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

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          <p>
            <s xml:id="echoid-s9221" xml:space="preserve">
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            ſunt æqualia. </s>
            <s xml:id="echoid-s9222" xml:space="preserve">In ſecunda verò figura, aggregatum triangulorum ex G ma-
              <lb/>
            ius eſt aggregato triangulorum ex F, vt ſatis patet (cum illud, ipſum poly-
              <lb/>
            gonum excedat) quare, & </s>
            <s xml:id="echoid-s9223" xml:space="preserve">aggregatum baſium triangulorum ex G, (quæ
              <lb/>
            ſuntipſæ perpendiculares ex G) maius eſt aggregato baſium triangulorum
              <lb/>
            ex F, (quæ ſunt perpendiculares ex F.) </s>
            <s xml:id="echoid-s9224" xml:space="preserve">Quapropter, &</s>
            <s xml:id="echoid-s9225" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9226" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s9227" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9228" xml:space="preserve"/>
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        <div xml:id="echoid-div961" type="section" level="1" n="387">
          <head xml:id="echoid-head398" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s9229" xml:space="preserve">HInc eſt, quod aggregatum perpendicularium ex centro dati polygoni
              <lb/>
            ſuper eius latera eductarum, ſemper eſt non maius quolibet ex alio
              <lb/>
            puncto perpendicularium aggregato, vbicunque aſſumptum ſit punctum
              <lb/>
            hoc, velintra, vel in perimetro, vel extra perimetrum dati polygoni.</s>
            <s xml:id="echoid-s9230" xml:space="preserve"/>
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        <div xml:id="echoid-div962" type="section" level="1" n="388">
          <head xml:id="echoid-head399" xml:space="preserve">THEOR. I. PROP. III.</head>
          <p>
            <s xml:id="echoid-s9231" xml:space="preserve">In quocunque polygono regulari, aggregatorum linearum ex
              <lb/>
            punctis vbicunque aſſumptis ad ipſius angulos eductarum, MINI-
              <lb/>
            MVM eſt, quod ex centro.</s>
            <s xml:id="echoid-s9232" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9233" xml:space="preserve">SIt polygonum regulare A B C D E, cuius centrum P, à quo ad angulos
              <lb/>
            eductæ ſint rectę P A, P B, P C, P D, P E, ſumptoq; </s>
            <s xml:id="echoid-s9234" xml:space="preserve">vbicunque alio
              <lb/>
            puncto O, vei intra polygonum A B C D E, vel in eius perimetro, vel ex-
              <lb/>
            tra, iungantur item O A, O B, O C, O D, O E. </s>
            <s xml:id="echoid-s9235" xml:space="preserve">Dico aggregatum edu-
              <lb/>
            ctarum ex centro P, minus eſſe aggregato ductarum ex O.</s>
            <s xml:id="echoid-s9236" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9237" xml:space="preserve">Ex punctis enim A, B, C, D, E, erigan-
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              <figure xlink:label="fig-0333-01" xlink:href="fig-0333-01a" number="264">
                <image file="0333-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0333-01"/>
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            turipſis P A, P B, P C, P D, P E perpen-
              <lb/>
            diculares L I, I H, H G, G F, F L vtrinq;
              <lb/>
            </s>
            <s xml:id="echoid-s9238" xml:space="preserve">productæ. </s>
            <s xml:id="echoid-s9239" xml:space="preserve">Patet has ſimul conuenire, & </s>
            <s xml:id="echoid-s9240" xml:space="preserve">
              <lb/>
            polygonum L I H G F dato ſimile conſti-
              <lb/>
            tuere circa idem centrum P, ad cuius late-
              <lb/>
            ra ex puncto O ducantur perpendiculares
              <lb/>
            O R, O Q, O N, O M, O S.</s>
            <s xml:id="echoid-s9241" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9242" xml:space="preserve">Iam per Coroll. </s>
            <s xml:id="echoid-s9243" xml:space="preserve">præcedentis Lemmatis
              <lb/>
            in polygono I H G F L aggregatum per-
              <lb/>
            pendicularium, quæ ex centro P eſt non
              <lb/>
            maius aggregato perpendicularium, quæ
              <lb/>
            ex puncto O vbicunq; </s>
            <s xml:id="echoid-s9244" xml:space="preserve">aſſumpto, ſed aggregatum perpendicularium ex O,
              <lb/>
            minus eſt aggregato obliquarum O A, O B, O C, O D, O E, ſuper ijſdem
              <lb/>
            lateribus circumſcripti polygoni eductarum, (eſt enim perpendicularis O
              <lb/>
            R, minor obliqua O A, & </s>
            <s xml:id="echoid-s9245" xml:space="preserve">O Q minor O B; </s>
            <s xml:id="echoid-s9246" xml:space="preserve">O N minor O C; </s>
            <s xml:id="echoid-s9247" xml:space="preserve">O M minor
              <lb/>
            O D, & </s>
            <s xml:id="echoid-s9248" xml:space="preserve">O S minor O E) ergo aggregatum perpendicularium ex P, hoc eſt
              <lb/>
            ad angulos dati polygoni A B C D E eductarum, eſt omnino minus aggre-
              <lb/>
            gato obliquarum ex O, nempe eductarum ad eoſdem angulos dati poly-
              <lb/>
            goni à puncto O, vbicunque ſit ipſum O. </s>
            <s xml:id="echoid-s9249" xml:space="preserve">Quare aggregatum ductarum ex
              <lb/>
            centro ad angulos polygoni regularis _MINIMVM_ eſt. </s>
            <s xml:id="echoid-s9250" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s9251" xml:space="preserve">c.</s>
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