 148
169 149
170 150
< >
page |< < (121) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div298" type="section" level="1" n="186">
          <pb o="121" file="0141" n="141" rhead="LIBER II."/>
          <p>
            <s xml:id="echoid-s2848" xml:space="preserve">Sint igitur parallelogramma, AM, MC, in eadem altitudine. </s>
            <s xml:id="echoid-s2849" xml:space="preserve">Di-
              <lb/>
              <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">A. Deſ. 8.
                <lb/>
              huius.</note>
            co omnia quadrata parallelogrammi, AM, ad omnia quadrata pa-
              <lb/>
            rallelogrammi, MC, regula, GH, eſſe vt quadratum, GM, ad
              <lb/>
            quadratum, MH. </s>
            <s xml:id="echoid-s2850" xml:space="preserve">Sit intra parallelogramma, AM, MC, ducta
              <lb/>
            vtcunque, DI, parallela ipſi, GH, cuius portio, DE, maneat in,
              <lb/>
              <figure xlink:label="fig-0141-01" xlink:href="fig-0141-01a" number="81">
                <image file="0141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0141-01"/>
              </figure>
            AM, &</s>
            <s xml:id="echoid-s2851" xml:space="preserve">, EI, in, BH, quoniam ergo, D
              <lb/>
            E, eſt æqualis ipſi, GM, figurę autem pla-
              <lb/>
            næ ſimiles deicriptæ à lateribus, vel lineis
              <lb/>
              <note position="right" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">25. lib. 1.</note>
            homologis æqualibus ſunt æquales, & </s>
            <s xml:id="echoid-s2852" xml:space="preserve">ideò
              <lb/>
            quadratum, DE, erit æquale quadrato, G
              <lb/>
            M, & </s>
            <s xml:id="echoid-s2853" xml:space="preserve">quadratum, EI, quadrato, MH,
              <lb/>
            ergo, vt quadratum, GM, ad quadratum,
              <lb/>
            MH, ita erit quadratum, DE, ad quadratum, EI, & </s>
            <s xml:id="echoid-s2854" xml:space="preserve">quia, DI, vt-
              <lb/>
            cunq; </s>
            <s xml:id="echoid-s2855" xml:space="preserve">ducta eſt parallela ipſi, GH, ideò, vt vnum ad vnum, ita om-
              <lb/>
              <note position="right" xlink:label="note-0141-03" xlink:href="note-0141-03a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            nia ad omnia idelt vt quadratum, GM, ad quadratum, MH, ita
              <lb/>
            erunt omnia quadrata parallelogrammi, AM, ad omnia quadrata
              <lb/>
            parallelogrammi, MC, regula, GH, quod erat oſtendendum.</s>
            <s xml:id="echoid-s2856" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div301" type="section" level="1" n="187">
          <head xml:id="echoid-head202" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2857" xml:space="preserve">_H_Inc patet, ſi vice quadratorum ſumamus alias quaſcunque figuras
              <lb/>
            ſimiles, quod eodem pacto oſtendemus omnes figuras ſimiles pa-
              <lb/>
              <note position="right" xlink:label="note-0141-04" xlink:href="note-0141-04a" xml:space="preserve">_A. Def. 8._
                <lb/>
              _huius._</note>
            rallelogrammi, AM, ad omnes ſimiles figuras parallelogrammi, MC,
              <lb/>
            vt ex. </s>
            <s xml:id="echoid-s2858" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s2859" xml:space="preserve">omnes circutos parallelogrammi, AM, ad omnes circulos pa-
              <lb/>
            rallelogrammi, MC, eſſe vt ſimiles ſiguras ab ipſis b ſibus, GM, MH,
              <lb/>
            d@ſcriptas, nam fi uræ planæ ſimiles quæcunq; </s>
            <s xml:id="echoid-s2860" xml:space="preserve">vt dictum eſt, deſcriptæ à
              <lb/>
            lateribus, vel lineis homologis æqualibus ſunt æquales; </s>
            <s xml:id="echoid-s2861" xml:space="preserve">omnibus pari-
              <lb/>
              <note position="right" xlink:label="note-0141-05" xlink:href="note-0141-05a" xml:space="preserve">_25. lib. 1._</note>
            ter aſſumptis figuris ſimilibus, regula eadem, GH.</s>
            <s xml:id="echoid-s2862" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div303" type="section" level="1" n="188">
          <head xml:id="echoid-head203" xml:space="preserve">THEOREMA X. PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s2863" xml:space="preserve">PArellelogrammorum in eadem baſiexiſtentium omnia
              <lb/>
            quadrata, regula ipſa baſi, ſunt vt altitudines, vel vt la-
              <lb/>
            tera, quę æqualiter baſi ſunt inclinata, ſi illa ſint ęquiangula.</s>
            <s xml:id="echoid-s2864" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2865" xml:space="preserve">Sint parallelogramma, AD, BD, in eadem b ſi, CD, exiſten-
              <lb/>
            tia, quorum ſint altitudines iuxta baſim, CD, ſumptæ, AO, CN.
              <lb/>
            </s>
            <s xml:id="echoid-s2866" xml:space="preserve">Dico omnia quadrata parallelogrammi, AD, adomnia quadrata
              <lb/>
            parallelogrammi, BD, regula, CD, eſſe vt, AO, ad, CN, vel
              <lb/>
            etiam vt, AC, ad, CB, ſi parallelogramma, BD, DA, fuerint æ-
              <lb/>
            quiangula, producantur autem, CA, CB, indefinitè ad partes </s>
          </p>
        </div>
      </text>
    </echo>
Impressum