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

Table of contents

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[111.] THEOR. XXIII. PROP. XXXXIV.
Page: 100 (76)
[112.] COROLL.
Page: 102 (78)
[113.] Quod ſuperiùs promiſimus oſtendetur ſic.
Page: 102 (78)
[114.] THEOR. XXIV. PROP. XXXXV.
Page: 103 (79)
[115.] COROLL.
Page: 105 (81)
[116.] LEMMA VI. PROP. XXXXVI.
Page: 105 (81)
[117.] THEOR. XXV. PROP. XXXXVII.
Page: 105 (81)
[118.] ALITER.
Page: 107 (83)
[119.] COROLL. I.
Page: 107 (83)
[120.] COROLL. II.
Page: 107 (83)
[121.] THEOR. XXVI. PROP. XXXXVIII.
Page: 108 (84)
[122.] MONITVM.
Page: 111 (87)
[123.] THEOR. XXVII. PROP. XXXXIX.
Page: 112 (88)
[124.] THEOR. XXVIII. PROP. L.
Page: 113 (89)
[125.] COROLL.
Page: 113 (89)
[126.] PROBL. XVII. PROP. LI.
Page: 114 (90)
[127.] PROBL. XVIII. PROP. LII.
Page: 115 (91)
[128.] ALITER.
Page: 116 (92)
[129.] ALITER breuiùs.
Page: 117 (93)
[130.] PROBL. XIX. PROP. LIII.
Page: 117 (93)
[131.] ALITER.
Page: 118 (94)
[132.] ALITER breuiùs.
Page: 119 (95)
[133.] PROBL. XX. PROP. LIV.
Page: 119 (95)
[134.] ALITER breuiùs.
Page: 120 (96)
[135.] PROBL. XXI. PROP. LV.
Page: 121 (97)
[136.] PROBL. XXII. PROP. LVI.
Page: 123 (99)
[137.] COROLL. I.
Page: 125 (101)
[138.] COROLL. II.
Page: 125 (101)
[139.] PROBL. XXIII. PROP. LVII.
Page: 125 (101)
[140.] COROLL.
Page: 126 (102)
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          <head xml:id="echoid-head126" xml:space="preserve">THEOR. XXVI. PROP. XXXXVIII.</head>
          <p>
            <s xml:id="echoid-s2804" xml:space="preserve">Similes Hyperbolæ per diuerſos vertices ſimul adſcriptæ habent
              <lb/>
            aſymptotos parallelas, & </s>
            <s xml:id="echoid-s2805" xml:space="preserve">quando centrum interioris cadat vltra
              <lb/>
            centrum exterioris, tunc huius aſymptotos interiorem Hyperbolen
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            ſecabit, ac ipſæ Hyperbolæ neceſſariò ſe mutuò ſecabunt. </s>
            <s xml:id="echoid-s2806" xml:space="preserve">Cum
              <lb/>
            verò centrum interioris idem ſit cum centro exterioris, tunc vnius
              <lb/>
            aſymptotos erit aſymptotos alterius; </s>
            <s xml:id="echoid-s2807" xml:space="preserve">& </s>
            <s xml:id="echoid-s2808" xml:space="preserve">ſectiones erunt ſimul nun-
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            quam coeuntes. </s>
            <s xml:id="echoid-s2809" xml:space="preserve">Et ſi interioris centrum cadat infra centrum ex-
              <lb/>
            terioris, tunc eædem ſectiones erunt inter ſe nunquam coeuntes; </s>
            <s xml:id="echoid-s2810" xml:space="preserve">& </s>
            <s xml:id="echoid-s2811" xml:space="preserve">
              <lb/>
            aſymptotos inſcriptæ ſecabit Hyperbolen circumſcriptam.</s>
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            <s xml:id="echoid-s2813" xml:space="preserve">SInt, vt in vtraque figura huius propoſitionis, duæ ſimiles Hyperbolæ
              <lb/>
            ABC, DEF per diuerſos vertices B, E ſimul adſcriptæ, quarum centra
              <lb/>
            ſint G, H, & </s>
            <s xml:id="echoid-s2814" xml:space="preserve">ſectionis ABC aſymptoti ſint GI, GO; </s>
            <s xml:id="echoid-s2815" xml:space="preserve">ſectionis verò DEF ſint
              <lb/>
            HM, HR; </s>
            <s xml:id="echoid-s2816" xml:space="preserve">Dico has aſymptotos eſſe inter ſe æquidiſtantes.</s>
            <s xml:id="echoid-s2817" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2818" xml:space="preserve">Nam in ſimilibus Hyperbolis ABC, DEF, anguli IGE, MHE, ab earum
              <lb/>
            aſymptotis, & </s>
            <s xml:id="echoid-s2819" xml:space="preserve">diametris ad homologas partes facti ſunt æquales,
              <note symbol="a" position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">Coroll.
                <lb/>
              40. huius.</note>
            alterni, quare ipſæ aſymptoti inter ſe æquidiſtabunt. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s2821" xml:space="preserve">c.</s>
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            <s xml:id="echoid-s2823" xml:space="preserve">Iam in hac prima figura, (in
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            qua centrum H interioris DEF
              <lb/>
            remotius eſt à verticibus B, E,
              <lb/>
            quàm ſit centrum G exterioris
              <lb/>
            Hyperbolæ ABC) cum ſint HM,
              <lb/>
            HR aſymptoti Hyperbolæ DEF,
              <lb/>
            & </s>
            <s xml:id="echoid-s2824" xml:space="preserve">in loco ab eis, & </s>
            <s xml:id="echoid-s2825" xml:space="preserve">ſectione ter-
              <lb/>
            minato ducta ſit GI alteri aſym-
              <lb/>
            ptoton
              <unsure/>
            HM æquidiſtans, ipſa
              <lb/>
            omnino ſectionem DEF ſecabit.
              <lb/>
            </s>
            <s xml:id="echoid-s2826" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s2827" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2828" xml:space="preserve"/>
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            <s xml:id="echoid-s2829" xml:space="preserve">Sed ipſa GI, cum ſit aſympto-
              <lb/>
            tos ſectionis ABC, tota cadit ex-
              <lb/>
            tra ipſam BA, quare occurſus
              <lb/>
            prædictæ aſymptoton GI cum ſe-
              <lb/>
            ctione ED, erit extra ſectionem
              <lb/>
            BA, vnde ipſa interior ſectio ED
              <lb/>
            neceſſariò ſecabit priùs exterio-
              <lb/>
            rem BA. </s>
            <s xml:id="echoid-s2830" xml:space="preserve">Quod tertiò, &</s>
            <s xml:id="echoid-s2831" xml:space="preserve">c.</s>
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            <s xml:id="echoid-s2833" xml:space="preserve">Ad pleniorem autem doctrinam, ſi quæratur, quo nam in puncto huiuſ-
              <lb/>
            modi Hyperbolæ ſe mutuò ſecent, ita id conſequetur.</s>
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          <p>
            <s xml:id="echoid-s2835" xml:space="preserve">Sumpta enim GS æquali GB, erit tota BS tranſuerſum exterioris ABC;
              <lb/>
            </s>
            <s xml:id="echoid-s2836" xml:space="preserve">item ſumpta HT æquali HE, erit tota TE tranſuerſum interioris DEF.</s>
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          <p>
            <s xml:id="echoid-s2838" xml:space="preserve">Iam, vel H centrum interioris cadit in ipſo puncto S; </s>
            <s xml:id="echoid-s2839" xml:space="preserve">vel ſupra inter S, & </s>
            <s xml:id="echoid-s2840" xml:space="preserve">
              <lb/>
            T, vel infra inter G, &</s>
            <s xml:id="echoid-s2841" xml:space="preserve">S.</s>
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