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
101 63
102 64
103 65
104 66
105 67
106 68
107 69
108 70
109 71
110 72
111 73
112 74
113 75
114 76
115 77
116 78
117 79
118 80
119 81
120 82
121 83
122 84
123 85
124 86
125 87
126 88
127 89
128 90
129 91
130 92
< >
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