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
91 53
92 54
93 55
94 56
95 57
96 58
97 59
98 60
99 61
100 62
101 63
102 64
103 65
104 66
105 67
106 68
107 69
108 70
109 71
110 72
111 73
112 74
113 75
114 76
115 77
116 78
117 79
118 80
119 81
120 82
< >
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