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
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
171 133
172 134
173 135
174 136
175 137
176 138
177 139
178 140
179 141
180 142
< >
page |< < (114) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div423" type="section" level="1" n="130">
          <p>
            <s xml:id="echoid-s4562" xml:space="preserve">
              <pb o="114" file="0152" n="152" rhead="Apollonij Pergæi"/>
            I D minus eſt, quàm quadratũ I C duplo trianguli N F M, quod æqua-
              <lb/>
            le eſt exemplari applicato ad D C, & </s>
            <s xml:id="echoid-s4563" xml:space="preserve">quadratum I R æquale eſt duplo
              <lb/>
            trianguli I X R, & </s>
            <s xml:id="echoid-s4564" xml:space="preserve">quadratum A R æquale eſt duplo trapezij R M (3. </s>
            <s xml:id="echoid-s4565" xml:space="preserve">ex
              <lb/>
            5.) </s>
            <s xml:id="echoid-s4566" xml:space="preserve">ergo quadratũ I A minus eſt, quàm quadratum I C duplo trianguli
              <lb/>
            F Z X, quod æquale ex exemplari applicato ad C R (6. </s>
            <s xml:id="echoid-s4567" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4568" xml:space="preserve">ſimiliter
              <lb/>
            quadratum I L minus eſt, quàm quadratum I C exemplari applicato ad
              <lb/>
            C Q; </s>
            <s xml:id="echoid-s4569" xml:space="preserve">eſtque C D maior, quàm C R, & </s>
            <s xml:id="echoid-s4570" xml:space="preserve">C R quàm C Q; </s>
            <s xml:id="echoid-s4571" xml:space="preserve">ergo I A ma-
              <lb/>
            ior eſt, quàm I D, & </s>
            <s xml:id="echoid-s4572" xml:space="preserve">I L, quàm I A; </s>
            <s xml:id="echoid-s4573" xml:space="preserve">quod erat propoſitum.</s>
            <s xml:id="echoid-s4574" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div426" type="section" level="1" n="131">
          <head xml:id="echoid-head176" xml:space="preserve">Notæ in Propoſit. XVI. XVII. XVIII.</head>
          <p style="it">
            <s xml:id="echoid-s4575" xml:space="preserve">COmparata ſi fuerit ex recto duorum axium ellipſis crit maximus ra-
              <lb/>
              <note position="right" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">a</note>
            morum, &</s>
            <s xml:id="echoid-s4576" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4577" xml:space="preserve">Addidi particulam illam axis minoris, quæ in textu defi-
              <lb/>
            ciebat, nunquam enim C F ſemiſsis lateris recti, eſſe poteſt maior C E ſemiſſe
              <lb/>
            lateris tranſuerſi, niſi C D fuerit axis minor ellipſis.</s>
            <s xml:id="echoid-s4578" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4579" xml:space="preserve">Conſtat, quemadmodum demonſtrauimus in propoſitione 6. </s>
            <s xml:id="echoid-s4580" xml:space="preserve">&</s>
            <s xml:id="echoid-s4581" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4582" xml:space="preserve">Quo-
              <lb/>
              <note position="right" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">b</note>
            niã menſura I C ſupponitur cõparata, ideſt æqualis ipſi C F ſemiſsi lateris recti;
              <lb/>
            </s>
            <s xml:id="echoid-s4583" xml:space="preserve">propterea triangulum I C F iſoſceleum erit, & </s>
            <s xml:id="echoid-s4584" xml:space="preserve">rectangulum in C; </s>
            <s xml:id="echoid-s4585" xml:space="preserve">& </s>
            <s xml:id="echoid-s4586" xml:space="preserve">ideo qua-
              <lb/>
            dratum I C æquale erit duplo trianguli I C F: </s>
            <s xml:id="echoid-s4587" xml:space="preserve">eadem ratione propter parallelas
              <lb/>
            S O, & </s>
            <s xml:id="echoid-s4588" xml:space="preserve">C F, erit triangulum I O S ſimile triangulo I C F, & </s>
            <s xml:id="echoid-s4589" xml:space="preserve">propterea illud
              <lb/>
            quoque iſoſceleum erit, & </s>
            <s xml:id="echoid-s4590" xml:space="preserve">rectangulum in O, & </s>
            <s xml:id="echoid-s4591" xml:space="preserve">ideo quadratum I O æquale,
              <lb/>
            erit duplo trianguli I O S: </s>
            <s xml:id="echoid-s4592" xml:space="preserve">eſt verò quadratum O H æquale duplo trapezij F T
              <lb/>
              <note position="left" xlink:label="note-0152-03" xlink:href="note-0152-03a" xml:space="preserve">1. huius.</note>
            O C; </s>
            <s xml:id="echoid-s4593" xml:space="preserve">igitur quadratum I H ( quod eſt æquale duobus quadratis I O, O H circa
              <lb/>
            angulum rectum O) æquale erit duplo trianguli I O S cum duplo trapezij F T
              <lb/>
            O C, ſed hæc duo ſpatia minora ſunt duplo integri trianguli I C F, eſtque de-
              <lb/>
            fectus duplum trianguli F T S, ſiue rectangulum S T b a; </s>
            <s xml:id="echoid-s4594" xml:space="preserve">igitur duplum trian-
              <lb/>
            guli I C F, ſiue quadratum I C maius eſt quadrato I H, & </s>
            <s xml:id="echoid-s4595" xml:space="preserve">exceſſus eſt rectan-
              <lb/>
            gulum T a: </s>
            <s xml:id="echoid-s4596" xml:space="preserve">quod vero rectangulum T a ſit exemplar demonſtrabitur modo, vt
              <lb/>
            in ſexta propoſitione huius.</s>
            <s xml:id="echoid-s4597" xml:space="preserve"/>
          </p>
          <figure number="140">
            <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0152-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s4598" xml:space="preserve">Et conſtat, vt dictum eſt, quod ſit exemplar applicatum ad O C, &</s>
            <s xml:id="echoid-s4599" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4600" xml:space="preserve">
              <note position="right" xlink:label="note-0152-04" xlink:href="note-0152-04a" xml:space="preserve">c</note>
            Quoniam rectæ S a, T b, I C ſunt parallelæ, erunt triangula I C F, & </s>
            <s xml:id="echoid-s4601" xml:space="preserve">S a </s>
          </p>
        </div>
      </text>
    </echo>
Impressum