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 |< < (162) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div602" type="section" level="1" n="202">
          <p style="it">
            <s xml:id="echoid-s6275" xml:space="preserve">
              <pb o="162" file="0200" n="200" rhead="Apollonij Pergæi"/>
            quando anguli vnius inæquales ſint angulis alterius, aut aliquaudo latera circa
              <lb/>
            angulos æquales non ſint proportionalia; </s>
            <s xml:id="echoid-s6276" xml:space="preserve">ita in definitione Mydorgiana, quia co-
              <lb/>
            niſectiones dicuntur ſimiles in quibus omnes axium abſcißæ, quæ proportionales
              <lb/>
            ſunt inter ſe in ijsdem ſunt rationibus ad conterminas potentiales, igitur eidem
              <lb/>
            ſubiecto deſinito, ideſt in duabus ſectionibus conicis ſimilibus, eſt impoſſibile, vt
              <lb/>
            reperiatur ſeries aliqua infinitarum ſimilium abſciſſarum in axibus, quæ ad con-
              <lb/>
            terminas potentiales non ſint in ijſdem rationibus, & </s>
            <s xml:id="echoid-s6277" xml:space="preserve">ſiquidem duæ paſſiones op-
              <lb/>
            poſitæ eidem ſubiecto definito conueniant nulla earum erit eius paſſio eſſentialis,
              <lb/>
            & </s>
            <s xml:id="echoid-s6278" xml:space="preserve">ideo definitio bona non erit: </s>
            <s xml:id="echoid-s6279" xml:space="preserve">vt exempli gratia quia in duobus ſimilibus cir-
              <lb/>
            culorum ſegmentis duo triangula inſcripta poſſunt eſſe æquiangula, & </s>
            <s xml:id="echoid-s6280" xml:space="preserve">etiam non
              <lb/>
            æquiangula; </s>
            <s xml:id="echoid-s6281" xml:space="preserve">ergo ſimilitudo inſcriptorum triangulorum non eſt paſſio eſſentialis
              <lb/>
            ſegmentorum circularium ſimilium inter ſe, & </s>
            <s xml:id="echoid-s6282" xml:space="preserve">ideo non erit bæc bona definitio:
              <lb/>
            </s>
            <s xml:id="echoid-s6283" xml:space="preserve">Similia circulorũ ſegmenta ſunt in quibus deſcribi poſſunt duo triangula ſi-
              <lb/>
            milia, & </s>
            <s xml:id="echoid-s6284" xml:space="preserve">ratio eſt, quia per definitionem nedum natura rei declaratur, & </s>
            <s xml:id="echoid-s6285" xml:space="preserve">indi-
              <lb/>
            catur, ſed etiam diftinguitur, & </s>
            <s xml:id="echoid-s6286" xml:space="preserve">diuerſificatur à qualibet alia; </s>
            <s xml:id="echoid-s6287" xml:space="preserve">& </s>
            <s xml:id="echoid-s6288" xml:space="preserve">quoniam in
              <lb/>
              <note position="left" xlink:label="note-0200-01" xlink:href="note-0200-01a" xml:space="preserve">Coroll.
                <lb/>
              Lem. 2.
                <lb/>
              huius.</note>
            ſectionibus ſimilibus reperiuntur duæ ſeries ſimilium abſciſſarum, quæ ad con-
              <lb/>
            terminas potentiales non ſunt in ijſdem rationibus; </s>
            <s xml:id="echoid-s6289" xml:space="preserve">& </s>
            <s xml:id="echoid-s6290" xml:space="preserve">è contra ex definitione,
              <lb/>
            Mydorgij duæ ſeries ſimilium abſciſſarum, quæ ad conterminas potentiales ſunt
              <lb/>
            in ijſdem rationibus, eſſentialiter conueniunt definito; </s>
            <s xml:id="echoid-s6291" xml:space="preserve">igitur hæ duæ oppoſitæ
              <lb/>
            paſſiones conueniunt eidem ſubiecto definito, ſcilicet ſectionibus ſimilibus iu-
              <lb/>
            xta Mydorgij ſententiam : </s>
            <s xml:id="echoid-s6292" xml:space="preserve">quapropter tradita definitio ſectionum ſimilium vi-
              <lb/>
            tioſa erit, & </s>
            <s xml:id="echoid-s6293" xml:space="preserve">manca.</s>
            <s xml:id="echoid-s6294" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6295" xml:space="preserve">Vt autem hoc clarius pateat ex-
              <lb/>
              <figure xlink:label="fig-0200-01" xlink:href="fig-0200-01a" number="217">
                <image file="0200-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0200-01"/>
              </figure>
            ponantur duæ ſectiones A B, E F
              <lb/>
            eiuſdem nominis, quarum axes B
              <lb/>
            C, F H, & </s>
            <s xml:id="echoid-s6296" xml:space="preserve">propoſitum primò ſit de-
              <lb/>
            monſtrare ſectiones illas eſſe ſimiles
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s6297" xml:space="preserve">ergo oſtendendum eſt paſ-
              <lb/>
            ſionem definitionis traditæ conueni-
              <lb/>
            re ſectionibus A B, E F; </s>
            <s xml:id="echoid-s6298" xml:space="preserve">quod ni-
              <lb/>
            mirum ſimiles axium abſcißæ in,
              <lb/>
            ijſdem rationibus debent eſſe adcõ-
              <lb/>
            terminas potentiales, & </s>
            <s xml:id="echoid-s6299" xml:space="preserve">quia in,
              <lb/>
            definitione nulla cautio, vel determinatio adhibetur, igitur ſumi poſſunt quæ-
              <lb/>
            libet axium abſciſſæ B C, F H, & </s>
            <s xml:id="echoid-s6300" xml:space="preserve">hæc ſecari proportionaliter in R, V, & </s>
            <s xml:id="echoid-s6301" xml:space="preserve">à
              <lb/>
            punctis diuiſionum duci poßunt ad axes ordinatim applicatæ A C, E H, Q R,
              <lb/>
            T V; </s>
            <s xml:id="echoid-s6302" xml:space="preserve">& </s>
            <s xml:id="echoid-s6303" xml:space="preserve">ſupponamus demonſtratum eſſe, quod B C ad C A ſit vt F H ad H E,
              <lb/>
            pariterque vt B R ad R Q ſit vt F V ad V T, tunc quidem ex vi definitionis
              <lb/>
            deducitur, quod ſimiles ſint ſectiones A B, & </s>
            <s xml:id="echoid-s6304" xml:space="preserve">E F. </s>
            <s xml:id="echoid-s6305" xml:space="preserve">At quia demonſtrari poteſt
              <lb/>
              <note position="left" xlink:label="note-0200-02" xlink:href="note-0200-02a" xml:space="preserve">ex Lem. 2.
                <lb/>
              huius.</note>
            in ijſdem ſectionibus (ſumendo abſciſſas B C, F H ad libitum, & </s>
            <s xml:id="echoid-s6306" xml:space="preserve">proportiona-
              <lb/>
            liter diuidendo eas in R, & </s>
            <s xml:id="echoid-s6307" xml:space="preserve">V) quod B C ad C A habet maiorem proportionem,
              <lb/>
              <note position="left" xlink:label="note-0200-03" xlink:href="note-0200-03a" xml:space="preserve">Coroll. 2.
                <lb/>
              Lem. 5.
                <lb/>
              huius.</note>
            quàm F H ad H E; </s>
            <s xml:id="echoid-s6308" xml:space="preserve">pariterque B R ad R Q maiorem proportionẽ habeat, quàm
              <lb/>
              <note position="left" xlink:label="note-0200-04" xlink:href="note-0200-04a" xml:space="preserve">Coroll. 2.
                <lb/>
              Lem. 5.
                <lb/>
              huius.</note>
            F V ad V T, & </s>
            <s xml:id="echoid-s6309" xml:space="preserve">ſic ſemper; </s>
            <s xml:id="echoid-s6310" xml:space="preserve">ergo non poterit deduci ſimilitudo potius quàm non
              <lb/>
            ſimilitudo; </s>
            <s xml:id="echoid-s6311" xml:space="preserve">ideoque definitio ſimilium ſectionum erit vitioſa, quandoquidem ex
              <lb/>
            ea duæ contradictoriæ deducuntur.</s>
            <s xml:id="echoid-s6312" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6313" xml:space="preserve">Secundo loco ſupponantur duæ ſectiones A B, & </s>
            <s xml:id="echoid-s6314" xml:space="preserve">E F ſimiles inter ſe, & </s>
            <s xml:id="echoid-s6315" xml:space="preserve">pro-
              <lb/>
            poſitum, ſit demonſtrare quod axium figuræ, ſeu rectangula G B D, & </s>
            <s xml:id="echoid-s6316" xml:space="preserve">K F </s>
          </p>
        </div>
      </text>
    </echo>
Impressum