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
371 332
372 333
373 334
374 335
375 336
376 337
377 338
378 339
379 340
380 341
381 342
382 343
383 344
384 345
385 346
386 347
387 348
388 349
389 350
390 351
391 352
392 353
393 354
394 355
395 356
396 357
397 358
398 359
399 360
400 361
< >
page |< < (389) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1115" type="section" level="1" n="354">
          <p style="it">
            <s xml:id="echoid-s13029" xml:space="preserve">
              <pb o="389" file="0427" n="428" rhead="Aſſumpt. Liber."/>
            pariterque proportio diametri ad circuli peripheriam ſatis compendioſe deduci
              <lb/>
            poteſt, quandoquidem inter figuram ordinatam eidem circulo inſcriptam, cuius
              <lb/>
            ſemilatus eſt E B, & </s>
            <s xml:id="echoid-s13030" xml:space="preserve">circumſcriptam duplo laterum numero, cuius duo ſemila-
              <lb/>
            tera ſunt C D B, circulus intermediat; </s>
            <s xml:id="echoid-s13031" xml:space="preserve">& </s>
            <s xml:id="echoid-s13032" xml:space="preserve">Perimeter circumſcriptæ figuræ ad
              <lb/>
            Perimetrum inſcriptæ eandem proportionem habet, quam diameter C A ad A E,
              <lb/>
            quæ proportio minui ſemper magis, ac magis poteſt in infinitum; </s>
            <s xml:id="echoid-s13033" xml:space="preserve">& </s>
            <s xml:id="echoid-s13034" xml:space="preserve">tandem ex
              <lb/>
            3. </s>
            <s xml:id="echoid-s13035" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s13036" xml:space="preserve">ſequenti, ex continua ſemipartitione quadrantis circuli elici poſſunt
              <lb/>
            ſubtenſæ ſucceſſiuè ſubdiuiſæ in infinitum, & </s>
            <s xml:id="echoid-s13037" xml:space="preserve">propterea dabitur proportio dia-
              <lb/>
            metri A C ad ſemiſubtenſam B E, ſed datur quadratum ipſius B E, igitur da-
              <lb/>
            tur rectangulum A E C ſub ſegmentis diametri, & </s>
            <s xml:id="echoid-s13038" xml:space="preserve">datur E C ex iam dicta 3.
              <lb/>
            </s>
            <s xml:id="echoid-s13039" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s13040" xml:space="preserve">igitur datur quoque E A; </s>
            <s xml:id="echoid-s13041" xml:space="preserve">eſtque B E ad C D B, vt E A ad diametrũ
              <lb/>
            A C, igitur quarta quantitas innoteſcet, ſcilicet rectæ C D B, quæ æqualia
              <lb/>
            ſunt vni lateri Poligoni circumſcripti duplo laterum numero, & </s>
            <s xml:id="echoid-s13042" xml:space="preserve">ideo habebitur
              <lb/>
            menſura totius Perimetri tum Poligoni inſcripti, cum circumſcripti, quare
              <lb/>
            menſura ipſius peripheriæ circuli, quæ intermedia eſt, facili negotio inueſtiga-
              <lb/>
            bitur.</s>
            <s xml:id="echoid-s13043" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1117" type="section" level="1" n="355">
          <head xml:id="echoid-head447" xml:space="preserve">PROPOSITIO III.</head>
          <p>
            <s xml:id="echoid-s13044" xml:space="preserve">S It C A ſegmentum circuli, & </s>
            <s xml:id="echoid-s13045" xml:space="preserve">B
              <lb/>
              <figure xlink:label="fig-0427-01" xlink:href="fig-0427-01a" number="492">
                <image file="0427-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0427-01"/>
              </figure>
            punctum ſuper illud vbicumque,
              <lb/>
            & </s>
            <s xml:id="echoid-s13046" xml:space="preserve">B D perpendicularis ſuper A C, & </s>
            <s xml:id="echoid-s13047" xml:space="preserve">
              <lb/>
            ſegmentum D E æquale D A, & </s>
            <s xml:id="echoid-s13048" xml:space="preserve">arcus
              <lb/>
            B F æqualis arcui B A, vtique iuncta
              <lb/>
            C F erit æqualis ipſi C E.</s>
            <s xml:id="echoid-s13049" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13050" xml:space="preserve">Demonſtratio. </s>
            <s xml:id="echoid-s13051" xml:space="preserve">Iungamus lineas A B, B F,
              <lb/>
            F E, E B; </s>
            <s xml:id="echoid-s13052" xml:space="preserve">& </s>
            <s xml:id="echoid-s13053" xml:space="preserve">quia arcus B A æqualis eſt arcui B F, erit A B æqualis
              <lb/>
            B F, & </s>
            <s xml:id="echoid-s13054" xml:space="preserve">quia A D æqualis eſt E D, & </s>
            <s xml:id="echoid-s13055" xml:space="preserve">duo anguli D ſunt recti, & </s>
            <s xml:id="echoid-s13056" xml:space="preserve">D B
              <lb/>
            communis, ergo A B æqualis eſt B E, & </s>
            <s xml:id="echoid-s13057" xml:space="preserve">propterea B F, B E ſunt æqua-
              <lb/>
            les; </s>
            <s xml:id="echoid-s13058" xml:space="preserve">& </s>
            <s xml:id="echoid-s13059" xml:space="preserve">duo anguli B F E, B E F ſunt æquales. </s>
            <s xml:id="echoid-s13060" xml:space="preserve">Et quia quadrilaterum.
              <lb/>
            </s>
            <s xml:id="echoid-s13061" xml:space="preserve">C F B A eſt in circulo, erit angulus C F B cum angulo C A B ipſi op-
              <lb/>
            poſito, immo cum angulo B E A, æqualis duobus rectis; </s>
            <s xml:id="echoid-s13062" xml:space="preserve">ſed angulus C
              <lb/>
            E B cum angulo B E A, æquales ſunt duobus rectis, ergo duo anguli C
              <lb/>
            F B, C E B ſunt æquales, & </s>
            <s xml:id="echoid-s13063" xml:space="preserve">remanent C F E, C E F æqualas; </s>
            <s xml:id="echoid-s13064" xml:space="preserve">ergo
              <lb/>
            C E æqualis eſt C F, & </s>
            <s xml:id="echoid-s13065" xml:space="preserve">hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13066" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1119" type="section" level="1" n="356">
          <head xml:id="echoid-head448" xml:space="preserve">Notæ in Propoſit. III.</head>
          <p style="it">
            <s xml:id="echoid-s13067" xml:space="preserve">HAEc eſt propoſ. </s>
            <s xml:id="echoid-s13068" xml:space="preserve">5. </s>
            <s xml:id="echoid-s13069" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s13070" xml:space="preserve">9. </s>
            <s xml:id="echoid-s13071" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13072" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13073" xml:space="preserve">Almag. </s>
            <s xml:id="echoid-s13074" xml:space="preserve">Ptol.</s>
            <s xml:id="echoid-s13075" xml:space="preserve">, ſed hic vniuerſalius pro-
              <lb/>
            nunciatur; </s>
            <s xml:id="echoid-s13076" xml:space="preserve">Ptolomeus enim ſupponit ſegmentum A B C ſemicirculum
              <lb/>
            eſſe, & </s>
            <s xml:id="echoid-s13077" xml:space="preserve">ex cognita circumferentia A F, & </s>
            <s xml:id="echoid-s13078" xml:space="preserve">corda F C, & </s>
            <s xml:id="echoid-s13079" xml:space="preserve">illius medietate A
              <lb/>
            B, quærit chordam A B; </s>
            <s xml:id="echoid-s13080" xml:space="preserve">eſt enim rectangulum ſub C A D æquale </s>
          </p>
        </div>
      </text>
    </echo>
Impressum