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
131 93
132 94
133 95
134 96
135 97
136 98
137 99
138 100
139 101
140 102
141 103
142 104
143 105
144 106
145 107
146 108
147 109
148 110
149 111
150 112
151 113
152 114
153 115
154 116
155 117
156 118
157 119
158 120
159 121
160 122
< >
page |< < (207) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div704" type="section" level="1" n="231">
          <p style="it">
            <s xml:id="echoid-s7760" xml:space="preserve">
              <pb o="207" file="0245" n="245" rhead="Conicor. Lib. VI."/>
            les cum diametris, quæ abſciſſis ſint proportionales, & </s>
            <s xml:id="echoid-s7761" xml:space="preserve">abſciſſæ quoque inter ſe.
              <lb/>
            </s>
            <s xml:id="echoid-s7762" xml:space="preserve">Vnde ſequitur, quod portiones eiuſdem diametri E K à centro M ad omnes or-
              <lb/>
            dinatim ad diametros applicatas ſint æquales inter ſe, vt oſtenſum eſt in propo-
              <lb/>
            ſitione 13. </s>
            <s xml:id="echoid-s7763" xml:space="preserve">huius: </s>
            <s xml:id="echoid-s7764" xml:space="preserve">quod eſt impoſſibile.</s>
            <s xml:id="echoid-s7765" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7766" xml:space="preserve">Quando verò ſectio A C eſt byperbole, ac ſectio D F eſt ellipſis, ſimiliter,
              <lb/>
            vt in 14. </s>
            <s xml:id="echoid-s7767" xml:space="preserve">propoſitione huius, oſtendetur; </s>
            <s xml:id="echoid-s7768" xml:space="preserve">quo abſciſſæ in hyperbola, & </s>
            <s xml:id="echoid-s7769" xml:space="preserve">ellipſi ſint
              <lb/>
            proportionales; </s>
            <s xml:id="echoid-s7770" xml:space="preserve">& </s>
            <s xml:id="echoid-s7771" xml:space="preserve">propterea omnes habebunt rationes maioris inæqualitatis, aut
              <lb/>
            omnes habebunt, proportiones inæqualitatis minoris, quod tamen in prædicta 14.
              <lb/>
            </s>
            <s xml:id="echoid-s7772" xml:space="preserve">propoſitione impoſſibile eſſe oſtenditur.</s>
            <s xml:id="echoid-s7773" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div706" type="section" level="1" n="232">
          <head xml:id="echoid-head292" xml:space="preserve">Notæ in Propoſit. XXIV.</head>
          <p style="it">
            <s xml:id="echoid-s7774" xml:space="preserve">SI enim hoc verum non eſt, &</s>
            <s xml:id="echoid-s7775" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7776" xml:space="preserve">Quod quælibet portio B A D ſectionis
              <lb/>
              <note position="left" xlink:label="note-0245-01" xlink:href="note-0245-01a" xml:space="preserve">a</note>
            conicæ A B G nullo pacto circumferentia circuli eſſe poſſit ſic oſtendetur.
              <lb/>
            </s>
            <s xml:id="echoid-s7777" xml:space="preserve">Quia in circulo rectæ lineæ diuidentes bifariam duas parallelas inter ſe ſunt
              <lb/>
            neceſſariò diametri circuli, qui perpendicu-
              <lb/>
              <figure xlink:label="fig-0245-01" xlink:href="fig-0245-01a" number="281">
                <image file="0245-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0245-01"/>
              </figure>
            lariter ſecant prædictas parallelas applica-
              <lb/>
            tas; </s>
            <s xml:id="echoid-s7778" xml:space="preserve">igitur ſi curua linea B G D fuerit cir-
              <lb/>
            culi peripheria rectæ lineæ K I, L M, & </s>
            <s xml:id="echoid-s7779" xml:space="preserve">
              <lb/>
            N O diametri circuli, erunt perpendicula-
              <lb/>
            res ad ordinatim applicatas æquidiſtantes
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s7780" xml:space="preserve">ſed quia etiam A B G ſupponitur
              <lb/>
            ſectio conica, erunt K I, L M, N O axes
              <lb/>
            prædictæ ſectionis conicæ eo quod bifariam,
              <lb/>
            & </s>
            <s xml:id="echoid-s7781" xml:space="preserve">ad angulos rectos diuidunt ordinatim ap-
              <lb/>
            plicatas. </s>
            <s xml:id="echoid-s7782" xml:space="preserve">Rurſus quia prædictæ ordinatim
              <lb/>
            applicatæ non ſunt omnes inter ſe parallelæ,
              <lb/>
            eo quodex conſtructione applicatæ A B, A C,
              <lb/>
            C D non fuerunt ductæ æquidiſtantes; </s>
            <s xml:id="echoid-s7783" xml:space="preserve">igi-
              <lb/>
            tur tres axes I K, L M, N O indirectum
              <lb/>
              <note position="right" xlink:label="note-0245-02" xlink:href="note-0245-02a" xml:space="preserve">48. lib. 2.</note>
            non coincidunt; </s>
            <s xml:id="echoid-s7784" xml:space="preserve">quare in ſectione conica B A G reperiri poſſent tres axes; </s>
            <s xml:id="echoid-s7785" xml:space="preserve">quod
              <lb/>
            eſt impoſſibile.</s>
            <s xml:id="echoid-s7786" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div708" type="section" level="1" n="233">
          <head xml:id="echoid-head293" xml:space="preserve">SECTIO NONA</head>
          <head xml:id="echoid-head294" xml:space="preserve">Continens Propoſit. XXV.</head>
          <p>
            <s xml:id="echoid-s7787" xml:space="preserve">SI duo plana æquidiſtantia conum aliquem ſecuerint, atque
              <lb/>
              <note position="left" xlink:label="note-0245-03" xlink:href="note-0245-03a" xml:space="preserve">b</note>
            in eo efficiant duas hyperbolas, aut ellipſes; </s>
            <s xml:id="echoid-s7788" xml:space="preserve">vtique ſectio-
              <lb/>
            nes ſimiles inter ſe erunt, ſed non erunt neceſſariò æquales.</s>
            <s xml:id="echoid-s7789" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum