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 |< < (171) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div619" type="section" level="1" n="207">
          <p>
            <s xml:id="echoid-s6556" xml:space="preserve">
              <pb o="171" file="0209" n="209" rhead="Conicor. Lib. VI."/>
            Q ſimile eſt M K S,
              <lb/>
              <figure xlink:label="fig-0209-01" xlink:href="fig-0209-01a" number="231">
                <image file="0209-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0209-01"/>
              </figure>
            quare angulus G æ-
              <lb/>
            qualis eſt angulo M,
              <lb/>
            & </s>
            <s xml:id="echoid-s6557" xml:space="preserve">propterea periphe-
              <lb/>
            riæ E F Q, & </s>
            <s xml:id="echoid-s6558" xml:space="preserve">K F S,
              <lb/>
            quibus inſiſtunt, æ-
              <lb/>
            quales erunt, quod
              <lb/>
            eſt abſurdũ: </s>
            <s xml:id="echoid-s6559" xml:space="preserve">eſt enim
              <lb/>
            E F Q maior, quàm
              <lb/>
            K F S; </s>
            <s xml:id="echoid-s6560" xml:space="preserve">ergo duo triã-
              <lb/>
            gula A B C, D E F
              <lb/>
            in omnibus figuris
              <lb/>
            ſunt ſimilia. </s>
            <s xml:id="echoid-s6561" xml:space="preserve">Quod e-
              <lb/>
            rat oſtendendum.</s>
            <s xml:id="echoid-s6562" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div623" type="section" level="1" n="208">
          <head xml:id="echoid-head263" xml:space="preserve">PROPOSITIO
            <lb/>
          Præmiſſa VI.</head>
          <p>
            <s xml:id="echoid-s6563" xml:space="preserve">DEinde ſint duo anguli B, E qualeſcunque; </s>
            <s xml:id="echoid-s6564" xml:space="preserve">ſed angulus
              <lb/>
              <note position="left" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">a</note>
            A B H, vel C B H æqualis angulo D E I, aut F E I:
              <lb/>
            </s>
            <s xml:id="echoid-s6565" xml:space="preserve">& </s>
            <s xml:id="echoid-s6566" xml:space="preserve">ſupponantur reliqua omnia iam dicta.</s>
            <s xml:id="echoid-s6567" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6568" xml:space="preserve">Quia proportio C H in H A ad quadratum H B ſuppoſita eſt, vt F I
              <lb/>
            in I D ad quadratum I E, & </s>
            <s xml:id="echoid-s6569" xml:space="preserve">H C, vel H A ad H B eſt, vt F I, vel D I
              <lb/>
            ad I E; </s>
            <s xml:id="echoid-s6570" xml:space="preserve">erit etiam H A ad H B, vt I D ad I E, & </s>
            <s xml:id="echoid-s6571" xml:space="preserve">duo anguli H, I ſunt
              <lb/>
            æquales; </s>
            <s xml:id="echoid-s6572" xml:space="preserve">igitur triangulum H B A, aut H B C ſimile eſt triangulo E D
              <lb/>
            I, aut E F I, quare duo triangula A B C, D E F ſimilia ſunt; </s>
            <s xml:id="echoid-s6573" xml:space="preserve">Et hoc
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s6574" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div625" type="section" level="1" n="209">
          <head xml:id="echoid-head264" xml:space="preserve">Notæ in Propoſit. Præmiſſas
            <lb/>
          I. II. III. IV. & V.</head>
          <p style="it">
            <s xml:id="echoid-s6575" xml:space="preserve">AFferuntur in hac ſectione aliquæ propoſitiones ſimul coaceruatæ, quæ lem-
              <lb/>
            maticæ ſunt, & </s>
            <s xml:id="echoid-s6576" xml:space="preserve">vſum habent in ſequentibus propoſitionibus; </s>
            <s xml:id="echoid-s6577" xml:space="preserve">ſanè conij-
              <lb/>
            citur ex hoc titulo PRAEMISS AE rubeis characteribus inſcripto, huiuſmodi lẽ-
              <lb/>
            mata T extui Apollonij ab Arabico Interprete, vel ab aliquo alio ſuperaddita fuiſſe;
              <lb/>
            </s>
            <s xml:id="echoid-s6578" xml:space="preserve">licet Pappus Alexandrinus libro 7. </s>
            <s xml:id="echoid-s6579" xml:space="preserve">afferat eadem ferè lemmata, tanquã propria,
              <lb/>
            & </s>
            <s xml:id="echoid-s6580" xml:space="preserve">conferentia ad Apollonij ſexti libri intelligentiam.</s>
            <s xml:id="echoid-s6581" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6582" xml:space="preserve">Poteſt tamen propoſitio vniuerſalis breuius exponi hac ratione. </s>
            <s xml:id="echoid-s6583" xml:space="preserve">Si à vertici-
              <lb/>
            bus duorum triangulorum à duobus circulis compræhenſorum rectæ lineæ ductæ
              <lb/>
            efficiant cum baſibus angulos æquales; </s>
            <s xml:id="echoid-s6584" xml:space="preserve">atque eorundem ſegmentorum inter baſim,
              <lb/>
            & </s>
            <s xml:id="echoid-s6585" xml:space="preserve">peripheriam interceptorum quadrata ad rectangula ſub factis ſegmentis </s>
          </p>
        </div>
      </text>
    </echo>
Impressum