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

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            C S V cum duplo trianguli F S V; </s>
            <s xml:id="echoid-s4825" xml:space="preserve">ideſt quadratum I B æquale eſt duplo trian-
              <lb/>
            guli I S C cum duplo trianguli F S V; </s>
            <s xml:id="echoid-s4826" xml:space="preserve">& </s>
            <s xml:id="echoid-s4827" xml:space="preserve">quoniam propter parallelas C S, & </s>
            <s xml:id="echoid-s4828" xml:space="preserve">
              <lb/>
            G V, triangulum I C S ſimile eſt iſoſcelio, & </s>
            <s xml:id="echoid-s4829" xml:space="preserve">rectangulo triangulo I G V, erit,
              <lb/>
            quadratum I C æquale duplo trianguli I C S iſoſcelei, & </s>
            <s xml:id="echoid-s4830" xml:space="preserve">rectanguli in C; </s>
            <s xml:id="echoid-s4831" xml:space="preserve">ergo
              <lb/>
            exceſſus quadrati I B ſupra quadratum I C æquale eſt duplo trianguli F S V;
              <lb/>
            </s>
            <s xml:id="echoid-s4832" xml:space="preserve">eſt verò rectangulum, cuius baſis F S, altitudo verò C G æquale duplo trianguli
              <lb/>
            F S V; </s>
            <s xml:id="echoid-s4833" xml:space="preserve">atque buiuſmodi rectangulum eſt exemplar applicatum ad abſciſſam G
              <lb/>
            C, vt in notis prop. </s>
            <s xml:id="echoid-s4834" xml:space="preserve">16. </s>
            <s xml:id="echoid-s4835" xml:space="preserve">17. </s>
            <s xml:id="echoid-s4836" xml:space="preserve">& </s>
            <s xml:id="echoid-s4837" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4838" xml:space="preserve">litera c. </s>
            <s xml:id="echoid-s4839" xml:space="preserve">oſtenſum eſt igitur quadrati I B
              <lb/>
            exceßus ſupra quadratum I C eſt exemplar applicatum ad abſciſſam G C: </s>
            <s xml:id="echoid-s4840" xml:space="preserve">Simili
              <lb/>
              <figure xlink:label="fig-0160-01" xlink:href="fig-0160-01a" number="153">
                <image file="0160-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0160-01"/>
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            modo quadratum I K oſtendetur æquale duplo trianguli I C S vna cum duplo
              <lb/>
            trapezij L T S F; </s>
            <s xml:id="echoid-s4841" xml:space="preserve">atque dupli trianguli I C S cum duplo trianguli F S V ex-
              <lb/>
            ceſſus ſupra duplum trianguli I C S cum duplo trapezij L T S F eſt duplum
              <lb/>
            trianguli L T V; </s>
            <s xml:id="echoid-s4842" xml:space="preserve">ergo quadrati I B exceſſus ſupra quadratum I K eſt duplum
              <lb/>
            trianguli L T V, ſeu exemplar applicatum ad G P differentiam abſciſſarum.
              <lb/>
            </s>
            <s xml:id="echoid-s4843" xml:space="preserve">Poſtea quia triangula ſimilia E C F, E D M ſunt æqualia, cum eorum bomologa
              <lb/>
            latera E C, E D æqualia ſint; </s>
            <s xml:id="echoid-s4844" xml:space="preserve">ergo addito communi triangulo I E V, erit trian-
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            gulum E C F cum triangulo E I V, ſeu triangulũ I C S cum triangulo F S V
              <lb/>
            æquale duobus triaugulis E D M, & </s>
            <s xml:id="echoid-s4845" xml:space="preserve">I E V, ſeu duobus triangulis M V N, & </s>
            <s xml:id="echoid-s4846" xml:space="preserve">
              <lb/>
            N I D: </s>
            <s xml:id="echoid-s4847" xml:space="preserve">erat autem quadratum I B æquale duplo trianguli I C S cum duplo tri-
              <lb/>
            anguli F S V; </s>
            <s xml:id="echoid-s4848" xml:space="preserve">igitur quadratum I B æquale erit duplo trianguli M N V cum
              <lb/>
            duplo trianguli N I D; </s>
            <s xml:id="echoid-s4849" xml:space="preserve">eſtque quadratum I D æquale duplo trianguli iſoſcelei,
              <lb/>
            rectanguli I D N; </s>
            <s xml:id="echoid-s4850" xml:space="preserve">igitur quadratum I B ſuperat quadratum I D, eſtque exceſ-
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            ſus duplum trianguli M N V ſeu exemplar applicatum ad G D. </s>
            <s xml:id="echoid-s4851" xml:space="preserve">Tandem quia
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            quadratum I Q æquale eſt duplo trianguli iſoſcelei rectanguli I Q X, atque
              <lb/>
            quadratum Q A æquale eſt duplo trapezij Q M; </s>
            <s xml:id="echoid-s4852" xml:space="preserve">igitur quadratũ bypotbenuſæ I
              <lb/>
            A æquale eſt duplo trianguli I D N cum duplo trapezij X N M Z; </s>
            <s xml:id="echoid-s4853" xml:space="preserve">ergo exceſ-
              <lb/>
            ſus quadrati I A ſupra quadratnm I D æqualis eſt duplo trapezij X N M Z; </s>
            <s xml:id="echoid-s4854" xml:space="preserve">exceſ-
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            ſus autem trianguli N M V ſupra trapezium N Z eſt triangulum X Z V; </s>
            <s xml:id="echoid-s4855" xml:space="preserve">& </s>
            <s xml:id="echoid-s4856" xml:space="preserve">
              <lb/>
            erat quadrati I B exceſſus ſupra quadratum I D, triangulum ipſum M V N bis
              <lb/>
            ſumptum. </s>
            <s xml:id="echoid-s4857" xml:space="preserve">Igitur quadrati I B exceſſus ſupra quadratum I A eſt duplum trian-
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            guli X Z V, ſeu exemplar applicatum ad G Q. </s>
            <s xml:id="echoid-s4858" xml:space="preserve">Quod autem exemplaria æqualia
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            ſint prædictis triangulis bis ſumptis, oſtenſum eſt in prop. </s>
            <s xml:id="echoid-s4859" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4860" xml:space="preserve">buius.</s>
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