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
201 163
202 164
203 165
204 166
205 167
206 168
207 169
208 170
209 171
210 172
211 173
212 174
213 175
214 176
215 177
216 178
217 179
218 180
219 181
220 182
221 183
222 184
223 185
224 186
225 187
226 188
227 189
228 190
229 191
230 192
< >
page |< < (151) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div567" type="section" level="1" n="185">
          <pb o="151" file="0189" n="189" rhead="Conicor. Lib. VI."/>
          <p style="it">
            <s xml:id="echoid-s5926" xml:space="preserve">In ſestione A B C ducatur ramus breuiſe-
              <lb/>
              <figure xlink:label="fig-0189-01" xlink:href="fig-0189-01a" number="202">
                <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0189-01"/>
              </figure>
            cans ſingularis I L ſecans axem in G, ſitque
              <lb/>
              <note position="right" xlink:label="note-0189-01" xlink:href="note-0189-01a" xml:space="preserve">51. 52. 53.
                <lb/>
              lib. 5,</note>
            I punctum concur ſus perpendicularis I K, & </s>
            <s xml:id="echoid-s5927" xml:space="preserve">
              <lb/>
            breuiſecantis; </s>
            <s xml:id="echoid-s5928" xml:space="preserve">& </s>
            <s xml:id="echoid-s5929" xml:space="preserve">à quolibet puncto B inter
              <lb/>
            L, & </s>
            <s xml:id="echoid-s5930" xml:space="preserve">verticem A ducatur alius ramus bre-
              <lb/>
            uiſecans B M, qui occurret L I vltra axim
              <lb/>
            in M, & </s>
            <s xml:id="echoid-s5931" xml:space="preserve">inter puncta G, & </s>
            <s xml:id="echoid-s5932" xml:space="preserve">I; </s>
            <s xml:id="echoid-s5933" xml:space="preserve">coniungatur-
              <lb/>
              <note position="right" xlink:label="note-0189-02" xlink:href="note-0189-02a" xml:space="preserve">28. lib. 5.
                <lb/>
              8. Addir.
                <lb/>
              lib. 5.</note>
            que recta linea B 1. </s>
            <s xml:id="echoid-s5934" xml:space="preserve">Quoniam angulus L G A acutus eſt, erit angnlus G M N
              <lb/>
            internus, & </s>
            <s xml:id="echoid-s5935" xml:space="preserve">oppoſitus in triangulo G M N minor illò, & </s>
            <s xml:id="echoid-s5936" xml:space="preserve">ideo acutus, & </s>
            <s xml:id="echoid-s5937" xml:space="preserve">pro-
              <lb/>
              <note position="right" xlink:label="note-0189-03" xlink:href="note-0189-03a" xml:space="preserve">13. 14. 15.
                <lb/>
              lib. 5.</note>
            pterea qui deinceps eſt angulus B M I erit obtuſus, & </s>
            <s xml:id="echoid-s5938" xml:space="preserve">ideo in triangulo I B M
              <lb/>
            latus I B ſubtendens maximum angulum obtuſum maius erit latera B M; </s>
            <s xml:id="echoid-s5939" xml:space="preserve">ſedra-
              <lb/>
            mus I L maior eſt, quàm I B, propterea quod remotior eſt à vertice A, igitur
              <lb/>
              <note position="right" xlink:label="note-0189-04" xlink:href="note-0189-04a" xml:space="preserve">67. lib. 5.</note>
            ramus I L maior erit, quàm B M: </s>
            <s xml:id="echoid-s5940" xml:space="preserve">Secari ergo poterunt æquales rectæ lineæ L R,
              <lb/>
            B S, quæ ſint minores quidẽ, quàm I L, ſed maiores, quàm M B; </s>
            <s xml:id="echoid-s5941" xml:space="preserve">& </s>
            <s xml:id="echoid-s5942" xml:space="preserve">deſcribantur
              <lb/>
            duo circuli, quorum radij ſint S B, & </s>
            <s xml:id="echoid-s5943" xml:space="preserve">R L æquales, atque centra ſint S, & </s>
            <s xml:id="echoid-s5944" xml:space="preserve">R;
              <lb/>
            </s>
            <s xml:id="echoid-s5945" xml:space="preserve">
              <note position="right" xlink:label="note-0189-05" xlink:href="note-0189-05a" xml:space="preserve">Ex 12.
                <lb/>
              Addit.
                <lb/>
              lib. 5.</note>
            Manifeſtum eſt circulum, cuius radius B S contingere coniſectionem A C in
              <lb/>
            puncto B, & </s>
            <s xml:id="echoid-s5946" xml:space="preserve">extrinſecùs incedere, propterea quod radius B S maior eſt maximo
              <lb/>
            breuiſecantium M B à concurſu M educto; </s>
            <s xml:id="echoid-s5947" xml:space="preserve">è contra circulus radio R L deſcri-
              <lb/>
              <note position="right" xlink:label="note-0189-06" xlink:href="note-0189-06a" xml:space="preserve">8. Addit.
                <lb/>
              lib. 5.
                <lb/>
              Ibidem.</note>
            ptus intrinſecùs continget eandem coniſectionem in L cum ramus M L minor ſit
              <lb/>
            ſingulari breuiſecante L I. </s>
            <s xml:id="echoid-s5948" xml:space="preserve">Tandẽ in ſectione D E F ſecetur axis abſcißa D H
              <lb/>
            æqualis A N, & </s>
            <s xml:id="echoid-s5949" xml:space="preserve">in angulo D H P æquali angulo A N B ducatur radius γ H P,
              <lb/>
            qui fiat æqualis S B, & </s>
            <s xml:id="echoid-s5950" xml:space="preserve">cẽtro γ radio verò γ P circulus deſcribatur. </s>
            <s xml:id="echoid-s5951" xml:space="preserve">Et quia in
              <lb/>
            ſectionibus æqualibus abſciſſæ, breuiſecantes, anguli ab eis contenti, & </s>
            <s xml:id="echoid-s5952" xml:space="preserve">circu-
              <lb/>
            li deſcripti ſunt æquales, & </s>
            <s xml:id="echoid-s5953" xml:space="preserve">congruentes; </s>
            <s xml:id="echoid-s5954" xml:space="preserve">igitur circulus radio γ P deſcriptus,
              <lb/>
            contingit coniſectionem D E F extrinſecùs; </s>
            <s xml:id="echoid-s5955" xml:space="preserve">ſicuti circulus radij S B tangebat
              <lb/>
            ſectionem A B C in B extrinſecùs. </s>
            <s xml:id="echoid-s5956" xml:space="preserve">Vterat propoſitum.</s>
            <s xml:id="echoid-s5957" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5958" xml:space="preserve">Hoc demonſtrat o oſtendetur, quod in duabus coniſectionibus A B C,
              <lb/>
              <note position="right" xlink:label="note-0189-07" xlink:href="note-0189-07a" xml:space="preserve">PROP. 1.
                <lb/>
              Addit.</note>
            D E F æqualibus, quarum axes A G, D H duæ portiones B C, & </s>
            <s xml:id="echoid-s5959" xml:space="preserve">
              <lb/>
            E F non æquè ab axium verticibus remotæ non erunt ſibi congruentes.</s>
            <s xml:id="echoid-s5960" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5961" xml:space="preserve">Si enim poſſibile eſt B C, & </s>
            <s xml:id="echoid-s5962" xml:space="preserve">E F ſibi mutuò congruant, & </s>
            <s xml:id="echoid-s5963" xml:space="preserve">ſumatur interme-
              <lb/>
            dium punctum commune, vel duo puncta coincidentia L, & </s>
            <s xml:id="echoid-s5964" xml:space="preserve">P, & </s>
            <s xml:id="echoid-s5965" xml:space="preserve">quia portio-
              <lb/>
            nes B C, E F inæqualiter diſtant à verticibus, ergo puncta coincidentia L, P
              <lb/>
            non erunt æquè à verticibus remota; </s>
            <s xml:id="echoid-s5966" xml:space="preserve">ſit ergo P propinquius vertici D, quàm eſt
              <lb/>
            L vertici A, & </s>
            <s xml:id="echoid-s5967" xml:space="preserve">per L, & </s>
            <s xml:id="echoid-s5968" xml:space="preserve">P ducantur rectæ
              <lb/>
              <figure xlink:label="fig-0189-02" xlink:href="fig-0189-02a" number="203">
                <image file="0189-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0189-02"/>
              </figure>
            lineæ L O, P Q tangentes ſectiones, & </s>
            <s xml:id="echoid-s5969" xml:space="preserve">ex lẽ-
              <lb/>
              <note position="right" xlink:label="note-0189-08" xlink:href="note-0189-08a" xml:space="preserve">33. 34.
                <lb/>
              lib. 1.</note>
            matæ præcedenti deſcribantur duo circuli æ-
              <lb/>
            quales Z P T, & </s>
            <s xml:id="echoid-s5970" xml:space="preserve">V L X radijs I L & </s>
            <s xml:id="echoid-s5971" xml:space="preserve">S
              <lb/>
            P, quorum Z T extrinſecus tangat ſectionẽ
              <lb/>
            in P, & </s>
            <s xml:id="echoid-s5972" xml:space="preserve">V X intrinſecus in L, cumque eo-
              <lb/>
            rum radij I L, S P ſint breuiſecantes, erunt
              <lb/>
            perpendiculares ad L O, P Q contingentes
              <lb/>
              <note position="right" xlink:label="note-0189-09" xlink:href="note-0189-09a" xml:space="preserve">29. 30.
                <lb/>
              lib. 5.</note>
            ſectionem in L, & </s>
            <s xml:id="echoid-s5973" xml:space="preserve">P; </s>
            <s xml:id="echoid-s5974" xml:space="preserve">atque portiones B C, E F ſibi mutuò congruunt, ideſt
              <lb/>
              <note position="right" xlink:label="note-0189-10" xlink:href="note-0189-10a" xml:space="preserve">35. 36.
                <lb/>
              lib. 1.</note>
            conſtituunt vnicam communem peripheriam, ergo rectæ lineæ L O, P Q
              <lb/>
            contingentes eandem ſectionem ſibi mutuò congruent, pariterque breuiſe-
              <lb/>
            cantes æquales L I, P M ad illas perpendiculariter inſiſtentes crunt congruentes
              <lb/>
            quoque; </s>
            <s xml:id="echoid-s5975" xml:space="preserve">& </s>
            <s xml:id="echoid-s5976" xml:space="preserve">propterea circuli V X, Z T ab ijs radijs geniti erunt quoque </s>
          </p>
        </div>
      </text>
    </echo>
Impressum