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

Table of contents

< >
[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
< >
page |< < (107) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div395" type="section" level="1" n="123">
          <p style="it">
            <s xml:id="echoid-s4301" xml:space="preserve">
              <pb o="107" file="0145" n="145" rhead="Conicor. Lib. V."/>
            culum Z A γ, qui coniſectionem in puncto A ſecat.</s>
            <s xml:id="echoid-s4302" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4303" xml:space="preserve">Sumatur enim quodlibet punctum G in productione breuiſsimæ A I ſupra,
              <lb/>
            vel infra punctum D: </s>
            <s xml:id="echoid-s4304" xml:space="preserve">manifeſtum eſt (ex 8. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">præcedentium propoſit.) </s>
            <s xml:id="echoid-s4306" xml:space="preserve">à puncto
              <lb/>
            G duci poſſe duos breuiſecantes ramos, quorum A G erit infimus, ſi punctum G
              <lb/>
            cadit ſupra punctum D, & </s>
            <s xml:id="echoid-s4307" xml:space="preserve">tunc circulus radio G A deſcriptus continget coniſe-
              <lb/>
              <note position="right" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">11.
                <lb/>
              Additarũ.</note>
            ctionem intrinſecus in A: </s>
            <s xml:id="echoid-s4308" xml:space="preserve">ſi vero punctum g cadat infra punctum D, tunc pa-
              <lb/>
              <note position="right" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">8.
                <lb/>
              Additarũ.</note>
            riter ex g duo breuiſecantes duci poſſunt ad ſectionem, quorum ſupremus erit
              <lb/>
            g A; </s>
            <s xml:id="echoid-s4309" xml:space="preserve">& </s>
            <s xml:id="echoid-s4310" xml:space="preserve">propterea circulus radio g A deſcriptus continget coniſectionem B AC
              <lb/>
              <note position="right" xlink:label="note-0145-03" xlink:href="note-0145-03a" xml:space="preserve">11.
                <lb/>
              Additarũ.</note>
            extrinſecus in A; </s>
            <s xml:id="echoid-s4311" xml:space="preserve">quaproptcr circulus radio D A deſcriptus (quem contingit
              <lb/>
            eadem recta linea X A quæ tangebat ſectionem in A) vnicus erit, qui ſectionem
              <lb/>
            B C ſecet in A, quod erat oſtendendum.</s>
            <s xml:id="echoid-s4312" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4313" xml:space="preserve">Circulorum omnium intrinſecus tangentium coniſectionem non in axis
              <lb/>
              <note position="right" xlink:label="note-0145-04" xlink:href="note-0145-04a" xml:space="preserve">PROP.
                <lb/>
              13.
                <lb/>
              Addit.</note>
            vertice, aſsignari non poteſt maximus: </s>
            <s xml:id="echoid-s4314" xml:space="preserve">tangentium vero intrinſecus ſe-
              <lb/>
            ctionem in termino axis maximus erit, cuius radius æqualis eſt ſemie-
              <lb/>
            recto.</s>
            <s xml:id="echoid-s4315" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4316" xml:space="preserve">Repetatur figura, & </s>
            <s xml:id="echoid-s4317" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0145-01" xlink:href="fig-0145-01a" number="132">
                <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0145-01"/>
              </figure>
            hypotheſis præcedẽtis pro
              <lb/>
            poſitionis. </s>
            <s xml:id="echoid-s4318" xml:space="preserve">Quoniã qui-
              <lb/>
            libet circulus radio G A
              <lb/>
            minori, quàm D A de-
              <lb/>
            ſcriptus ſemper intrin-
              <lb/>
            ſecus tangit coniſectio-
              <lb/>
            nem in A (vt in præce-
              <lb/>
            dẽti propoſitione dictum
              <lb/>
            eſt) vbicumque ponatur
              <lb/>
            centrum G ſupra punctũ
              <lb/>
            D; </s>
            <s xml:id="echoid-s4319" xml:space="preserve">neque augendo ra-
              <lb/>
            dium G A efſicitur alius
              <lb/>
            contactus circuli, & </s>
            <s xml:id="echoid-s4320" xml:space="preserve">ſe-
              <lb/>
            ctionis, quàm intrinſe-
              <lb/>
            cus, & </s>
            <s xml:id="echoid-s4321" xml:space="preserve">tunc primo cir-
              <lb/>
            culus deſinit intrinſecus
              <lb/>
            tangere ſectionem in A,
              <lb/>
            quando D A efſicitur
              <lb/>
            radius, ſcilicet quando
              <lb/>
            non amplius intrinſecus ſectionem tangit, ſed eam ſecat in A; </s>
            <s xml:id="echoid-s4322" xml:space="preserve">quapropter aſsi-
              <lb/>
            gnari non poteſt maximus circulorum tangentium intrinſecus ſectionem in A.
              <lb/>
            </s>
            <s xml:id="echoid-s4323" xml:space="preserve">Quod verò circulorum intrinſecus tangentium eandem ſectionem in vertice axis
              <lb/>
            B, ille, cuius radius B K æqualis eſt ſemierecto B H ſit maximus, oſtenſum eſt
              <lb/>
            à Maurolico propoſ: </s>
            <s xml:id="echoid-s4324" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4325" xml:space="preserve">8. </s>
            <s xml:id="echoid-s4326" xml:space="preserve">& </s>
            <s xml:id="echoid-s4327" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4328" xml:space="preserve">libri 5. </s>
            <s xml:id="echoid-s4329" xml:space="preserve">Conicorum. </s>
            <s xml:id="echoid-s4330" xml:space="preserve">Patet ergo propoſitum.</s>
            <s xml:id="echoid-s4331" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4332" xml:space="preserve">Iiſdem poſitis: </s>
            <s xml:id="echoid-s4333" xml:space="preserve">dico circulorum omnium extrinſecus tangentium coni-
              <lb/>
              <note position="right" xlink:label="note-0145-05" xlink:href="note-0145-05a" xml:space="preserve">PROP.
                <lb/>
              14.
                <lb/>
              Addit.</note>
            ſectionem minimum aſsignari non poſſe.</s>
            <s xml:id="echoid-s4334" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum