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

Table of contents

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[141.] THEOR. XXIX. PROP. LIIX.
Page: 126 (102)
[142.] ALITER.
Page: 126 (102)
[143.] THEOR. XXX. PROP. LIX.
Page: 127 (103)
[144.] THEOR. XXXI. PROP. LX.
Page: 127 (103)
[145.] THEOR. XXXII. PROP. LXI.
Page: 128 (104)
[146.] THEOR. XXXIII. PROP. LXII.
Page: 129 (105)
[147.] SCHOLIVM.
Page: 130 (106)
[148.] THEOR. XXXIV. PROP. LXIII.
Page: 131 (107)
[149.] THEOR. XXXV. PROP. LXIV.
Page: 131 (107)
[150.] PROBL. XXIV. PROP. LXV.
Page: 132 (108)
[151.] LEMMA VII. PROP. LXVI.
Page: 133 (109)
[152.] SCHOLIVM.
Page: 133 (109)
[153.] PROBL. XXV. PROP. LXVII.
Page: 134 (110)
[154.] MONITVM.
Page: 134 (110)
[155.] PROBL. XXVI. PROP. LXVIII.
Page: 135 (111)
[156.] PROBL. XXVII. PROP. LXIX.
Page: 137 (113)
[157.] PROBL. XXVIII. PROP. LXX.
Page: 138 (114)
[158.] LEMMA VIII. PROP. LXXI.
Page: 139 (115)
[159.] LEMMA IX. PROP. LXXII.
Page: 140 (116)
[160.] PROBL. XXIX. PROP. LXXIII.
Page: 141 (117)
[161.] LEMMA X. PROP. LXXIV.
Page: 141 (117)
[162.] PROBL. XXX. PROP. LXXV.
Page: 142 (118)
[163.] COROLL. I.
Page: 143 (119)
[164.] COROLL. II.
Page: 143 (119)
[165.] MONITVM.
Page: 143 (119)
[166.] THEOR. XXXVI. PROP. LXXVI.
Page: 144 (120)
[167.] SCHOLIVM.
Page: 145 (121)
[168.] THEOR. XXXVII. PROP. LXXVII.
Page: 146 (122)
[169.] PROBL. XXXI. PROP. LXXVIII.
Page: 147 (123)
[170.] MONITVM.
Page: 148 (124)
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          <p>
            <s xml:id="echoid-s4011" xml:space="preserve">
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            nor eſt; </s>
            <s xml:id="echoid-s4012" xml:space="preserve">quæ verò cum maioribus eſt quidem maior, ſed omnino ſecat
              <note symbol="a" position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">5. Co-
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              roll. 19. h.</note>
              <note symbol="b" position="right" xlink:label="note-0143-02" xlink:href="note-0143-02a" xml:space="preserve">ibidem.</note>
            rabolen ABC, vti oſtenſum fuit in præcedentibus. </s>
            <s xml:id="echoid-s4013" xml:space="preserve">Quamobrem Ellipſis
              <lb/>
            AECH, datæ Parabolæ per datum intra ipſam punctum E eſt _MAXIMA_ in-
              <lb/>
            ſcripta quæſita. </s>
            <s xml:id="echoid-s4014" xml:space="preserve">Quod primò erat, &</s>
            <s xml:id="echoid-s4015" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4016" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4017" xml:space="preserve">IAM ſit data Ellipſis AECH, cuius centrum N, & </s>
            <s xml:id="echoid-s4018" xml:space="preserve">datum extra ipſam pun-
              <lb/>
            ctum ſit B, per quod oporteat _MINIMAM_ Parabolen circumſcribere.</s>
            <s xml:id="echoid-s4019" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4020" xml:space="preserve">Iungatur BN ſecans Ellipſim in E, & </s>
            <s xml:id="echoid-s4021" xml:space="preserve">poſita NE media geometrica, & </s>
            <s xml:id="echoid-s4022" xml:space="preserve">NB
              <lb/>
            media arithmetica inter eaſdem ignotas extremas, reperiantur ipſæ
              <note symbol="c" position="right" xlink:label="note-0143-03" xlink:href="note-0143-03a" xml:space="preserve">74. h.</note>
            mę, quę ſint ND, NL, & </s>
            <s xml:id="echoid-s4023" xml:space="preserve">per Dad Ellipſis diametrum EH applicetur ADC,
              <lb/>
            & </s>
            <s xml:id="echoid-s4024" xml:space="preserve">per verticem B, circa diametri ſegmentum BD, & </s>
            <s xml:id="echoid-s4025" xml:space="preserve">per terminos A, C de-
              <lb/>
            ſcribatur Parabole ABC. </s>
            <s xml:id="echoid-s4026" xml:space="preserve">Dico hanc eſſe _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s4027" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4028" xml:space="preserve">Cum enim ſit NE media geometrica inter LN, ND, erit rectangulum
              <lb/>
            LND æquale quadrato NE; </s>
            <s xml:id="echoid-s4029" xml:space="preserve">& </s>
            <s xml:id="echoid-s4030" xml:space="preserve">per D applicata eſt in Ellipſi recta ADC, ſi
              <lb/>
            iungantur LA, LC ipſæ Ellipſim contingent in A, C; </s>
            <s xml:id="echoid-s4031" xml:space="preserve">cumque ſit NB
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            dia arithmetica inter eaſdem LN, ND, erunt ipſarum differentiæ LB, BD
              <lb/>
            inter ſe æquales; </s>
            <s xml:id="echoid-s4032" xml:space="preserve">vnde eædem LA, LC Parabolen contingent,
              <note symbol="e" position="right" xlink:label="note-0143-05" xlink:href="note-0143-05a" xml:space="preserve">conuer.
                <lb/>
              37. primi
                <lb/>
              conic. ex
                <lb/>
              Comand.</note>
            hæc datæ Ellipſi erit circumſcripta. </s>
            <s xml:id="echoid-s4033" xml:space="preserve">Eritque _MINIMA_: </s>
            <s xml:id="echoid-s4034" xml:space="preserve">quoniam quæ per B
              <lb/>
            eidem Ellipſi adſcribitur cum recto maiori, maior eſt ABC, quæ verò
              <note symbol="f" position="right" xlink:label="note-0143-06" xlink:href="note-0143-06a" xml:space="preserve">2. h.</note>
            minori eſt quidem minor, ſed omnino ſecat Ellipſim, vti ex
              <note symbol="g" position="right" xlink:label="note-0143-07" xlink:href="note-0143-07a" xml:space="preserve">2. Co-
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              roll. 19. h.</note>
            & </s>
            <s xml:id="echoid-s4035" xml:space="preserve">per ſe ſatis conſtat. </s>
            <s xml:id="echoid-s4036" xml:space="preserve">Quapropter Parabole ABC eſt _MINIMA_ circumſcri-
              <lb/>
            pta quæſita. </s>
            <s xml:id="echoid-s4037" xml:space="preserve">Quod ſecundò faciendum, ac demonſtrandum erat.</s>
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        <div xml:id="echoid-div390" type="section" level="1" n="163">
          <head xml:id="echoid-head168" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s4039" xml:space="preserve">EX prima parte huius patet, quod ſi datum punctum D fuerit in axe Para-
              <lb/>
            bolæ, & </s>
            <s xml:id="echoid-s4040" xml:space="preserve">data ratio ſit æqualitatis, inſcribenda Ellipſis, idem erit, ac
              <lb/>
            circulus; </s>
            <s xml:id="echoid-s4041" xml:space="preserve">tunc enim applicata ADC erit axi perpendicularis, & </s>
            <s xml:id="echoid-s4042" xml:space="preserve">quadratum
              <lb/>
            AD æquabitur rectangulo HDE; </s>
            <s xml:id="echoid-s4043" xml:space="preserve">ideoque AECH erit circulus: </s>
            <s xml:id="echoid-s4044" xml:space="preserve">ex quo ha-
              <lb/>
            bebitur, quo pacto per punctum E in axe Parabolæ, _MAXIMVS_ circulus in-
              <lb/>
            ſcribatur: </s>
            <s xml:id="echoid-s4045" xml:space="preserve">applicata enim EF, cui ſumpta æquali ED, iunctaque FD, & </s>
            <s xml:id="echoid-s4046" xml:space="preserve">pro-
              <lb/>
            ducta in G, & </s>
            <s xml:id="echoid-s4047" xml:space="preserve">applicata GH, ipſa dabit EH diametrum quæſiti circuli.</s>
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        <div xml:id="echoid-div391" type="section" level="1" n="164">
          <head xml:id="echoid-head169" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s4049" xml:space="preserve">PAtet etiam ſemi-applicatas in Parabola, ex terminis diametri _MAXIMI_
              <lb/>
            inſcripti circuli, ęquari contiguis ſegmentis eiuſdem diametri, ab appli-
              <lb/>
            cata ex contactu circuli cum ſectione abſciſſis. </s>
            <s xml:id="echoid-s4050" xml:space="preserve">Sienim ſit FE æqualis ED,
              <lb/>
            ob ſimilitudinem triangulorum, crit etiam GH æqualis HD.</s>
            <s xml:id="echoid-s4051" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div392" type="section" level="1" n="165">
          <head xml:id="echoid-head170" xml:space="preserve">MONITVM.</head>
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            <s xml:id="echoid-s4052" xml:space="preserve">SI quis in vigeſimo nono, ac trigeſimo antecedenti Problemate, a
              <lb/>
            ſeueritate geometricæ demonſtrationis expeteret, nontantum El-
              <lb/>
            lipſes, per datum punctum ibi contingenter inſcriptas, ad par-
              <lb/>
            tes verticis, tum anguli, tum Parabolæ oppoſitas, MAXI-
              <lb/>
            MAS eſſe ſibi ipſis ſimilium per idem punctum, adeaſdem partes </s>
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