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
261 223
262 224
263 225
264 226
265 227
266 228
267 229
268 230
269 231
270 232
271 233
272 234
273 235
274 236
275 237
276 238
277 239
278 240
279 241
280 242
281 243
282 244
283 245
284 246
285 247
286 248
287 249
288 250
289 251
290 252
< >
page |< < (105) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div382" type="section" level="1" n="122">
          <pb o="105" file="0143" n="143" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div395" type="section" level="1" n="123">
          <head xml:id="echoid-head166" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4248" xml:space="preserve">HInc conſtat, ſupremam circuli peripheriam A Z cadere in locum à tan-
              <lb/>
            gente X A, & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">coniſectionem B A contentum, infimam vero circuferen-
              <lb/>
            tiam A γ cadere ne dum infra tangentem, ſed etiam infra coniſectionem A G;
              <lb/>
            </s>
            <s xml:id="echoid-s4250" xml:space="preserve">eoquod recta A X cadit extra circuli peripheriam A Z, quàm contingit in A,
              <lb/>
            & </s>
            <s xml:id="echoid-s4251" xml:space="preserve">eadem circumferentia A Z cadit extra ſectionem A B, quàm ſecat in A, vt
              <lb/>
            dictum eſt.</s>
            <s xml:id="echoid-s4252" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4253" xml:space="preserve">Mirabile quidem hoc videri poterit aliquibus, qui contingentiæ angulos, quos
              <lb/>
            vocant, verè angulos eſſe cenſent; </s>
            <s xml:id="echoid-s4254" xml:space="preserve">nam hic duæ circumſerentiæ curuæ, conica
              <lb/>
            nimirum B A G, & </s>
            <s xml:id="echoid-s4255" xml:space="preserve">circularis Z A γ ſe mutuo ſecant in A, & </s>
            <s xml:id="echoid-s4256" xml:space="preserve">tamen ambo
              <lb/>
            tanguntur ab eadẽ recta linea A X in eodem puncto A, in quo illæ ſe mutuò ſecant.
              <lb/>
            </s>
            <s xml:id="echoid-s4257" xml:space="preserve">Vnde colligent etiam, quod anguli contingentiæ facti à coniſectione B A G, & </s>
            <s xml:id="echoid-s4258" xml:space="preserve">
              <lb/>
            recta linea X A non ſunt æquales inter ſe, quando punctum A in vertice axis
              <lb/>
            non exiſtit; </s>
            <s xml:id="echoid-s4259" xml:space="preserve">nam duo anguli contingentiæ circumſerentiæ circularis, & </s>
            <s xml:id="echoid-s4260" xml:space="preserve">rectæ
              <lb/>
            tangentis X A æquales ſunt inter ſe: </s>
            <s xml:id="echoid-s4261" xml:space="preserve">at angulus contingentiæ ſectionis conicæ ſu-
              <lb/>
            premus reſpiciens verticem B maior eſt angulo contingentiæ circularis, vt dictũ
              <lb/>
            eſt: </s>
            <s xml:id="echoid-s4262" xml:space="preserve">infimus vero angulus contingentiæ à ſectione conica, & </s>
            <s xml:id="echoid-s4263" xml:space="preserve">eadem tangente
              <lb/>
            contentus minor eſt eodem angulo contingentiæ circularis, & </s>
            <s xml:id="echoid-s4264" xml:space="preserve">propterea ſupremus
              <lb/>
            angnlus contingentiæ ſectionis conicæ maior erit inferiori.</s>
            <s xml:id="echoid-s4265" xml:space="preserve"/>
          </p>
          <figure number="129">
            <image file="0143-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0143-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s4266" xml:space="preserve">Sit perpendicularis D E
              <lb/>
              <note position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">PROP.
                <lb/>
              II.
                <lb/>
              Addit.
                <lb/>
              Ex 51. 52.
                <lb/>
              53. huius.</note>
            minor trutina L, ſintque D
              <lb/>
            A, & </s>
            <s xml:id="echoid-s4267" xml:space="preserve">D C duo illi rami,
              <lb/>
            qui tantummodo breuiſecantes
              <lb/>
            eſſe poſſunt omnium ramorum
              <lb/>
            ex concurſu D ad ſectionem
              <lb/>
            B C cadentium; </s>
            <s xml:id="echoid-s4268" xml:space="preserve">atque cen-
              <lb/>
            tro D, interuallo D A deſcri-
              <lb/>
            batur circulus Z A γ; </s>
            <s xml:id="echoid-s4269" xml:space="preserve">pari-
              <lb/>
            terque centro D, interuallo D
              <lb/>
            C deſcribatur circulus O C Q;
              <lb/>
            </s>
            <s xml:id="echoid-s4270" xml:space="preserve">ducanturque rectæ X P, M
              <lb/>
            P contingentes coniſectionem
              <lb/>
            in A, & </s>
            <s xml:id="echoid-s4271" xml:space="preserve">C. </s>
            <s xml:id="echoid-s4272" xml:space="preserve">Dico, circulũ
              <lb/>
            Z A γ contingere coniſectio-
              <lb/>
            nem in A, & </s>
            <s xml:id="echoid-s4273" xml:space="preserve">extra ipſam
              <lb/>
            cadere, at circulum O C Q contingere eandem coniſectionem in C, & </s>
            <s xml:id="echoid-s4274" xml:space="preserve">
              <lb/>
            intra ipſam cadere.</s>
            <s xml:id="echoid-s4275" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4276" xml:space="preserve">Ducantur quilibet rami D F, D G ſupra, & </s>
            <s xml:id="echoid-s4277" xml:space="preserve">infra breuiſecantem D A, ſe-
              <lb/>
            cantes circulum Z A γ in Z, & </s>
            <s xml:id="echoid-s4278" xml:space="preserve">γ; </s>
            <s xml:id="echoid-s4279" xml:space="preserve">pariterque ducantur quilibet rami D </s>
          </p>
        </div>
      </text>
    </echo>
Impressum