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
131 93
132 94
133 95
134 96
135 97
136 98
137 99
138 100
139 101
140 102
141 103
142 104
143 105
144 106
145 107
146 108
147 109
148 110
149 111
150 112
151 113
152 114
153 115
154 116
155 117
156 118
157 119
158 120
159 121
160 122
< >
page |< < (168) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div614" type="section" level="1" n="205">
          <p style="it">
            <s xml:id="echoid-s6482" xml:space="preserve">
              <pb o="168" file="0206" n="206" rhead="Apollonij Pergæi"/>
            natim ad axium applicatæ, numero pares, quæ ad abſciſſas ſint proportionales,
              <lb/>
            tum abſcißæ inter ſe: </s>
            <s xml:id="echoid-s6483" xml:space="preserve">V nde ſequitur poſtrema concluſio, quæ in textu habetur,
              <lb/>
            quod nimirum rectangulum a L B ad rectangulum a K B eandem proportionem
              <lb/>
            habeat, quàm abſciſſa, L B ad abſciſſam K B: </s>
            <s xml:id="echoid-s6484" xml:space="preserve">ſed quotieſcunque duo rectangu-
              <lb/>
            la eandem proportionem habent, quàm baſes, illa ſunt æque alta: </s>
            <s xml:id="echoid-s6485" xml:space="preserve">igitur altitu-
              <lb/>
            dines a L, & </s>
            <s xml:id="echoid-s6486" xml:space="preserve">a K æquales ſunt inter ſe, pars, & </s>
            <s xml:id="echoid-s6487" xml:space="preserve">totum: </s>
            <s xml:id="echoid-s6488" xml:space="preserve">quod eſt absurdum.</s>
            <s xml:id="echoid-s6489" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div617" type="section" level="1" n="206">
          <head xml:id="echoid-head260" xml:space="preserve">Notæ in Propoſit. XIV.</head>
          <p style="it">
            <s xml:id="echoid-s6490" xml:space="preserve">ALioquin ſequitur, quod quadratum R L ad quadratum K P, &</s>
            <s xml:id="echoid-s6491" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6492" xml:space="preserve">In
              <lb/>
              <note position="right" xlink:label="note-0206-01" xlink:href="note-0206-01a" xml:space="preserve">a</note>
            propoſitione deficit expoſitio, quæ talis eſt. </s>
            <s xml:id="echoid-s6493" xml:space="preserve">Sit A B quælibet hyperbolc,
              <lb/>
            & </s>
            <s xml:id="echoid-s6494" xml:space="preserve">E F quælibet ellipſis. </s>
            <s xml:id="echoid-s6495" xml:space="preserve">Dico A B ipſi E
              <lb/>
              <figure xlink:label="fig-0206-01" xlink:href="fig-0206-01a" number="226">
                <image file="0206-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0206-01"/>
              </figure>
            F ſimilem non eße. </s>
            <s xml:id="echoid-s6496" xml:space="preserve">Sint eorum axes late-
              <lb/>
            ra tranſuerſa, & </s>
            <s xml:id="echoid-s6497" xml:space="preserve">recta eadem, quæ in præ-
              <lb/>
            cedenti propoſitione poſita ſunt. </s>
            <s xml:id="echoid-s6498" xml:space="preserve">Et ſiqui-
              <lb/>
            dem ſectiones A B, & </s>
            <s xml:id="echoid-s6499" xml:space="preserve">E F ſimiles credan-
              <lb/>
            tur, neceßario ex definitione ſecunda, duci
              <lb/>
            poterunt ad axes ordinatim applicatæ nu-
              <lb/>
            mero pares proportionales abſciſſis, tum
              <lb/>
            abſciſſæ inter ſe proportionales: </s>
            <s xml:id="echoid-s6500" xml:space="preserve">& </s>
            <s xml:id="echoid-s6501" xml:space="preserve">vt in
              <lb/>
            præcedenti propoſitione oſtenſum eſt, qua-
              <lb/>
            dratum R L ad quadratum P K, ſcilicet
              <lb/>
            rectangulum a L B ad rectangulum a K B in hyperbola eandem proportionem
              <lb/>
              <note position="left" xlink:label="note-0206-02" xlink:href="note-0206-02a" xml:space="preserve">21. lib. 1.</note>
            habebit, quàm quadratum γ N ad quadratum V M, ſeu quàm rectangulum b
              <lb/>
              <note position="left" xlink:label="note-0206-03" xlink:href="note-0206-03a" xml:space="preserve">Ibidem.</note>
            N F ad rectangulum b M F in ellipſi, ergo rectangulum a L B ad rectangulum
              <lb/>
            a K B eandem proportionem habet, quàm rectangulum b N F ad rectangulum
              <lb/>
            b M F: </s>
            <s xml:id="echoid-s6502" xml:space="preserve">ſed eorundem rectangulorum baſes proportionales ſunt, eo quod L B ad
              <lb/>
            B K erat vt N F ad F M; </s>
            <s xml:id="echoid-s6503" xml:space="preserve">igitur eorundem altitudines proportionales erunt,
              <lb/>
            ſcilicet a L ad a K eandem proportionem habebit, quàm b N ad b M, ſed in
              <lb/>
            hyperqola a L maior eſt, quàm a K; </s>
            <s xml:id="echoid-s6504" xml:space="preserve">in ellipſi verò contra b N minor eſt, quã
              <lb/>
            b M; </s>
            <s xml:id="echoid-s6505" xml:space="preserve">igitur maior a L ad minorem a K eandem proportionem habebit, quàm
              <lb/>
            minor b N ad maiorem b M. </s>
            <s xml:id="echoid-s6506" xml:space="preserve">Luod erat abſurdum.</s>
            <s xml:id="echoid-s6507" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div619" type="section" level="1" n="207">
          <head xml:id="echoid-head261" xml:space="preserve">SECTIO QVINTA</head>
          <head xml:id="echoid-head262" xml:space="preserve">Continens ſex Propoſitiones Præmiſſas,
            <lb/>
          PROPOSITIO I. II. III. IV. & V.</head>
          <p>
            <s xml:id="echoid-s6508" xml:space="preserve">SI in triangulis A B C, D E F in duobus circulorum ſeg-
              <lb/>
              <note position="right" xlink:label="note-0206-04" xlink:href="note-0206-04a" xml:space="preserve">I</note>
            mentis A T C, D G F deſcriptis, à duobus angulis B,
              <lb/>
            E, educantur duæ rectæ lineæ B T H, E G I efficientes cum
              <lb/>
            baſibus A C, D F duos angulos H, I æquales (incidentes </s>
          </p>
        </div>
      </text>
    </echo>
Impressum