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
121 83
122 84
123 85
124 86
125 87
126 88
127 89
128 90
129 91
130 92
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
< >
page |< < (140) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div519" type="section" level="1" n="170">
          <pb o="140" file="0178" n="178" rhead="Apollonij Pergæi"/>
          <figure number="179">
            <image file="0178-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0178-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s5467" xml:space="preserve">Quoniam facta conuenienti ſuperpoſitione axis A M ſuper axim D
              <lb/>
            O, cadet quoque ſectio A B ſuper ſectionem D E: </s>
            <s xml:id="echoid-s5468" xml:space="preserve">ſi enim non cadit ſu-
              <lb/>
            per illam, ſumatur (ſi fieri poteſt) eius punctum B, extra ſectionem.
              <lb/>
            </s>
            <s xml:id="echoid-s5469" xml:space="preserve">D E cadens; </s>
            <s xml:id="echoid-s5470" xml:space="preserve">& </s>
            <s xml:id="echoid-s5471" xml:space="preserve">producatur ad axim perpendicularis B L vſque ad P: </s>
            <s xml:id="echoid-s5472" xml:space="preserve">& </s>
            <s xml:id="echoid-s5473" xml:space="preserve">
              <lb/>
            perficiatur planum A P applicatum comparatum; </s>
            <s xml:id="echoid-s5474" xml:space="preserve">& </s>
            <s xml:id="echoid-s5475" xml:space="preserve">ſecetur D N æqua-
              <lb/>
            lis A L, & </s>
            <s xml:id="echoid-s5476" xml:space="preserve">erigatur per N ad axim perpendicularis N E, & </s>
            <s xml:id="echoid-s5477" xml:space="preserve">producatur
              <lb/>
            vſque ad R, perficiendo planum D R applicatum comparatum; </s>
            <s xml:id="echoid-s5478" xml:space="preserve">Et quia
              <lb/>
            A I æqualis eſt D K, & </s>
            <s xml:id="echoid-s5479" xml:space="preserve">A L æqualis D N: </s>
            <s xml:id="echoid-s5480" xml:space="preserve">erit planum I L, æquale pla-
              <lb/>
            no K N; </s>
            <s xml:id="echoid-s5481" xml:space="preserve">cumque G I, H K ſint duæ figuræ ſimiles, & </s>
            <s xml:id="echoid-s5482" xml:space="preserve">æquales, pariter-
              <lb/>
              <note position="right" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">b</note>
            que I P, K R; </s>
            <s xml:id="echoid-s5483" xml:space="preserve">ergo duo plana A P, D R ſunt æqualia: </s>
            <s xml:id="echoid-s5484" xml:space="preserve">& </s>
            <s xml:id="echoid-s5485" xml:space="preserve">propterea E
              <lb/>
            N, B L, quæ illa ſpatia poſſunt (13. </s>
            <s xml:id="echoid-s5486" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5487" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5488" xml:space="preserve">ſunt æquales. </s>
            <s xml:id="echoid-s5489" xml:space="preserve">Si autem
              <lb/>
              <note position="left" xlink:label="note-0178-02" xlink:href="note-0178-02a" xml:space="preserve">12. 13.
                <lb/>
              lib. I.</note>
            ſuperponatur axis axi cadet B L ſuper E N, eoquod duo anguli N, & </s>
            <s xml:id="echoid-s5490" xml:space="preserve">L
              <lb/>
            ſunt æquales; </s>
            <s xml:id="echoid-s5491" xml:space="preserve">igitur B cadit ſuper E, quod prius cadere non concedeba-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s5492" xml:space="preserve">& </s>
            <s xml:id="echoid-s5493" xml:space="preserve">hoc eſt abſurdum. </s>
            <s xml:id="echoid-s5494" xml:space="preserve">Quapropter ſectio ſectioni æqualis eſt.</s>
            <s xml:id="echoid-s5495" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5496" xml:space="preserve">Deinde ponamus duas ſe-
              <lb/>
              <figure xlink:label="fig-0178-02" xlink:href="fig-0178-02a" number="180">
                <image file="0178-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0178-02"/>
              </figure>
            ctiones æquales, vtique con-
              <lb/>
            gruet ſectio A B ſectioni D E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5497" xml:space="preserve">axis A L axi D N, quia ſi
              <lb/>
            non cadit ſuper illum, eſſent
              <lb/>
              <note position="right" xlink:label="note-0178-03" xlink:href="note-0178-03a" xml:space="preserve">c</note>
            in hyperbola duo axes, & </s>
            <s xml:id="echoid-s5498" xml:space="preserve">in
              <lb/>
            ellipſi tres axes, quod eſt ab-
              <lb/>
            ſurdum (52. </s>
            <s xml:id="echoid-s5499" xml:space="preserve">53. </s>
            <s xml:id="echoid-s5500" xml:space="preserve">ex 2.) </s>
            <s xml:id="echoid-s5501" xml:space="preserve">Et fi-
              <lb/>
              <note position="left" xlink:label="note-0178-04" xlink:href="note-0178-04a" xml:space="preserve">48. lib. 2.</note>
            at A L æqualis D N, & </s>
            <s xml:id="echoid-s5502" xml:space="preserve">reli-
              <lb/>
            qua perficiantur, vt prius ca-
              <lb/>
            dent duo puncta L, B ſuper
              <lb/>
            N, E; </s>
            <s xml:id="echoid-s5503" xml:space="preserve">ideoque B L æqualis
              <lb/>
              <note position="right" xlink:label="note-0178-05" xlink:href="note-0178-05a" xml:space="preserve">d</note>
            erit E N; </s>
            <s xml:id="echoid-s5504" xml:space="preserve">& </s>
            <s xml:id="echoid-s5505" xml:space="preserve">poterunt æqua-
              <lb/>
            lia rectangula A P, D R applicata ad æquales A L, D N (13. </s>
            <s xml:id="echoid-s5506" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5507" xml:space="preserve">ex 1.)
              <lb/>
            </s>
            <s xml:id="echoid-s5508" xml:space="preserve">
              <note position="left" xlink:label="note-0178-06" xlink:href="note-0178-06a" xml:space="preserve">12. 13.
                <lb/>
              lib. 1.</note>
            ergo L P æqualis eſt N R. </s>
            <s xml:id="echoid-s5509" xml:space="preserve">Similiter ponatur A M æqualis D O, & </s>
            <s xml:id="echoid-s5510" xml:space="preserve">edu-
              <lb/>
            cantur C M Q, F O S duæ ordinationes, oſtendetur, quod M Q æqua-
              <lb/>
            lis eſt O S, & </s>
            <s xml:id="echoid-s5511" xml:space="preserve">L M æqualis N O; </s>
            <s xml:id="echoid-s5512" xml:space="preserve">& </s>
            <s xml:id="echoid-s5513" xml:space="preserve">propterea duo plana P Q, R S ſunt
              <lb/>
            æqualia, & </s>
            <s xml:id="echoid-s5514" xml:space="preserve">ſimilia; </s>
            <s xml:id="echoid-s5515" xml:space="preserve">igitur duo plana G P, H R ſunt æqualia, & </s>
            <s xml:id="echoid-s5516" xml:space="preserve">ſimilia,
              <lb/>
            & </s>
            <s xml:id="echoid-s5517" xml:space="preserve">L P oſtenſa eſt æqualis N R: </s>
            <s xml:id="echoid-s5518" xml:space="preserve">ergo G L æqualis eſt H N, & </s>
            <s xml:id="echoid-s5519" xml:space="preserve">A L æ-
              <lb/>
            qualis D N; </s>
            <s xml:id="echoid-s5520" xml:space="preserve">& </s>
            <s xml:id="echoid-s5521" xml:space="preserve">propterea G A æqualis eſt D H, & </s>
            <s xml:id="echoid-s5522" xml:space="preserve">A I æqualis D K.</s>
            <s xml:id="echoid-s5523" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum