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

Table of contents

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[11.] THEOR. I. PROP. I.
[12.] Definitiones Primæ. I.
[13.] II.
[14.] III.
[15.] IV.
[16.] V.
[17.] VI.
[18.] VII.
[19.] VIII.
[20.] IX.
[21.] COROLL.
[22.] MONITVM.
[23.] PROBL. I. PROP. II.
[24.] ALITER.
[25.] ALITER.
[26.] MONITVM.
[27.] LEMMAI. PROP. III.
[28.] PROBL. II. PROP. IV.
[29.] MONITVM.
[30.] PROBL. III. PROP. V.
[31.] PROBL. IV. PROP. VI.
[32.] PROBL. V. PROP. VII.
[33.] MONITVM.
[34.] THEOR. II. PROP. VIII.
[35.] MONITVM.
[36.] LEMMA II. PROP. IX.
[37.] THEOR. III. PROP. X.
[38.] COROLL. I.
[39.] COROLL. II.
[40.] MONITVM.
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        <div xml:id="echoid-div80" type="section" level="1" n="49">
          <head xml:id="echoid-head54" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s1045" xml:space="preserve">HInc patet, quod ſi recta linea in Parabola vtcunque applicata ex
              <lb/>
              <note position="right" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">Vni-
                <lb/>
              uerſalius
                <lb/>
              quàm in
                <lb/>
              4. prop.
                <lb/>
              exerc. 6.
                <lb/>
              Caual.</note>
            vtraque parte ſectioni occurrens cum diametro, vel intra, vel extra
              <lb/>
            ſectionem conueniat, atque ex ipſius terminis cum ſectione, ad diametrum
              <lb/>
            ducantur ordinatæ, erunt ab his abſciſſa diametri ſegmenta ex vertice ſum-
              <lb/>
            pta, extremæ, & </s>
            <s xml:id="echoid-s1046" xml:space="preserve">abſciſſum ab applicata, erit media trium continuè propor-
              <lb/>
            tionalium. </s>
            <s xml:id="echoid-s1047" xml:space="preserve">Demonſtratum eſt enim in figuris Theorematis quando AH dia-
              <lb/>
            metrum ſecat in M, & </s>
            <s xml:id="echoid-s1048" xml:space="preserve">ſectionem in A, H, quod ordinatim applicatis AF,
              <lb/>
            HI, eſt FB ad BM, vt BM ad BI.</s>
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        <div xml:id="echoid-div82" type="section" level="1" n="50">
          <head xml:id="echoid-head55" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s1050" xml:space="preserve">EX quo etiam elicitur, quod ſi in Parabola ABC ducta AH diametrum
              <lb/>
            ſecans in M producatur vſque ad occurſum cum contingente ex verti-
              <lb/>
            ce B in S, ſemper rectangulum ſub ſegmentis AS, & </s>
            <s xml:id="echoid-s1051" xml:space="preserve">SH, inter ſectionem, & </s>
            <s xml:id="echoid-s1052" xml:space="preserve">
              <lb/>
            contingentem interceptis æqua†@ quadrato ſegmenti SM inter contingẽtem,
              <lb/>
            ac diametrum intercepti. </s>
            <s xml:id="echoid-s1053" xml:space="preserve">Nam cum ſit vt FB ad BM, ita BM ad BI erit quo-
              <lb/>
            que ob parallelas, AS ad SM, vt SM ad SH, quare rectangulum ASH æqua-
              <lb/>
            bitur quadrato SM.</s>
            <s xml:id="echoid-s1054" xml:space="preserve"/>
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          <head xml:id="echoid-head56" xml:space="preserve">COROLL. III.</head>
          <p>
            <s xml:id="echoid-s1055" xml:space="preserve">HInc etiam eſt, quod, ſi ijſdem poſitis,
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            interior Parabole ADG habuerit ver-
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              <figure xlink:label="fig-0049-01" xlink:href="fig-0049-01a" number="26">
                <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0049-01"/>
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            ticẽ in D puncto medio rectæ AB, ipſa quo-
              <lb/>
            que tranſibit per F medium punctum baſis
              <lb/>
            AC, & </s>
            <s xml:id="echoid-s1056" xml:space="preserve">quæcunque educta ex contactu A,
              <lb/>
            qualis eſt AH, bifariam ſecabitur in O ab in-
              <lb/>
            terna ſectione; </s>
            <s xml:id="echoid-s1057" xml:space="preserve">quare ſi ex O ducatur OLM
              <lb/>
            diametro BF æquidiſtans, ipſa erit diameter
              <lb/>
            portionis ALH, & </s>
            <s xml:id="echoid-s1058" xml:space="preserve">AH vna applicatarum,
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            AO verò ſemi-applicata. </s>
            <s xml:id="echoid-s1059" xml:space="preserve">Cumque ſit AP
              <lb/>
            contingens ABC in A, erit OL in trilineo
              <lb/>
            mixto ADFB, æqualis LM in trilineo mixto
              <lb/>
            ALBP, & </s>
            <s xml:id="echoid-s1060" xml:space="preserve">ſic de omnibus vbicunque inter-
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            ceptis in ijſdem trilineis.</s>
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          <head xml:id="echoid-head57" xml:space="preserve">THEOR. VI. PROP. XIV.</head>
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            <s xml:id="echoid-s1062" xml:space="preserve">Parabolæ æqualium altitudinum inter ſe ſunt vt baſes.</s>
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            <s xml:id="echoid-s1064" xml:space="preserve">SInt duæ Parabolæ ABC, DEF æqualium altitudinum, hoc eſt concipian-
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            tur diſpoſitæ inter eaſdem parallelas BE, AF: </s>
            <s xml:id="echoid-s1065" xml:space="preserve">dico eſſe vt baſis AC
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            vnius, ad baſim DF alterius, ita Parabole ABC ad Parabolen DEF.</s>
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