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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        <div xml:id="echoid-div1121" type="section" level="1" n="357">
          <p>
            <s xml:id="echoid-s13102" xml:space="preserve">
              <pb o="391" file="0429" n="430" rhead="Aſſumpt. Liber."/>
            ergo circulus, cuius diameter eſt A C, æqualis eſt duplo circuli, cuius
              <lb/>
            diameter eſt D B cum duobus circulis, quorum diametri ſunt A D, D
              <lb/>
            C, & </s>
            <s xml:id="echoid-s13103" xml:space="preserve">ſemicirculus A C æqualis eſt circulo, cuius diameter eſt D B
              <lb/>
            cum duobus ſemicirculis A D, D C; </s>
            <s xml:id="echoid-s13104" xml:space="preserve">& </s>
            <s xml:id="echoid-s13105" xml:space="preserve">auferamus duos ſemicirculi A
              <lb/>
            D, D C communiter, remanet figura, quàm continent ſemicirculi A
              <lb/>
            C, A D, D C, & </s>
            <s xml:id="echoid-s13106" xml:space="preserve">eſt figura, quàm vocauit Archimedes Arbelos æqua-
              <lb/>
            lis circulo, cuius diameter eſt D B, & </s>
            <s xml:id="echoid-s13107" xml:space="preserve">hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13108" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1123" type="section" level="1" n="358">
          <head xml:id="echoid-head450" xml:space="preserve">Notæ in Propoſit. IV.</head>
          <p style="it">
            <s xml:id="echoid-s13109" xml:space="preserve">H AEc forſan eſt vna earum propoſitionum, quas Pappus legit in libro an-
              <lb/>
            tiquo de menſura ARBELI, ſeu ſpatij àtribus ſemicircumferentijs circulo-
              <lb/>
            rum comprehenſi, vt ait Proclus, quæ quidem elegantiſſima eſt, eiuſque inuen-
              <lb/>
            tionis Lunulæ Hyppocratis Chij originem extitiße puto; </s>
            <s xml:id="echoid-s13110" xml:space="preserve">eſt enim Hyppocratis
              <lb/>
            Lunula ſuperficies plana à quadrante peripheriæ circuli maioris, & </s>
            <s xml:id="echoid-s13111" xml:space="preserve">ſemiſſe pe-
              <lb/>
            ripheriæ circuli ſubdupli comprehenſa: </s>
            <s xml:id="echoid-s13112" xml:space="preserve">Arbelus vero recentiorum eſt ſpatium
              <lb/>
            à triente, & </s>
            <s xml:id="echoid-s13113" xml:space="preserve">à duobus ſextantibus circumferentiarum trium circulorum æqua-
              <lb/>
            lium comprehenſum, & </s>
            <s xml:id="echoid-s13114" xml:space="preserve">hiſce duobus ſpatijs facilè quadrata æqualia reperiri
              <lb/>
            poſſunt; </s>
            <s xml:id="echoid-s13115" xml:space="preserve">at Arbeli Archimedis, & </s>
            <s xml:id="echoid-s13116" xml:space="preserve">Procli hucuſque reperta non eſt quadratura;
              <lb/>
            </s>
            <s xml:id="echoid-s13117" xml:space="preserve">ſed poteſt quidem aſſignari circulus prædicto ſpatio æqualis.</s>
            <s xml:id="echoid-s13118" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1124" type="section" level="1" n="359">
          <head xml:id="echoid-head451" xml:space="preserve">PROPOSITIO V.</head>
          <p>
            <s xml:id="echoid-s13119" xml:space="preserve">SI fuerit ſemicirculus A B, & </s>
            <s xml:id="echoid-s13120" xml:space="preserve">ſignatum fuerit in eius diametro
              <lb/>
            punctum C vbicumque, & </s>
            <s xml:id="echoid-s13121" xml:space="preserve">fiant ſuper diametrum duo ſe-
              <lb/>
            micirculi A C, C B, & </s>
            <s xml:id="echoid-s13122" xml:space="preserve">educatur ex C perpendicularis C D ſu-
              <lb/>
            per A B, & </s>
            <s xml:id="echoid-s13123" xml:space="preserve">deſcribantur ad vtraſque partes duo circuli tan-
              <lb/>
            gentes illam, & </s>
            <s xml:id="echoid-s13124" xml:space="preserve">tangentes ſemicirculos, vtique illi duo circuli
              <lb/>
            ſunt æquales.</s>
            <s xml:id="echoid-s13125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13126" xml:space="preserve">Demonſtratio. </s>
            <s xml:id="echoid-s13127" xml:space="preserve">Sit al-
              <lb/>
              <figure xlink:label="fig-0429-01" xlink:href="fig-0429-01a" number="495">
                <image file="0429-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0429-01"/>
              </figure>
            ter circulorum tangens
              <lb/>
            D C in E, & </s>
            <s xml:id="echoid-s13128" xml:space="preserve">ſemicircu-
              <lb/>
            lum A B in F, & </s>
            <s xml:id="echoid-s13129" xml:space="preserve">ſemi-
              <lb/>
            circulum A C in G, & </s>
            <s xml:id="echoid-s13130" xml:space="preserve">
              <lb/>
            educamus diametrũ H E,
              <lb/>
            erit parallela diametro A
              <lb/>
            B, eo quod duo anguli H
              <lb/>
            E C, A C E, ſunt recti,
              <lb/>
            & </s>
            <s xml:id="echoid-s13131" xml:space="preserve">iungamus F H, H A,
              <lb/>
            ergo linea A F eſt recta,
              <lb/>
            vti dictum eſt in propo-
              <lb/>
            ſitione 1. </s>
            <s xml:id="echoid-s13132" xml:space="preserve">& </s>
            <s xml:id="echoid-s13133" xml:space="preserve">occurrent A F, C E in D, eo quod egrediuntur ab </s>
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