Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <head xml:id="echoid-head400" xml:space="preserve">THEOR. II. PROP. IV.</head>
          <p>
            <s xml:id="echoid-s9253" xml:space="preserve">Si quotcunque rectæ lineæ terminatæ (non minus verò quam
              <lb/>
            tres) cuiuslibet longitudinis, ad vnum idemque punctum occur-
              <lb/>
            rant, totidem angulos inter ſe æquales conſtituentes, & </s>
            <s xml:id="echoid-s9254" xml:space="preserve">quatuor
              <lb/>
            rectos complentes. </s>
            <s xml:id="echoid-s9255" xml:space="preserve">Erit aggregatum harum ſimul omnium occur-
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            rentium, MINIMVM aggregatorum rectarum, à quibuſcunque
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            alijs aſſumptis punctis, ad eoſdem datarum terminos eductarum.</s>
            <s xml:id="echoid-s9256" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9257" xml:space="preserve">SInt quotcunque rectę A B, A C, A D, A E, A F, A G terminatę, quę
              <lb/>
            ad punctum A ſimul occurrant, conſtituantque angulos B A C, C A
              <lb/>
            D, D A E, E A F, F A G, G A B inter ſe æquales, & </s>
            <s xml:id="echoid-s9258" xml:space="preserve">ſimul ſumpti ęquales
              <lb/>
            quatuor rectis: </s>
            <s xml:id="echoid-s9259" xml:space="preserve">dico aggregatum harum omniũ minus eſſe aggregato linea-
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            rum, quæ ex quolibet alio puncto I ad eoſdem terminos B, C, D, E, F, G,
              <lb/>
            educi poſſunt, quales ſunt I B, I C, I D, I E, I F, I G.</s>
            <s xml:id="echoid-s9260" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9261" xml:space="preserve">Sit enim A G _MAXIMA_ ductarum ex A, ſuper qua ſumatur A P ipſa A
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            G non minor, cui demantur æquales A H, A L, A M, A N, A O, & </s>
            <s xml:id="echoid-s9262" xml:space="preserve">com-
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            pleatur polygonum H L M N O P, quod erit æquilaterum, & </s>
            <s xml:id="echoid-s9263" xml:space="preserve">æquiangulũ,
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            ſiue regulare, cum anguli ad A ſint æquales, eiuſque centrum erit A; </s>
            <s xml:id="echoid-s9264" xml:space="preserve">deni-
              <lb/>
            que iungantur I H, I L, I M, I N, I O, I P.</s>
            <s xml:id="echoid-s9265" xml:space="preserve"/>
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          <figure number="265">
            <image file="0334-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0334-01"/>
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          <p>
            <s xml:id="echoid-s9266" xml:space="preserve">Iam aggregatum ductarum A H, A L, A M, A N, A O, A P ex centro
              <lb/>
            A ad angulos polygoni, cum ſit _MINIMVM_, erit minus aggregato
              <note symbol="*" position="left" xlink:label="note-0334-01" xlink:href="note-0334-01a" xml:space="preserve">per 3.
                <lb/>
              Append.</note>
            rum I H, I L, I M, I N, I O, I P ex puncto I, ſed harum aggregatum mi-
              <lb/>
            nus eſt aggregato binarum I B, B H; </s>
            <s xml:id="echoid-s9267" xml:space="preserve">I C, C L; </s>
            <s xml:id="echoid-s9268" xml:space="preserve">I D, D M; </s>
            <s xml:id="echoid-s9269" xml:space="preserve">I E, E N; </s>
            <s xml:id="echoid-s9270" xml:space="preserve">I F,
              <lb/>
            F O; </s>
            <s xml:id="echoid-s9271" xml:space="preserve">I G, G P; </s>
            <s xml:id="echoid-s9272" xml:space="preserve">nam I B, B H maiores ſunt I H, & </s>
            <s xml:id="echoid-s9273" xml:space="preserve">I C, C L maiores I
              <lb/>
            L, &</s>
            <s xml:id="echoid-s9274" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9275" xml:space="preserve">quare eò magis aggregatum, ex A ductarum, A H, A L, A M, A
              <lb/>
            N, A O, A P minus erit aggregato binarum I B, B H; </s>
            <s xml:id="echoid-s9276" xml:space="preserve">I C, C L; </s>
            <s xml:id="echoid-s9277" xml:space="preserve">I D, D
              <lb/>
            M; </s>
            <s xml:id="echoid-s9278" xml:space="preserve">I E, E N; </s>
            <s xml:id="echoid-s9279" xml:space="preserve">I F, F O; </s>
            <s xml:id="echoid-s9280" xml:space="preserve">I G, G P; </s>
            <s xml:id="echoid-s9281" xml:space="preserve">demptis ergo communibus ſegmentis B
              <lb/>
            H, C L, D M, E N, F O, G P, erit reliquum aggregatum datarum A B,
              <lb/>
            A C, A D, A E, A F, A G minus reliquo aggregato ductarum I B, I </s>
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