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

Page concordance

< >
Scan Original
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
171 151
172 152
173 153
174 154
175 155
176 156
177 157
178 158
179 159
180 160
< >
page |< < (153) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div374" type="section" level="1" n="227">
          <p>
            <s xml:id="echoid-s3613" xml:space="preserve">
              <pb o="153" file="0173" n="173" rhead="LIBER II."/>
            nia quadrata, AS, ad omnia quadrata, FR, erunt vt omnia qua-
              <lb/>
              <note position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve">9. huius.</note>
            drata, Τ β, ad omnia quadrata, 4 Σ: </s>
            <s xml:id="echoid-s3614" xml:space="preserve">Eodem pacto oſtendemus om-
              <lb/>
            nia quadrata, AS, ad omnia quadrata, GQ, elle vt omnia quadra-
              <lb/>
            ta, Τ β, ad omnia quadrata, Λ Δ, & </s>
            <s xml:id="echoid-s3615" xml:space="preserve">tandem omnia quadrata, AS,
              <lb/>
            ad omnia quadrata, LP, eſſe vt omnia quadrata, Τ β, ad omnia
              <lb/>
            quadrata, Φ ℟, vnde, colligendo, omnia quadrata, AS, ad omnia
              <lb/>
            quadrata parallelogrammorum, DS, FR, GQ, LP, ideſt figurę
              <lb/>
            circumſcriptæ, erunt vt omnia quadrata, Τ β, ad omnia quadrata
              <lb/>
              <note position="right" xlink:label="note-0173-02" xlink:href="note-0173-02a" xml:space="preserve">Defin. @@
                <lb/>
              lib. 10</note>
            parallelogrammorum, Φ ℟, Λ Δ, 4 Σ, Υ β, ideſt ad omnia quadrata
              <lb/>
            figuræ circumicriptæ triangulo, & </s>
            <s xml:id="echoid-s3616" xml:space="preserve">Ζ β, ſed omnia quadrata, AS,
              <lb/>
            ad omnia quadrata figuræ circumſcriptæ triangulo, OES, oſtenſa
              <lb/>
            ſunt habere maiorem rationem, quam omnia quadrata, Τ β, ad om-
              <lb/>
            nia quadrata trianguli, & </s>
            <s xml:id="echoid-s3617" xml:space="preserve">Ζ β, ergo omnia quadrata, Τ β, ad om-
              <lb/>
            nia quadrata figuræ circumſcriptæ triangulo, & </s>
            <s xml:id="echoid-s3618" xml:space="preserve">Ζ β, habebunt ma-
              <lb/>
            iorem rationem, quam ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3619" xml:space="preserve">Ζ β, ergo
              <lb/>
            omnia quadrata figuræ circumſcriptæ triangulo, & </s>
            <s xml:id="echoid-s3620" xml:space="preserve">Ζ β, minora c-
              <lb/>
            runt omnibus quadratis trianguli, & </s>
            <s xml:id="echoid-s3621" xml:space="preserve">Ζ β, quod eſt abſurdum, non
              <lb/>
            ergo omnia quadrata, AS, ad maius, quam ſint omnia quadrata
              <lb/>
            trianguli, OES, habenteandem rationem, quam omnia quadrata,
              <lb/>
            Τ β, ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3622" xml:space="preserve">Ζ β.</s>
            <s xml:id="echoid-s3623" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3624" xml:space="preserve">Dico autem neque ad minus eiuſdem habere eandem rationem,
              <lb/>
            ſint enim defectus adhuc omnia quadra a figurę, Ω, & </s>
            <s xml:id="echoid-s3625" xml:space="preserve">ſit circumſcri-
              <lb/>
            pta triangulo, OES, figura ex parallelogrammis, LP, GQ, FR,
              <lb/>
            DS, & </s>
            <s xml:id="echoid-s3626" xml:space="preserve">al@a inſcripta ex parallelogrammis, MQ, IR, HS, com-
              <lb/>
            poſita, ita vt omnia quadrata circumſcriptæ ſuperent omnia qua-
              <lb/>
            drata inſcriptę minori quantitate, quam ſint omnia quadrata, Ω, er-
              <lb/>
            go omnia quadrata trianguli, OES, ſuperabunt omnia quadrata in-
              <lb/>
            icriptæ figuræ multo minoriquan@tate, ſunt autem omnia quadra-
              <lb/>
            ta, AS, ad omnia quadrata trianguli, OES, detractis omnibus qua-
              <lb/>
            drat@s, Ω, vt omnia quadrata, Τ β, ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3627" xml:space="preserve">
              <lb/>
            Ζ β, ergo omnia quadrata, AS, ad omnia quadrata inſcriptæ figu-
              <lb/>
            ræ habebunt minorem rationem, quam omnia quadrata, Τ β, ad
              <lb/>
            omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3628" xml:space="preserve">Ζ β. </s>
            <s xml:id="echoid-s3629" xml:space="preserve">Diuidatur nunc pariter latus, & </s>
            <s xml:id="echoid-s3630" xml:space="preserve">
              <lb/>
            β, in punctis, ℟, Δ, Σ, ſimiliter ac, OS, diuiditur in, P, Q, R, & </s>
            <s xml:id="echoid-s3631" xml:space="preserve">
              <lb/>
            cæ@era, vt ſupra, fiant, vt habeamus figuram inſcriptam ex paralle-
              <lb/>
            logrammis, Τ Δ, 3 Σ, 6 β, compoſitam, oſtendemus igitur, vt ſu-
              <lb/>
            pra, omnia quadrata, AS, ad omnia quadrata figurę inſcriptę trian-
              <lb/>
            gulo, OES, eſſe vt omnia quadrata, Τ β, ad omnia quadrata figu-
              <lb/>
            ræ inſcriptæ triangulo, & </s>
            <s xml:id="echoid-s3632" xml:space="preserve">Ζ β, ſunt autem omnia quadrata, AS, ad
              <lb/>
            omnia quadrata figuræ inſcriptæ triangulo, OES, in minori ratio-
              <lb/>
            ne, quam ſint omnia quadrata, Τ β, ad omnia quadrata trianguli,
              <lb/>
            & </s>
            <s xml:id="echoid-s3633" xml:space="preserve">Ζ β, ergo omnia quadrata, Τ β, ad omnia quadrata figurę </s>
          </p>
        </div>
      </text>
    </echo>
Impressum