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 |< < (111) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div414" type="section" level="1" n="127">
          <p>
            <s xml:id="echoid-s4450" xml:space="preserve">
              <pb o="111" file="0149" n="149" rhead="Conicor. Lib. V."/>
            ticulam in hyperbole, quæ in textu deſideratur. </s>
            <s xml:id="echoid-s4451" xml:space="preserve">Vocat interpres Arabicus li-
              <lb/>
            neam diſtantem ipſam A E, quæ contingit hyperbolem in vertice axis A, & </s>
            <s xml:id="echoid-s4452" xml:space="preserve">
              <lb/>
            interponitur inter verticem A, & </s>
            <s xml:id="echoid-s4453" xml:space="preserve">continentem, ſeu asymptoton D E.</s>
            <s xml:id="echoid-s4454" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4455" xml:space="preserve">Sit ſectio, D C diameter illius, &</s>
            <s xml:id="echoid-s4456" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4457" xml:space="preserve">Legendum puto; </s>
            <s xml:id="echoid-s4458" xml:space="preserve">Sit hyperbole A B
              <lb/>
              <note position="left" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">b</note>
            eius axis D C. </s>
            <s xml:id="echoid-s4459" xml:space="preserve">Poſtea quia D A, ad A G, ſeu latus tranſuer ſum ad rectum eſt,
              <lb/>
              <note position="right" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">Ex 14.
                <lb/>
              huius.</note>
            vt D H ad H C, atque I A ad A D eſt, vt B H ad H D (propter ſimilitudi-
              <lb/>
            nem triangulorum I A D, & </s>
            <s xml:id="echoid-s4460" xml:space="preserve">B H D) ergo ex æqualitate ordinata I A ad A
              <lb/>
            G eſt vt B H ad H C: </s>
            <s xml:id="echoid-s4461" xml:space="preserve">deinde quia linea A E media proportionalis eſt inter ſe-
              <lb/>
            miaxim tranſuerſum D A, & </s>
            <s xml:id="echoid-s4462" xml:space="preserve">ſemierectum A G, cum quadratum ipſius A E
              <lb/>
            quadrans ſit figuræ quæ ad diametrum per A ductum conſtituitur; </s>
            <s xml:id="echoid-s4463" xml:space="preserve">igitur E A
              <lb/>
              <note position="right" xlink:label="note-0149-03" xlink:href="note-0149-03a" xml:space="preserve">3. lib. 2.</note>
            ad A G erit, vt D A ad A E, eſt vero E A maior, quàm I A; </s>
            <s xml:id="echoid-s4464" xml:space="preserve">igitur I A ad A
              <lb/>
            G minorem proportionem habet, quàm E A ad A G, ſeu quàm D A ad A E:
              <lb/>
            </s>
            <s xml:id="echoid-s4465" xml:space="preserve">erat autem B H ad H C, vt I A ad A G: </s>
            <s xml:id="echoid-s4466" xml:space="preserve">igitur B H ad H C minorem propor-
              <lb/>
            tionem habet, quàm D A ad A E: </s>
            <s xml:id="echoid-s4467" xml:space="preserve">fiat poſtea L A ad A E, vt B H ad H C
              <lb/>
            circa angulos rectos A, H, coniungaturq; </s>
            <s xml:id="echoid-s4468" xml:space="preserve">L E, manifeſtum eſt, L A minorem
              <lb/>
            eſſe-D A, & </s>
            <s xml:id="echoid-s4469" xml:space="preserve">angulum A E L minorem eſſe angulo A E D: </s>
            <s xml:id="echoid-s4470" xml:space="preserve">ſed propter ſimili-
              <lb/>
            tudinem triangulorum B H C, L A E eſt angulus C æqualis angulo A E L; </s>
            <s xml:id="echoid-s4471" xml:space="preserve">& </s>
            <s xml:id="echoid-s4472" xml:space="preserve">
              <lb/>
            proptrea angulus A E D maior eſt angulo B C H.</s>
            <s xml:id="echoid-s4473" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div416" type="section" level="1" n="128">
          <head xml:id="echoid-head172" xml:space="preserve">Notæ in Propoſ. XXXXII.</head>
          <p>
            <s xml:id="echoid-s4474" xml:space="preserve">QVia eſt linea recta ſecans diametrum paraboles; </s>
            <s xml:id="echoid-s4475" xml:space="preserve">&</s>
            <s xml:id="echoid-s4476" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4477" xml:space="preserve">Addo illam par-
              <lb/>
              <note position="left" xlink:label="note-0149-04" xlink:href="note-0149-04a" xml:space="preserve">a</note>
            ticulam breuiſſimam, quæ in textu deſiderari videtur.</s>
            <s xml:id="echoid-s4478" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div418" type="section" level="1" n="129">
          <head xml:id="echoid-head173" xml:space="preserve">Notæ in Propoſit. XXXXIII.</head>
          <p style="it">
            <s xml:id="echoid-s4479" xml:space="preserve">INclinatum ſi non excedit erectum, nulla linearum, &</s>
            <s xml:id="echoid-s4480" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4481" xml:space="preserve">Addo, quæeui-
              <lb/>
              <note position="left" xlink:label="note-0149-05" xlink:href="note-0149-05a" xml:space="preserve">a</note>
            denter deſiciunt in textu, legi enim debet: </s>
            <s xml:id="echoid-s4482" xml:space="preserve">Axis inclinatus ideſt tranſuer-
              <lb/>
            ſus ſi non excedit erectum, &</s>
            <s xml:id="echoid-s4483" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4484" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4485" xml:space="preserve">Et quia D A ad A G eſt vt quadratum D A ad quadratum A E, &</s>
            <s xml:id="echoid-s4486" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4487" xml:space="preserve">
              <note position="left" xlink:label="note-0149-06" xlink:href="note-0149-06a" xml:space="preserve">b</note>
            Eo quod quadratum A E æquale eſt quartæ parti figuræ, quæ ad duplam ſemia-
              <lb/>
              <note position="right" xlink:label="note-0149-07" xlink:href="note-0149-07a" xml:space="preserve">3. lib. 2.</note>
            xis D A applicatur, ſcilicet æquale eſt rectangulo D A G; </s>
            <s xml:id="echoid-s4488" xml:space="preserve">igitur D A, A E,
              <lb/>
            A G ſunt continuæ proportionales: </s>
            <s xml:id="echoid-s4489" xml:space="preserve">ponitur vero D A æqualis, aut minor, quàm
              <lb/>
            A G; </s>
            <s xml:id="echoid-s4490" xml:space="preserve">igitur D A æqualis, aut minor quoque erit, quàm A E; </s>
            <s xml:id="echoid-s4491" xml:space="preserve">& </s>
            <s xml:id="echoid-s4492" xml:space="preserve">propterea in
              <lb/>
            triangulo D E A erit angulus D E A æqualis, aut maior angulo A D E, ſeu
              <lb/>
            A D F (cum angulus continentiæ ſecetur bifariam ab axi) & </s>
            <s xml:id="echoid-s4493" xml:space="preserve">prius erat an-
              <lb/>
              <note position="right" xlink:label="note-0149-08" xlink:href="note-0149-08a" xml:space="preserve">41. huius.</note>
            gulus C minor angulo A E D; </s>
            <s xml:id="echoid-s4494" xml:space="preserve">igitur angulus B C D minor erit alterno angulo
              <lb/>
            F D C; </s>
            <s xml:id="echoid-s4495" xml:space="preserve">vnde conſtat rectas lineas F D, C B concurrere poſſe, ſi vlterius pro-
              <lb/>
            ducantur ad partes D, B; </s>
            <s xml:id="echoid-s4496" xml:space="preserve">non autem ad partes C, & </s>
            <s xml:id="echoid-s4497" xml:space="preserve">F.</s>
            <s xml:id="echoid-s4498" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4499" xml:space="preserve">Quia ſi occurreret illi occurreret D F (7. </s>
            <s xml:id="echoid-s4500" xml:space="preserve">ex 2.) </s>
            <s xml:id="echoid-s4501" xml:space="preserve">ſecaretque ſectionem
              <lb/>
              <note position="left" xlink:label="note-0149-09" xlink:href="note-0149-09a" xml:space="preserve">c</note>
            in duobus punctis, &</s>
            <s xml:id="echoid-s4502" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4503" xml:space="preserve">Senſus huius textus talis eſt. </s>
            <s xml:id="echoid-s4504" xml:space="preserve">Quoniam, vt oſtensũ
              <lb/>
            eſt, recta B C inſinite producta non occurrit asymptoto D F ad partes F C; </s>
            <s xml:id="echoid-s4505" xml:space="preserve">igi-
              <lb/>
              <note position="right" xlink:label="note-0149-10" xlink:href="note-0149-10a" xml:space="preserve">8. lib. 2.</note>
            tur recta C B producta non ſecabit peripheriam hyperboles ad partes K; </s>
            <s xml:id="echoid-s4506" xml:space="preserve">nam
              <lb/>
            ſi ipſam ſecaret, ſecaret quoque asymptoton D F ad partes F, quod non poni-
              <lb/>
              <note position="right" xlink:label="note-0149-11" xlink:href="note-0149-11a" xml:space="preserve">Ibidem.</note>
            tur. </s>
            <s xml:id="echoid-s4507" xml:space="preserve">Ex his inferri debet concluſio principalis, nimirum, quod B C non occurrit
              <lb/>
            ſectioni duobus in punctis: </s>
            <s xml:id="echoid-s4508" xml:space="preserve">& </s>
            <s xml:id="echoid-s4509" xml:space="preserve">hac ratione textum alioqui corruptum emendaui.</s>
            <s xml:id="echoid-s4510" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum