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
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
161 123
162 124
163 125
164 126
165 127
166 128
167 129
168 130
169 131
170 132
< >
page |< < (256) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div804" type="section" level="1" n="247">
          <p style="it">
            <s xml:id="echoid-s9621" xml:space="preserve">
              <pb o="256" file="0294" n="294" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0294-01" xlink:href="fig-0294-01a" number="342">
                <image file="0294-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0294-01"/>
              </figure>
            V æqualis eſt V H, quod eſt abſurdum.</s>
            <s xml:id="echoid-s9622" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9623" xml:space="preserve">Patet quadratum L P nempe N E, ſeu O N in N L ad quadratum E P,
              <lb/>
              <note position="left" xlink:label="note-0294-01" xlink:href="note-0294-01a" xml:space="preserve">f</note>
            nempe ad quadratum N L, ſcilicet O N ad N L habere minorem pro-
              <lb/>
            portionem, quàm H E ad E I: </s>
            <s xml:id="echoid-s9624" xml:space="preserve">ponamus iam O N ad Z X, vt H E ad E
              <lb/>
            I; </s>
            <s xml:id="echoid-s9625" xml:space="preserve">& </s>
            <s xml:id="echoid-s9626" xml:space="preserve">per X ducamus X R, & </s>
            <s xml:id="echoid-s9627" xml:space="preserve">iungamus E R, &</s>
            <s xml:id="echoid-s9628" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9629" xml:space="preserve">Suppoſita conſtructione
              <lb/>
            prioris caſus, quandò conus rectus E L K factus eſt ſimilis cono A B C quadra-
              <lb/>
            tum L P ad quadratum E P habebat eandem proportionem, quàm O N ad N L,
              <lb/>
            ſeu quàm quadratum B Q ad quadratum Q A: </s>
            <s xml:id="echoid-s9630" xml:space="preserve">modò in hac altera ſuppoſitione
              <lb/>
            conceditur quadratum B Q ad quadratum Q A habere minorem proportionem,
              <lb/>
            quàm E H ad E I; </s>
            <s xml:id="echoid-s9631" xml:space="preserve">igitur O N ad N L minorem proportionem habebit, quàm,
              <lb/>
            H E ad E I; </s>
            <s xml:id="echoid-s9632" xml:space="preserve">& </s>
            <s xml:id="echoid-s9633" xml:space="preserve">fiat O N ad N X vt H E ad E I, erit N X minor quàm N L,
              <lb/>
            & </s>
            <s xml:id="echoid-s9634" xml:space="preserve">ideo punctum X intra circulum cadet, & </s>
            <s xml:id="echoid-s9635" xml:space="preserve">per X ducta R X Y parallelæ H E;
              <lb/>
            </s>
            <s xml:id="echoid-s9636" xml:space="preserve">vtique ſecabit circulum in duobus punctis, vt in R, & </s>
            <s xml:id="echoid-s9637" xml:space="preserve">Y. </s>
            <s xml:id="echoid-s9638" xml:space="preserve">Quod verò recta,
              <lb/>
            R X Y duci debeat parallela ipſi H E, non quomodocunque, patet ex contextu
              <lb/>
            ſequenti, nam debent O X, O R ſecari in N, & </s>
            <s xml:id="echoid-s9639" xml:space="preserve">V proportionaliter, quarè tex-
              <lb/>
            tus debuit omnino corrigi.</s>
            <s xml:id="echoid-s9640" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9641" xml:space="preserve">Oſtendetur, quemadmodum dictum eſt, quod E T R, & </s>
            <s xml:id="echoid-s9642" xml:space="preserve">A B C ſunt
              <lb/>
              <note position="right" xlink:label="note-0294-02" xlink:href="note-0294-02a" xml:space="preserve">g</note>
            iſoſcelia, & </s>
            <s xml:id="echoid-s9643" xml:space="preserve">ſimilia, &</s>
            <s xml:id="echoid-s9644" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9645" xml:space="preserve">Quoniam arcus circuli E O, & </s>
            <s xml:id="echoid-s9646" xml:space="preserve">O H æquales ſunt
              <lb/>
            inter ſe ex conſtructione, erunt anguli E R O, & </s>
            <s xml:id="echoid-s9647" xml:space="preserve">O R H æquales inter ſe, & </s>
            <s xml:id="echoid-s9648" xml:space="preserve">
              <lb/>
            propter parallelas O R, & </s>
            <s xml:id="echoid-s9649" xml:space="preserve">E T eſt angulus O R E æqualis alterno T E R; </s>
            <s xml:id="echoid-s9650" xml:space="preserve">at-
              <lb/>
            què externus H R O æqualis eſt interno, & </s>
            <s xml:id="echoid-s9651" xml:space="preserve">oppoſito R T E; </s>
            <s xml:id="echoid-s9652" xml:space="preserve">igitur duo anguli
              <lb/>
            R E T, & </s>
            <s xml:id="echoid-s9653" xml:space="preserve">R T E æquales ſunt inter ſe; </s>
            <s xml:id="echoid-s9654" xml:space="preserve">& </s>
            <s xml:id="echoid-s9655" xml:space="preserve">propterea triangulum E R T erit
              <lb/>
            iſoſcelium. </s>
            <s xml:id="echoid-s9656" xml:space="preserve">Rurſus quia duo anguli E L H, E R H in eodem circuli ſegmento
              <lb/>
            couſtituti æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s9657" xml:space="preserve">erat ex conſtructione angulus M B C æqualis
              <lb/>
            angulo H L E; </s>
            <s xml:id="echoid-s9658" xml:space="preserve">igitur anguli H R E, & </s>
            <s xml:id="echoid-s9659" xml:space="preserve">M B C æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s9660" xml:space="preserve">ideo
              <lb/>
            conſequentes anguli verticales E R T, & </s>
            <s xml:id="echoid-s9661" xml:space="preserve">A B C æquales erunt inter ſe, eſt quo-
              <lb/>
            que triangulum A B C per axim coni recti iſoſcelium igitur duo triangula,
              <lb/>
            E R T, & </s>
            <s xml:id="echoid-s9662" xml:space="preserve">A B C ſimilia ſunt inter ſe. </s>
            <s xml:id="echoid-s9663" xml:space="preserve">Et quia vt dictum eſt O N ad N X
              <lb/>
            eandem proportionem habet, quàm H E ad E I, atque propter parallelas V N,
              <lb/>
            & </s>
            <s xml:id="echoid-s9664" xml:space="preserve">R X eſt O V ad V R vt O N ad N X, & </s>
            <s xml:id="echoid-s9665" xml:space="preserve">ſumpta cõmuni altitudine V R </s>
          </p>
        </div>
      </text>
    </echo>
Impressum