Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Page concordance

< >
Scan Original
171 133
172 134
173 135
174 136
175 137
176 138
177 139
178 140
179 141
180 142
181 143
182 144
183 145
184 146
185 147
186 148
187 149
188 150
189 151
190 152
191 153
192 154
193 155
194 156
195 157
196 158
197 159
198 160
199 161
200 162
< >
page |< < (112) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div418" type="section" level="1" n="129">
          <pb o="112" file="0150" n="150" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s4511" xml:space="preserve">Lineæ vero breuiſſimæ, quæ ca-
              <lb/>
              <figure xlink:label="fig-0150-01" xlink:href="fig-0150-01a" number="136">
                <image file="0150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0150-01"/>
              </figure>
              <note position="right" xlink:label="note-0150-01" xlink:href="note-0150-01a" xml:space="preserve">d</note>
            dunt ad peripheriam ſectionis B
              <lb/>
            A, continent angulos minores,
              <lb/>
            quàm B C D, vtique non occur-
              <lb/>
            runt D F, &</s>
            <s xml:id="echoid-s4512" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4513" xml:space="preserve">Ideſt: </s>
            <s xml:id="echoid-s4514" xml:space="preserve">quia quælibet
              <lb/>
            breuiſsima ex puncto peripheriæ A B
              <lb/>
            ad axim ducta efſicit angulum propin-
              <lb/>
              <note position="left" xlink:label="note-0150-02" xlink:href="note-0150-02a" xml:space="preserve">26. 27.
                <lb/>
              huius.</note>
            quiorem vertici, minorem ipſo angulo
              <lb/>
            C; </s>
            <s xml:id="echoid-s4515" xml:space="preserve">& </s>
            <s xml:id="echoid-s4516" xml:space="preserve">propterea quælibet breuiſsima,
              <lb/>
            ad peripheriam A B extenſa ſecabit ne-
              <lb/>
              <note position="left" xlink:label="note-0150-03" xlink:href="note-0150-03a" xml:space="preserve">28. huius.</note>
            ceſſario ipſam B C vlterius productam
              <lb/>
            ad partes C: </s>
            <s xml:id="echoid-s4517" xml:space="preserve">ſed prius oſtenſa fuit B
              <lb/>
            C parallela asymptoto D F; </s>
            <s xml:id="echoid-s4518" xml:space="preserve">igitur quæ-
              <lb/>
            libet breuiſsima ad peripheriam A B
              <lb/>
            educta ideſt inter parallelas poſita non
              <lb/>
            occurret alteri æquidiſtantium D F ad partes F, ſed ad partes oppoſitas verſus
              <lb/>
            D; </s>
            <s xml:id="echoid-s4519" xml:space="preserve">eo quod quælibet recta linea intra hyperbolam ducta non ſecat peripheriam ſe-
              <lb/>
              <note position="left" xlink:label="note-0150-04" xlink:href="note-0150-04a" xml:space="preserve">Conuerſ.
                <lb/>
              8. lib. 2.
                <lb/>
              26. 27.
                <lb/>
              huius.
                <lb/>
              28. huius.</note>
            ctionis in ea parte, in qua continentem D F nõ ſecat; </s>
            <s xml:id="echoid-s4520" xml:space="preserve">At quælibet alia breuiſsima
              <lb/>
            infra C B ducta, neceſſario efſiciet ad axim angulum maiorem, quàm C; </s>
            <s xml:id="echoid-s4521" xml:space="preserve">& </s>
            <s xml:id="echoid-s4522" xml:space="preserve">pro-
              <lb/>
            pterea vlterius producta ſecabit ipſam B C ad partes C; </s>
            <s xml:id="echoid-s4523" xml:space="preserve">ſed quælibet breuiſsima
              <lb/>
            extra parallelas poſita quæ ſecat vnam æquidiſtantium B C, ſecabit quoq; </s>
            <s xml:id="echoid-s4524" xml:space="preserve">reli-
              <lb/>
            quam ad eaſdem partes F C; </s>
            <s xml:id="echoid-s4525" xml:space="preserve">quare prius ſectioni occurret, vt dictum eſt.</s>
            <s xml:id="echoid-s4526" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div423" type="section" level="1" n="130">
          <head xml:id="echoid-head174" xml:space="preserve">SECTIO DECIMASEXTA</head>
          <head xml:id="echoid-head175" xml:space="preserve">Continens XVI. XVII. XVIII. Propoſ.
            <lb/>
          Apollonij.</head>
          <p>
            <s xml:id="echoid-s4527" xml:space="preserve">SI menſura comparata ſumpta fuerit in axe recto minore elli-
              <lb/>
              <note position="right" xlink:label="note-0150-05" xlink:href="note-0150-05a" xml:space="preserve">a</note>
            pſis, erit maximus ramorum ab eius origine egredientium,
              <lb/>
            & </s>
            <s xml:id="echoid-s4528" xml:space="preserve">illi propinquior maior eſt remotiore: </s>
            <s xml:id="echoid-s4529" xml:space="preserve">minimus vero ramorũ
              <lb/>
            eſt differentia recti, & </s>
            <s xml:id="echoid-s4530" xml:space="preserve">comparatæ, & </s>
            <s xml:id="echoid-s4531" xml:space="preserve">illi propinquior, minor
              <lb/>
            eſt remotiore, atque exceſſus quadrati comparatæ ſupra qua-
              <lb/>
            dratum cuiuſcunque rami aſſignati æqualis eſt exemplari appli-
              <lb/>
            cato ad abſciſſam illius rami, ſiue comparata ſit minor, aut
              <lb/>
            æqualis, aut maior recto.</s>
            <s xml:id="echoid-s4532" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4533" xml:space="preserve">Sit D C rectus a-
              <lb/>
              <figure xlink:label="fig-0150-02" xlink:href="fig-0150-02a" number="137">
                <image file="0150-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0150-02"/>
              </figure>
            xis minor ſectionis
              <lb/>
            ellipticæ A B C ſit-
              <lb/>
            que C I comparata,
              <lb/>
            & </s>
            <s xml:id="echoid-s4534" xml:space="preserve">rami I H, I K, I
              <lb/>
            B, I L, I A, I D, & </s>
            <s xml:id="echoid-s4535" xml:space="preserve">
              <lb/>
            ſemiſſis erecti ſit C
              <lb/>
            F, & </s>
            <s xml:id="echoid-s4536" xml:space="preserve">centrum E, &</s>
            <s xml:id="echoid-s4537" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum